Algebra
Example 2: From what number is 3 subtracted to get the difference 6?
Solution
3 is subtracted from y to get the difference 6. So, y – 3 = 6
3 is subtracted from 9 to get the difference 6. So, y = 6 + 3 = 9
Example 3: What number is subtracted from 12 to get the difference 8?
Solution
p is subtracted from 12 to get the difference 8. So, 12 – p = 8
4 is subtracted from 12 to get the difference 8. So, p = 12 – 8 = 4
Example 4: What number is multiplied by 5 to get the product 15?
Solution
a is multiplied by 5 to get the product 15. So, 5 × a = 15
3 is multiplied by 5 to get the product 15. So, a = 15 ÷ 5 = 3
Example 5: By what number is 4 multiplied to get the product 28?
Solution
4 is multiplied by b to get the product 28. So, 4 × b = 28
4 is multiplied by 7 to get the product 28. So, b = 28 ÷ 4 = 7
Example 6: What number is divided by 2 to get the quotient 8?
Solution
x is divided by 2 to get the quotient 8. So, x ÷ 2 = 8
16 is divided by 2 to get the quotient 8. So, x = 8 × 2 = 16
Example 7: By what number is 27 divided to get the quotient 9?
Solution
27 is divided by a to get quotient 9. So, 27 ÷ a = 9
27 is divided by 3 to get the quotient 9. So, a = 27 ÷ 9 = 3
Example 8: Find the values of the letters in the following mathematical
sentences.
a) x + 4 = 10 b) y – 5 = 5
c) a × 6 = 18 d) p ÷ 7 = 2
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Solution
a) x + 4 = 10
6 is added to 4 to get 10. So, x = 10 – 4 = 6
b) y – 5 = 5
5 is subtracted from 10 to get 5. So, y = 5 + 5 = 10
c) a × 6 = 18
6 is multiplied by 3 to get 18. So, a = 18 ÷6 = 3
d) p ÷7 = 2
14 is divided by 7 to get 2. So, p = 2 × 7 = 14
Exercise - 10.2
Section A - Classwork
1. Let's write the correct number inside each symbol of shape. Then, say
and write the values of letters.
Mathematical Mathematical Values of letters
sentences with symbol sentences with letters
of shapes
a) + 1 = 3 x+1=3 x=
b) – 1 = 3 y–1=3 y=
c) 2 × = 4 2×a=4 a=
d) ÷3 = 2 x÷3=2 x=
2. Let's say and write the values of letters as quickly as possible.
a) x + 1 = 2, x = b) y – 1 = 2, y = c) a + 2 = 3, a =
d) p – 2 = 4, p = e) 2 × x = 2, x = f) y ÷3 = 1, y =
g) 2 × x = 4, x = h) a ÷ 3 = 2, a = i) 3 × x = 9, x =
vedanta Excel in Mathematics - Book 4 200 Approved by Curriculum Development CentreSanothimi, Bhaktapur
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Section B
3. Let's make mathematical sentences using letters. Then, find the values
of the letters.
a) What number is added to 1 to get the sum 5?
b) What number is added to 4 get the sum 6?
c) From what number is 2 subtracted to get the difference 3?
d) What number is subtracted from 9 to get difference 5?
e) What number is multiplied by 2 to get the product 12?
f) By what number is 5 multiplied to get the product 15?
g) What number is divided by 3 to get the quotient 6?
h) By what number is 36 divided to get the quotient 4?
4. Let's find the values of the letters in the following mathematical
sentences.
a) x + 1 = 2 b) x + 2 = 4 c) x + 3 = 7 d) y + 5 = 12
e) y + 4 = 9 f) a + 6 = 13 g) a + 7 = 10 h) x + 10 = 15
5. a) x – 1 = 2 b) x – 2 = 3 c) x – 3 = 4 d) y – 4 = 5
e) y – 5 = 5 f) a – 6 = 2 g) a – 7 = 1 h) x – 10 = 6
6. a) 2 × x = 2 b) 2 × x = 4 c) 3 × x = 6 d) 3 × y = 15
e) 4 × y = 12 f) 5 × a = 10 g) 6 × a = 24 h) 7 × x = 49
7. a) x ÷ 2 = 1 b) x ÷ 2 = 2 c) x ÷ 3 = 1 d) y ÷ 3 = 4
e) y ÷ 2 = 4 f) a ÷ 3 = 5
8. a) 2 × x + 1 = 5 b) 2 × y – 1 = 5 g) a ÷ 4 = 3 h) x ÷ 5 = 2
e) 3 × y + 2 = 8 f) 3 × x – 1 = 8
c) 2 × a + 3 = 7 d) 2 × x – 3 = 7
g) 4 × a + 3 = 15 h) 5 × x – 2 = 3
i) 2x ÷ 3 = 2 j) 2y ÷ 5 = 4 k) 3a ÷ 2 = 6 l) 3x ÷ 4 = 9
9. Let's make mathematical sentences from these balances, then, find
the value of the letters.
a) b) c) d)
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Algebra
10. The lengths of the straight line segments are given. Make mathematical
sentences and find the value of the letters.
a) x cm = ? 5 cm b)
7 cm
y=? 6 cm
9 cm
x + 5 = 7
or, x + 5 – 5 = 7 – 5
or, x = 2
c) p cm p cm d) x = ? x 5
13 cm
10 cm
11. Perimeter of each plane shape = total sum of the length of all sides.
From the given perimeter of each shape, let's make mathematical
sentences and find the values of the letters.
a) b) c) 3x cm
2x cm
x cm
2x cm
2x cm
4 cm
3 cm
4 cm x cm 3x cm
Perimeter = 9 cm Perimeter = 13 cm Perimeter = 20 cm
x + 4 cm + 3 cm = 9 cm
or, x + 7 cm = 9 cm – 7 cm
or, x = 2 cm
10.6 Use of mathematical sentences
We use mathematical sentences to find the unknown number (or number
of quantity) in our real life situations. We take a variable (x, y, z, a, b, c, ...) to
represent the unknown number. Then we make a mathematical sentence. By
solving the mathematical sentence we find the unknown number (or quantity).
Let's make mathematical sentence using box .
Example 1: The sum of two numbers is 7 and one of them is 2. Find the
other number.
Solution
Let the other number is . (Let, the box represents the other number)
Then, + 2 = 7
or, 5 + 2 = 7
Hence, the other number is 5. 202 Approved by Curriculum Development CentreSanothimi, Bhaktapur
vedanta Excel in Mathematics - Book 4
Algebra
Example 2: Bhurashi has 3 sweets. Father gives her some more sweets
and she has now 5 sweets. How many sweets does father
give her?
Solution
Let father gives her sweets. (Let, the box represents the sweets
given by father)
Then, + 3 = 5
or, 2 + 3 = 5
Hence, father gives her 2 sweets.
Example 3: The difference of two number is 2 and the smaller number
is 4. Find the bigger number.
Solution It's easy!
Let the box represents the bigger number. I can think it by another
Then, – 2 = 4 way.
Bigger number is 4 + 2 = 6.
or, 6 – 2 = 4
Hence, the bigger number is 6.
Example 4: In a class, the number of girls are 5 more than the number
of boys. If there are 12 boys, find the number of girls.
Solution
Let the box represents the number of girls. Interesting!
Then, – 5 = 12 Number of girls = 12 + 5
= 17
or, 17 – 5 = 12
Hence, the number of girls are 17.
Example 5: A number is double than that of other number. If the bigger
number is 18, find the smaller number.
Solution I got it!
Let the box represents the smaller number. Smaller number = 18 ÷ 2
= 9
Then, 2 × = 18
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Algebra
or, 2 × 9 = 18
Hence, the smaller number is 9.
Example 6: Bishwant has three times more money than that of
Sunayana has. If Bishwant has 30 rupees, how much
money does Sunayana have?
Solution
Let the box represents the money that Sunayana has. I have a trick!
Then, 3 × rupees = 30 rupees 30 ÷ 3 = 10
or, 3 × 10 rupees = 30
Hence, Sunayana has 10 rupees.
Example 7: Teacher divides 24 sweets equally among some children
and each child gets 6 sweets. Find the number of children.
Solution
Let the box represents the number of children. I got it!
Then, 24 ÷ = 6 Numer of children = 24 ÷ 6
or, 24 ÷ 4 = 6
=4
Hence, the number of children are 4.
Now, let's make mathematical sentences by using letters in the place of
box.
Example 1: The sum of two numbers is 9. If one of them is 5, find the
other number. It's interesting!
The sum of two number is 9.
Solution
Let the other number is x. So, x + 5 = 9
Then, x + 5 = 9 or, x = 9 – 5 = 4
I could easily find the unknown number!!
or, x + 5 – 5 = 9 – 5
or, x = 4
Hence, the other number is 4.
Example 2: A brother is 3 years younger than his sister. If brother is 5
years old, how old is the sister?
Solution
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Let the sister's age is x year. Algebra
Then, x – 5 = 3 I got it!
Brother's age is 3 years
or, x – 5 + 5 = 3 + 5 less than sister's age.
So, x – 5 = 3
or, x = 8 or, x = 3 + 5 = 8
Hence, the sister is 8 years old.
Exercise - 10.3
Section A - Classwork
1. Let's make mathematical sentences of each of the following statements.
Statements Mathematical sentences
a) The sum of x and 4 is 7.
b) The difference of y and 5 is 4.
c) Two times x is 10.
d) Two times y added to 3 is 9.
e) x is more than 2 by 1.
f) 3 is less than y by 2.
2. Let's say and write the value of x as quickly as possible.
a) The sum of x and 2 is 5. x=
b) The difference of x and 3 is 4. x=
c) The product of x and 5 is 10. x=
d) The quotient of x divided by 2 is 3. x =
e) Double of x is 8. x=
f) One-third of x is 3. x=
205Approved by Curriculum Development Centre, Sanothimi, Bhaktapur
vedanta Excel in Mathematics - Book 4
Algebra
Section B
Let's make mathematical sentences and solve them to find the
unknown number or quantity.
3. a) If the sum of x and 4 is 10, find x.
b) If the difference of y and 5 is 7, find y.
c) If the product of 3 and p is 12, find p.
d) If the quotient of x divided by 2 is 5, find x.
e) If the double of a is 16, find a.
f) If the half of b is 10, find b.
g) If x increased by 2 is 8, find x.
h) If y decreased by 3 is 7, find y.
i) If x is more than 10 by 5, find x.
j) If 5 is less than y by 4, find y.
4. a) The sum of two numbers is 17. If one of them is 9, find the other number.
b) The difference of two numbers is 10. If the smaller number is 5, find the
bigger number.
c) When a number is multiplied by 7, the product is 56. Find the number.
d) When a number is divided by 4, the quotient is 6. Find the number.
e) When a number is increased by 8 it becomes 15. Find the number.
f) When 9 is decreased from a number it becomes 7. Find the number.
g) When two times a number is added to 4, the sum is 10. Find the number.
h) When 5 is subtracted from three times a number, the difference is 7.
Find the numbers.
5. a) There are 30 students in a class. If 18 of them are girls, find the number
of boys.
b) There are 540 students in a school. If 260 of them are boys, find the
number of girls.
c) A box contains 50 kg of fruits. If it contains 30 kg of apples and the rest
is oranges, find the weight of oranges.
6. a) There are some students in a class. When 4 more new students join
the class the number becomes 30. Find the number of students before
joining the new students in the class.
b) Sunayana has some money. When she spends Rs 25, she has Rs 50 left.
How much money does she have at the beginning?
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c) Pemba Lama had a few number of marbles. When he bought 7 more
marbles, he had 35 marbles altogether. How many marbles did he have
at the beginning?
7. a) The number of girls in a class is 3 less than the number of boys. If there
are 14 girls, find the number of boys.
b) The number of girls in a class is 5 more than the number of boys. If there
are 17 girls, find the number of boys.
c) Aarshiya has Rs 10 more than Diyoshana. If Diyoshana has Rs 15, how
much money does Aarshiya have?
8. a) Anu Gupta is 4 years younger than her brother. If Anu is 8 years old, how
old is her brother?
b) Bikash Tamang is 3 years elder than his sister. If Bikash is 10 years old,
how old is his sister?
c) Mickey Mouse is 2 years younger than Bugs Bunny. If Bugs Bunny is 9
years old, how old is Mickey Mouse?
It's your time - Project work
9. a) There are x number of girls in your class. Let's count the number
of boys and the total number of students in your class. Then, make a
mathematical sentence and find the value of x.
b) There are y number of boys in your class. Let's count the number
of girls and the total number of students in your class. Then, make a
mathematical sentence and find the value of y.
c) There are x number of male teachers in your school. Let's count the
number of female teachers and the total number of teachers in your
school. Then, make a mathematical sentence and find the value of x.
10. Let's cut a longer and a shorter paper strips of any lengths from a chart
paper.
a) By how many centimetres is one strip longer or shorter than another
strip? Let's use this answer and do these activities.
b) Let the length of the shorter strip is x cm. Now, make a mathematical
sentence and find x. [Hint: x + .......... = longer strip]
c) Let the length of the longer strip is y cm. Now, make a mathematical
sentence and find y. (Hint: y – .......... = shorter strip)
207Approved by Curriculum Development Centre, Sanothimi, Bhaktapur vedanta Excel in Mathematics - Book 4
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10.7 Constant and variable - Introduction
Let's have a discussion on the following questions.
a) How many number of things does 1 always represent?
b) How many number of things does 5 always represent?
c) Does 8 sometimes represent 7, 9, or any other number of things?
Therefore, the numbers 1, 2, 3, 4, 5, ... always represent the fixed number of
things. The numbers are called constants.
Again, let's have discussion on the following questions:
a) x represents the height of students in your school. Does x represent the
same value?
b) y represents the age of students in your school. Does y represent the same
value?
c) p represents the natural numbers less than 10. Does p represent the same
value?
Furthermore, let's find the values of letters in the following mathematical
sentences.
x+3=8 x –3 = 8
5+3=8 11–3 = 8
So, x = 5 So, x = 11
Here, x represents 5. Here, x represents 11.
2×x=8 12 ÷ x = 4
2×4=8 12 ÷ 3 = 4
So, x = 4 So, x = 3
Here, x represents 4. Here, x represents 3.
Thus, in the above mathematical sentences, the letters x does not represent
the same value. Therefore, the letter x can be used to represent any number.
x is called a variable.
The letters like x, y, z, a, b, p, q, ... do not represent a fixed or constant number
of things. We can use such letters to represent any number of things.
Therefore, these letters are called variables. The word 'variable' means
something that can vary or change.
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10.8 Operation on constant and variable
Let's learn about the operations (addition, subtraction, multiplication, and
division) between constant and variables from the following illustrations.
How many marbles are there altogether in bags on each skateboard?
a) b) c)
55
x xx y yy2
5 + 5 x + x + x y+y+y+2
5 is added 2 times x is added 3 times 3 times y and 3 more
2 × 5 = 10 3 × x = 3x 3 × y + 2 = 3y + 2
Now, let's make a few more operations on constant and variables.
a) p is added to 2 = p + 2
b) 7 is subtracted from 2 times q = 2q – 7
c) The sum of x and 4 is divided by 2 = x + 4
2
In p + 2, p is a variable, 2 is a constant, and p + 2 is a variable.
In 2q – 7, q is a variable, 2 and 7 are constant, 2q is a variable, and 2q – 7
is also a variable.
In x + 4, x is a variable, 4 and 2 are constants, and x + 4 is also a variable.
2 2
Exercise - 10.4
Section A - Classwork
1. Let's circle the variables. Then, list the constants and variables
separately. Constants Variables
4 y 3x 7 5x
10 2a 6p 6 x + 9
2. Let's say and tick (√) whether these letters represent constant or
variable.
a) x represents the number of students in your class.
x is a (constant/variable)
b) x represents the height of students in your class.
x is a (constant/variable) vedanta Excel in Mathematics - Book 4
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c) y represents the number of sides of a triangle.
y is a (constant/variable)
d) p represents the even numbers less than 7.
p is a (constant/variable)
3. Let's fill in the blanks. and variables is x .
a) In 2x, constant is 2
b) In 7y, constant is and variables is .
c) In a + 3, constant is and variables is .
d) In 2x + 1, constant are , and variables is .
4. Let's say and write the values of letters in the number lines.
a)
0 1 2 3 x 5 6 7 8 y 10 11 12 13 14 z 16 17 18 19 20
Value of x is Value of y is Value of z is
b) 5b 10 15 c 20
0a Value of b is Value of c is
Value of a is
5. Let's say and write how many letters and numbers are there altogether
in bags on each skateboard?
a) b) y y y c) x x 3
xx
e) f)
d) p p25 x xx19
a aa4
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Algebra
6. Let's study each diagram until you investigate how it works. Then
complete the empty circles.
23 x4 xx 3
7 x+8
3x + 3
3 2x 2x 4
y 5 aa 7 xx 9
7. Let's play a game! In each game below, the players start with 5 points and
move one board at a time. Follow each board from 'START' to 'FINISH' to
find the total score.
S F
T win I
A3 win lose +win lose N 5
R x2 1 I 3
T 2x
S
H
S F
T win I
Ax win lose win lose N
R 2 3x
T 3x 5 I
S
H
S F
T win I
A2 win lose win lose N
R 4y y
T 3 2y I
S
H
211Approved by Curriculum Development Centre, Sanothimi, Bhaktapur vedanta Excel in Mathematics - Book 4
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8. Let's answer the following questions.
a) x represents the whole numbers less than 5.
(i) What are the values of x?
(ii) Is x a constant or variable? x is a
b) y represents a whole number between 8 and 10.
(i) What is the values of x?
(ii) Is y a constant or variable? y is a
Section B
Let's read these statements carefully. Then, express them in
mathematical operations with constants and variables.
9. a) x is added to 3. b) 2 times x is added to 5.
c) 4 is subtracted from y. d) 7 is subtracted from 3 times y.
e) a is increased by 6. f) b is decreased by 2.
g) 3 times the sum of x and 1. h) 5 times the difference of y and 9.
i) The sum of p and 8 is divided by 3.
j) The difference of q and 10 is divided by 7.
10. a) You are now x years old. After 2 years your age will be (x + 2) years.
b) Brother is now x years old. How old will he be after 1 year?
c) Sister is now y years old. How old will she be after 3 years?
d) Pratik has Rs x. Prabin gives him Rs 5 more. How much money does
Pratik have now?
e) Bishu aunty has Rs y. She gives Rs 10 to Devasis. How much money is left
with Bishu aunty now?
f) The cost of a pencil is Rs p. What is the cost of 6 pencils?
10.9 Like and unlike terms
Classwork - Exercise
1. Let's write 'Yes' or 'No' and answer the following questions.
a) Do the both packets have the same type of things.
b) Do the both bags have the same type of things?
c) Do the both plates have the same type of things?
d) Do the both packets have same type of things?
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2. Let's write the 'Like' for the same type of things and 'Unlike' for the
different types of things.
a) The plates have things.
b) The bags have thing.
c) The cards have letters. xx
d) The cards have letters. ab
Let's study these illustrations and investigate the idea about Plate A
like and unlike algebraic terms. Plate B
There are 2 apples in plate A and 3 apples in plate B. Both
the plates have the same (like) things.
Suppose, x represents an apple. Then, plate A has 2x and B
has 3x. So, 2x nd 3x are like terms.
Plate A There are 2 apples in plate A and 2 cakes in plate B. These
Plate B plates do not have same things. They have different (unlike)
things. Suppose x represents an apple and y represents a
cake. Then, plate A has 2x and plate B has 3y. So, 2x and 3y
are unlike terms.
Classwork - Exercise
2. Let's circle the unlike terms and list like terms separately.
a) 2a, 2b, 3a, 3y and are like terms.
b) p, q, 5p, pq and are like terms.
c) 4y, 6x, x, xy and are like terms.
3. It's your time. Let's write your own like and unlike terms.
a) and are like terms. b) and are unlike terms.
c) and are unlike terms. d) and are like terms.
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10.10 Addition and subtraction of like terms
Classwork - Exercise
1. Let's say and write the answer as quickly as possible.
a) + +
2x + 3x = 5x
2 pencils + 3 pencils = pencils
b) + +
apples
2 apples + 2 apples = 2x + 2x = x
c) + +
4 marbles + 3 marbles = marbles 4y + 3y = y
2. How many letters are there in each balloon? Let's find the letters
altogether.
a) x xx x b) a aaaaa c) z zzzzzz
aa z
a
+ = + = +=
3. Let's take away the letter-cards. Tell and write how many letters are
left?
a) From x x take away x = x is left.
From 2x take away x = 2x – x = x
b) From y y y take away y = y y are left
From take away = –=
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Algebra
c) From a a a a take away a a = a a
From take away = – =
d) From p p p p p take away p p = p p p
From take away = – =
Now, let's investigate the rule of addition and subtraction of like terms from
the examples given below.
a) x + 3x = (1 + 3)x = 4x
b) 2y + 5y = (2 + 5)y = 7y
c) 5a – 3a = (5 – 3)a = 2a
d) 8p – 5p = (8 – 5)p = 3p
4. Let's say and write the sum or difference as quickly as possible.
a) x + x = b) x + 2x = c) 3y + 2y =
d) 2a + 4a = e) 5p + 3p = f) 4x + x =
g) 5x – 2x = h) 7y – 4y = i) 9a – 5a =
j) 6p – 3p = k) 8k – k = l) 10x – 7x =
Exercise - 10.5
Section A - Classwork
1. Let's say and write the total number of letters in each of two balloons.
a) x xx b) y y y c) a a + aaaaaa
y y y y aa
x + xx y +
2x + 4x = + = +=
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Algebra
2. Let's subtract the letter-cards which are taken away. Tell and write
how many letters are left.
a) x x x x – x = 4x – x = 3x
b) y y y y y – y y y = – =
c) a a a a a a – a a = – =
3. How many letters are there altogether ? Let's add the same letters.
a) x + 2x = b) x + 3x = c) 4y + 2y =
d) 3x + 3x = e) 3a + 4a = f) 5p + 6p =
4. Let's subtract and find how many letters are left?
a) 2x – x = b) 3x – 2x = c) 6y – y =
d) 8y – 5y = e) 7a – 3a = f) 10p – 4p =
5. Let's say and write the correct terms in the blank spaces.
a) 3x + = 5x b) + 2y = 8y c) 5a + = 11a
d) 6x – = x e) 10y – = 9y f) – 2p = 7p
6. Let's write any two appropriate like terms to match each of the given
sums or differences.
a) + = 4x b) + = 7y c) + = 8a
d) – = x e) – = 2y f) – = 3p
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7. Let's fill in the missing terms to complete the sums.
5x + = 9x – 5y = 12y
+ + +– – –
+= – 2y =
= = == = =
8x + = 15x 11y – =
Section B
8. Let's find the sum of the following like terms:
a) 3x + 5x b) 4x + 2x c) 6y + 3y d) 2y + 9y
e) 7p + 4p f) 8m + 6m g) 9x + 8x h) 7p + 6p
i) 5y + 10y j) 12q + 4q k) 10m + 7m l) 9x + 6x
9. Let's find the difference of the following like terms:
a) 8x – 3x b) 9y – 4y c) 7p – 5p d) 10x – 5x
f) 9m – 5m g) 8p – 6p g) 12x – 7x h) 13y – 4y
i) 15q – 8q j) 16x – 10x k) 17y – 9y l) 18m – 8m
It's your time - Project work!
Let's make a few paper flowers by cutting a chart paper as shown in the
diagrams. Write an algebraic term (x, 2x, 3x, ...) in the circle. Write a pair
of terms in each of 4 petals using '+' or '–' sign between them to get the
term in the circle. Colour the petals. You can stick your flowers on the
wall-magazine.
x + 2x
3x 4x – x
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GGeeoommeettrryy:-LSihnaepseasnd Angles
Unit Geometry: Lines and Angles
11
11.1 Point, line, and line segment - Looking back
Classwork - Exercise
1. Let's choose the correct answer from the box and fill in the blanks.
straight line point line segment curved line
a) The dot P represents a P B
b) AB is a A Y
c) XY is a X Q
S tatisdti)c sPQ is a P
2. Let's say and write ' vertical', 'horizontal', or 'slanting' in the blank spaces.
a) AB is a line segment. C BA
b) AC is a line segment.
c) BC is a line segment. AB C
3. Let's name the vertical, horizontal, and slanting line segments.
a) is a vertical line segment. P R Q
b) is a horizontal segment. Q R P
c) is a slanting line segment.
11.2 Measuring the length of line segments
We use a centimetre - scale (or ruler) to measure the length of a line segment.
We also use it to draw the given length of a line segment.
1 cm 4.5 cm 8.4 cm 11.7 cm
0.5 1.5 2.5 3.5 4.5 5.5 6.5 7.5 8.5 9.5 10.5 11.5 12.5 13.5 14.5
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
10 mm =
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GeometryG:eLoimneestrayn-dSAhnagpleess
In a centimetre - scale, 1 cm is divided into 10 equal parts. Each part
represents 1 millimetre (mm).
So, 1 mm = 1 of 1 cm = 0.1 cm and 5 mm = 5 of 1 cm = 0.5 cm and so on.
10 10
Exercise - 11.1
Section A - Classwork
1. Let's say and write the name of straight line, line segment, curved line,
vertical line, horizontal line, and slanting line in the blanks.
XD
A BP Q MN AB
C
Y
a) is a straight line. b) is a straight line segment.
c) is a curved line. d) is a vertical line segmSteantitst.ics
e) is a horizontal line segment.
f) is a slanting line segment.
2. Let's say and write the correct answer as quickly as possible.
a) How many millimetres (mm) make 1 cm?
b) Express 5 mm in cm.
c) A straight line segment is 3 cm 4 mm. Express this length in the decimal
of centimetres.
d) A straight line segment is 5.6 cm. The length of the line segment is
cm mm.
3. Let's measure and write the length of line segments.
a) A B b)P Q
0.5 1.5 2.5 3.5 4.5 5.5 6.5 7.5 80.5 19.5 120.5.5 31.15.5 41.25.5 51.35.5 61.45.5 7.5 8.5 9
0 1 2 3 4 5 6 7 80 19 120 131 142 153 164 175 8 9
AB = 3.5 cm PQ = N
c) X Y d)M
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 7.5 80 8.05.5 91 91.5.5102102..55131 131..55142 142..55153153..55164 164..55157 7.5 8 8.5 9
XY = 219 MN =
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GGeeoommeettrryy:- LSihnaepseasnd Angles
4. Let's measure and write the length of sides of these triangles.
a) A b) R
AB = PQ =
BC = QR =
CA = RP =
BC PQ
5. Let's measure and write the length of sides of these rectangle and square.
a) D C b) H G
AB = EF =
BC =
CD = FG =
DA = GH =
AB HE =
EF
Section B
6. Let's draw straight line segments of the given lengths.
a) 3 cm b) 4 cm c) 7 cm d) 3.5 cm
e) 4.4 cm f) 6.5 cm g) 5.8 cm h) 8.2 cm
7. a) Let's draw a vertical line segment of the length 5 cm.
b) Let's draw a horizontal line segment of the length 4.5 cm.
c) Let's draw a slanting line segment of the length 7.3 cm.
It's your time - Project work!
8. a) Let's draw a vertical line segment. Measure and write its length.
b) Let's draw a horizontal line segment. Measure and write its length.
c) Let's draw a slanting line segment. Measure and write its length.
9. a) Draw a triangle ABC. Measure and write the length of its sides. Then,
calculate the perimeter of the triangle.
b) Draw triangle PQR. Measure and write the length of its sides. Then, find
the perimeter of the triangle.
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GeometrGy:eLoimnestrayn-dSAhnagpleess
11.3 Angle - Looking back
Classwork - Exercise
1. Let's observe the pictures and answer the following questions.
picture (i) picture (ii) picture (iii)
a) Where are the angles formed in pictures (i), (ii) and (iii)?
b) In which picture is the greatest angle formed?
c) Let's look around your classroom and list three angles formed by
different object.
In the given figure, name of the angle is ∠ABC or ∠CBA. B C
The point B at which an angle is made is called the vertex A
of ∠ABC. The straight line segments AB and BC that make
∠ABC are called the arms of ∠ABC.
Let's say and write the correct answer as quickly as possible.
2. a) Straight line segments AO and BO meet each other B
at the point
b) Name of the angle made by AO and BO at the point O A
O is
c) The vertex of ∠AOB is and arms are and
3. a) Name of two angles in the given R Z
figures are and
b) Between ∠PQR and ∠XYZ, the Q PY X
greater angle is
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GGeeoommeettrryy:-LSihnaepseasnd Angles
11.4 Measurement of angles
The given figure is a protractor. Can outside inside
you identify a protractor inside your scale scale
instrument box?
A protractor is a semi-circular
instrument. Its curved surface is
divided into 180 equal parts and each
part represent 1 degree(1°).
We use protractor to measure angles. It is also used to draw angles of the
given measurement.
Degree is the unit of measurement of angles. Degree is represented by the
symbol (°). So, we write 30 degree as 30°, 45 degree as 45°, and so on.
Now, study the following illustrations carefully and learn how to measure
the given angles.
BQ
AO OP
In this case, we use outside scale. In this case, we use inside scale.
So, ∠AOB = 60°. So, ∠POQ = 110°.
11.5 Construction of angles C
Let's learn to construct angles by
using a protractor.
Construct ∠ABC = 50°. B A
(i) Draw an arm AB and place the
centre your protector at B as shown in figure.
(ii) Count round the edge from 0° to 50°, and mark C.
(iii) Remove the protractor and join BC, using a ruler and a sharpen pencil.
Now, you have constructed ∠ABC = 50°.
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Exercise - 11.2
Section A - Classwork
1. Look at the angles marked below carefully. Name the angles made by
part of the objects.
a) b) Q c) X
Y
P Z
AB C R
2. Let's say and write the names, vertices and arms of the following angles:
a) A b) F c) P
O B E D O R
Name Name Name
Vertex Vertex Vertex
Arms Arms Arms
3. Let's compare the size of each pair of angles using the signs '<' or '>'.
a) R C b) Y XE
Q PB A OF G
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GGeeoommeettrryy:-LSihnaepseasnd Angles
4. Let's say and write the names and measurements of these angles.
a) b)
R
C
A B QP
∠ ABC = =
d)
F
c) Z
E DX Y
= f) =
e)
B D
O A O C
= =
5. Let's measure the sizes of these angles using protractor. Say and write
the measurements as quickly as possible.
a) b) N c) X
A
B C O MO Y
∠ ABC =
==
vedanta Excel in Mathematics - Book 4 224 Approved by Curriculum Development CentreSanothimi, Bhaktapur
d) R e) D GeometryG:eLoimneestrayn-dSAhnagpleess
f) R
Q P S T
F
E
=
= =
Section B
6. Answer the following questions.
a) What is an angle?
b) What do you mean by vertex and arms of an angle?
c) In ∠PQR, name its vertex and arms.
d) What are the vertex and arms of ∠PRQ?
e) How do you write 70 degree by using the symbol of degree?
f) What is the instrument used to construc and measure angles?
g) What is the shape of a protractor?
h) In how many equal parts is the curved surface of a protractor divided?
7. Let's construct the following angles by using protractor:
a) 30° b) 40° c) 50° d) 60° e) 70° f) 80°
g) 90° h) 100° i) 120° j) 45° k) 75° l) 105°
It's your time!
8. a) Let's draw two straight line segments using a ruler and a sharpen pencil
such that the angle between them is less than 90°. Name the angle and
measure its size using protractor.
b) Let's draw two straight line segments using a ruler and a sharpen pencil
such that the angle between them is greater than 90°. Name the angle
and measure its size using a protractor.
c) Let's trace the instruments of your geometry box in chart paper. Write
the name of the instruments. Discuss the uses of the instrument.
? vedanta Excel in Mathematics - Book 4
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Geometry - Shapes Geometry: Shapes
Unit
12
12.1 Plane figures (or shapes)
Let's discuss about the answer of the following questions.
a) What is the shape of the surface of the traffic signal board?
b) What is the shape of the surface of the book?
c) What is the shape of the surface of the given cubical die?
d) What is the shape of the surface of the given coin?
Triangle, rectangle, square, circle, etc. are called the plane figures. The
shape of the surface of a triangle is triangular, a rectangle is rectangular, a
square is square shape, and a circle is circular.
12.2 Triangle
Let's take a sheet of paper and fold it along one of its corner
as shown in the figure. Now, cut the folded corner. The cut
out part represents a triangle. The shape of this part is
triangular.
It is a triangle ABC. We write triangle ABC as DABC.
We use the symbol 'D' for the word 'triangle'.
AB, BC, and CA are 3 sides of DABC.
∠A, ∠B, and ∠C are 3 angles of DABC.
A, B, and C are 3 vertices of DABC.
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Geometry - Shapes
Exercise - 12.1
Section A - Classwork
1. Let's say and write the name, vertices, sides, and angles of these triangles.
a) R Name Vertices , ,
Sides , ,
Q P Angles ,,
b) F Name Vertices , ,
Sides ,,
E D
Angles ,,
2. Let's measure the length of sides of each of the following triangles and
write the measurements in the table .
C PZ
A B X Y
DABC Q R DXYZ
DPQR
AB = QR = XY =
YZ =
BC = RP = ZX =
AC = PQ = vedanta Excel in Mathematics - Book 4
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Geometry - Shapes
3. Let's measure the angles of each of the following triangles and write
the measurements in the table .
AF R
B C ES T
DABC D DSTR
DDEF
∠A = ∠D = ∠S =
∠B = ∠E = ∠T =
∠C = ∠F = ∠R =
4. It's your time - Project work!
a) Let's name any three objects which have triangular shaped surface.
b) Draw a triangle using a ruler. Write the vertices of the triangle. Then,
write the name, sides, and angles of the triangle.
c) Let's open your instrument box and find two triangular shaped
instruments. What are these instruments called?
12.3 Quadrilaterals
In the given figures, ABCD is a quadrilateral. D S R
PQRS is also a quadrilateral. A quadrilateral A C Q
is a plane shape bounded by 4 straight line
segments. A rectangle and a square are the BP
special type of quadrilaterals.
Rectangle
Let's discuss about the answer of the following questions.
a) What is the shape of the surface of your maths book?
b) What is the shape of the surface of the walls of your classroom?
c) What is the shape of the surface of your desk (or table)?
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Geometry - Shapes
D lC ABCD is a rectangle.
90° 90°
b b AB, BC, CD, and DA are the 4 sides of the rectangle.
90° 90° ∠A, ∠B, ∠C, and ∠D are the 4 angles of the rectangle.
A lB
AB and CD are the length (l) of the rectangle.
BC and DA are the breadth (b) of the rectangle.
(i) Lengths of a rectangle are always equal. So, AB = CD = l
(ii) Breadths of a rectangle are always equal. o, BC = DA = b.
(iii) Each angle of a rectangle are always equal and of 90° (right angle).
So, ∠A = ∠B = ∠C = ∠D = 90° Sl R
90° 90°
Square
PQRS is a square. l l
PQ, QR, RS, and SP are the 4 sides of the square.
∠P, ∠Q, ∠R, and ∠S are the 4 angles of the square. 90° 90°
(i) All four sides of a square are always equal.
Pl Q
So, PQ = QR = RS = SP = l
(ii) All four angles of a square are always equal and they are 90°.
So, ∠P = ∠Q = ∠R = ∠S = 90° (a right angle)
12.4 Circle
Let's take a coin and place it on a sheet of paper. Move the
tip of a sharpen pencil along it's edge. What type of shape Diameter
is formed? Can you tell the name of any two objects which Centre
have circular shape?
B
The figure given alongside is a circle. It is a Radius
rounded plane figure.
A O C
O is called the centre of the circle.
AB is the diameter of the circle.
OC is the radius of the circle. circumference
OA and OB are also the radii (plural of radius) of the circle.
The rounded boundary line is the circumference of the circle.
(i) Radii (plural of radius) of the same circle are always equal.
So, OC = OA = OB.
229Approved by Curriculum Development Centre, Sanothimi, Bhaktapur vedanta Excel in Mathematics - Book 4
Geometry - Shapes
(ii) Length of a diameter of a circle is always two times the length of its
radius.
So, AB = 2 × OC or 2 × OA or 2 × OB
Similarly, OC = 1 AB, OA = 1 AB and OB = 1 AB
2 2 2
Exercise - 12.2
Section A - Classwork
1. Let's say and write the name, vertices, sides, and angles of the given
rectangle and square.
G F Vertices , , ,
a) Name
Sides , , ,
E Angles , , ,
D
Z Y Vertices , ,,
,
b) Name
,
Sides , ,
R
Angles , ,
W X
S
2. a) In the given rectangle PQRS, if PQ = 5 cm,
QR = 4 cm, find the length of RS = 4 cm
and SP = P 5 cm Q
D C
b) In the given square ABCD, if AB = 3.5 cm, find the length
of BC = , CD = and DA =
A 3.5 cm B
c) In the given rectangle EFGH, ∠E = ,H G
∠F = , ∠G = and ∠H =
EF
vedanta Excel in Mathematics - Book 4 230 Approved by Curriculum Development CentreSanothimi, Bhaktapur
d) In the given square KLMN, ∠K = , ∠L = Geometry - Shapes
NM
∠M = and ∠N =
,
KL
3. Let's say and write the name of center, radius, and diameter of these
circles.
A Z X centre is
centre is
O radius is P radii are ,
C diameter is Y diameter is
B
Section B
4. Let's find the length of the sides marked by letters. G
2 cm
a) D x C b) S y R c)
H
x F
p
A 4 cm B P 3 cm Q
ABCD is a rectangle. PQRS is a square. E
PQRS is a rectangle.
d) Z e) N 2 cm M f) A
p
b
2.5 cm D
3 cm 5 cm q
Y
W a y 4.5 cm C
c B ABCD is a rectangle.
X KxL
KLMN is a rectangle.
WXYZ is a square.
5. Let's find the size of angles marked by letters.
a) D C b) S R c) H d cG
a
xy b a b
AB PQ E F
ABCD is a square. PQRS is a rectangle. EFGH is a rectangle.
231Approved by Curriculum Development Centre, Sanothimi, Bhaktapur vedanta Excel in Mathematics - Book 4
Geometry - Shapes
6. Let's find the diameter of each circle.
a) B b) P c)
A 1.5cm O O 2cm R Y O Z
2.5cm
C Q X
radius = 2 cm radius = 2.5 cm
radius = 1.5 cm
7. Let's find the radius of each circle.
a) A b) D c) P R
4cm 5cm O
O EO 6 cm
F
C diameter = 5 cm Q
B diameter = 6 cm
diameter = 4 cm
It's your time - Project work
8. a) Let's name any two objects which have rectangular shaped surface.
b) Let's name any two objects which have square shaped surface.
c) Let's name any two objects which have circular surface.
9. a) Let's measure the lengths and breadths of your maths book by using a
30 cm - scale.
(i) Are the lengths equal? (ii) Are the breadths equal?
b) Let's measure the lengths and breadths of your bed by using a measuring
tape.
(i) Are the lengths equal? (ii) Are the breadth equal?
12.5 Solid figures (or shapes)
Cube, cuboid, cylinder, sphere, cone, pyramid, etc. are called solid figures.
Solid figures are also called 3 dimensional figures or 3 - D figures. Length,
breadth, and height are the 3 dimensions.
Cube Face 1
The given solid figure is a cube. It has got 52
Edge 4 36
6 square faces, 12 edges, and 8 corners Corner
(vertices).
The length (l), breadth (b), and height (h).
vedanta Excel in Mathematics - Book 4 232 Approved by Curriculum Development CentreSanothimi, Bhaktapur
Geometry - Shapes
Cuboid Face
The given solid figure is a cuboid. It has Edge 5 1
got 6 square rectangular faces, 12 edges, Corner 46 2
and 8 corners (vertices). 3
breadth (b),
A cuboid also has (l), and
height (h).
Cylinder Circular face
Curved surface
The given solid figure is a cylinder. It has got
2 circular faces, 1 curved surface, and 2 circular
edges. It does not have any corner (vertex).
Cone Circular edge
The given solid figure is a cone. It has got 1 circular Circular surface
Circular edge
face, 1 curved surface, circular edge, and 1 corner Curved surface
(vertex). Corner
Curved surface
Sphere
The given solid figure is a sphere. It does not have
any face, edge, and corner. It has a curved surface.
Exercise - 12.3
Section A - Classwork
1. Let's say and write the names of these solid figures. Also name an
object similar to each of these shapes.
a) b)
It is a It is a
c) d)
It is a It is a
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Geometry - Shapes
e) f)
It is a It is a
2. Which solid shapes are these objects similar to?
a) b) c)
d) e) f)
3. Let's say and write the number of faces. Edges and corners of these
solid shapes?
a) faces, edges
and corners.
b) faces, edges, and
c) corners. curved surface
circular faces,
edges
d circular faces Does it have any
curved surface faces, edges, and
corners. corners?
4. Let's say and write the name of solid figures in the blank spaces.
a) A has 1 circular face, 1 curved surface, 1 edge, and 1 corner.
b) A has 6 rectangular faces, 12 edges, and 8 corners.
c) A has 2 circular faces, 1 curved surface, and 2 edges.
d) A has 6 square faces, 12 edges, and 8 corners.
?
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Geometry - Shapes
Unit Statistics
13
13.1 Bill
Have you ever got a piece of paper from a
shopkeeper when you buy goods? This piece
of paper is a bill. Have you ever read a bill?
In a bill, a shopkeeper writes the customer's
name and address, quantity, rate of cost, and
total cost of goods that we buy from the shop.
Classwork - Exercise
1. Let's read the price of various types of fruits displayed in fruit shop
and answer the following questions.
Rs 200 per kg Rs 120 per kg Rs 350 per kg Rs 80 per kg
a) Which one is the most expensive fruit?
b) Which are the cheapest fruit?
c) By how much is the rate of cost of apples more expensive than the rate
of cost of oranges?
d) If you have only Rs 100, which fruit can you buy?
e) If you have Rs 200, which two fruits each of 1 kg can you buy?
f) If you have Rs 500, which three fruits each of 1 kg can you buy?
235Approved by Curriculum Development Centre, Sanothimi, Bhaktapur vedanta Excel in Mathematics - Book 4
Statistics
2. Father bought some fruits and the shopkeeper gave him a bill. Answer
the following questions.
Fresh Fruit Shop
Chhatachok, Dharan
Date: 7 Shrawan, 2077
Customer's Name and Address: Ganesh Gurung, Zeropoint, Dharan
S. No. Particulars Quantity Rate (Rs) Amount
(Rs)
1 Apple 2 200.00 400.00
2 Kiwi 1 350.00 350.00
3 Mango 3 80 240.00
Total 990.00
Amount in words: Nine hundred ninety only. ...............................
Sold by
a) What is the name of the fruit shop?
b) What is the address of the fruit shop?
c) What is the name of the customer?
d) What types of fruits did the customer buy?
e) How much is the total bill amount?
f) If the customer gave a Rs 1000 note, how much change did he receive
back?
3. Mrs Yadav bought the following grocery items at the given rate of cost
from a shop.
Rice - Rs 90 per kg Sugar - Rs 85 per kg Flour - Rs 60 per kg
Cooking oil - Rs 310 pr litre
Imagine you are the shopkeeper. Now prepare a bill for Mrs Yadav in the
following sample of a bill.
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Statistics
Sagarmatha Grocery Store
Kapan - Nilopul, Kathmandu
Date: ..................................................
Customer's Name and address:
......................................................................................................................................................................
S. No. Particulars Quantity Rate (Rs) Amount (Rs)
Total
Amount in words: ........................................................................................... ...................
Sold by
13.2 Budget
A budget is a description of income of a family or organisation from different
sources and a plan of how it will be spent over a period of time. A budget
may help to balance between income and expenditure and manges saving.
Example 2: The annual earning of a family from different sources
and the planning of expenses on different titles are given
below. Prepare an annual budget of the family.
Sources and income Titles and expenditure
Service Rs 2,50,000 Food and cloths Rs 1,10,000
Business Rs 1,80,000 Education Rs 1,20,000
Farming Rs 90,000 Taxes Rs 25,000
Insurance Rs 50,000
237Approved by Curriculum Development Centre, Sanothimi, Bhaktapur vedanta Excel in Mathematics - Book 4
Statistics
Solution
Income Expenditure)
Sources Amounts (Rs) Titles Amount (Rs)
Services 2,50,000 Food and cloths 1,10,000
Business 1,80,000 Education 1,20,000
Farming Taxes 25,000
90,000 Insurance 50,000
Total 5,20,000 Total 3,05,000
Saving = Rs 5,20,000 – Rs 3,05,000 = Rs 2,15,000
Exercise - 13.1
Section A - Classwork
1. Let's read the given bill. Tell and write the answer of the following
questions as quickly as possible.
Vedanta Stationery Traders
Budha Subba chowk, Rajabas - 9
Bill No. 0345 Date: 7 Shrawan, 2079
Customer's Name: Badri Rai Address: Prakashpur
S. No. Particulars Quantity Rate (Rs) Amount
(Rs)
1 Crayons 6 20.00 120.00
2 Instrument box 1 115.00 115.00
3 Drawing books 3 60 180.00
Sold by: Anamol Grand Total 415.00
a) What is the name of the shop?
b) What is the name of the customer?
c) How many crayons are purchased?
d) What is the rate of cost of crayons?
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Statistics
e) What is the amount of the crayons?
f) What amount is paid for instrument box?
g) How much is the cost of 1 drawing book?
h) What is the total amount of the bill?
Section B
2. Let's prepare the similar format of bill as given in Q. No. 1. Then,
workout these problems.
a) Kopila purchased 4 exercise books at Rs 35 each, 2 pens at Rs 25 each,
and 6 colour pencils at Rs 10 each. Prepare a bill given to her by the
shopkeeper.
b) The price list of different food items displayed by a provision shop is
given. Prepare bills given to the customers by the shopkeeper.
(i) Bill of 5 kg of rice, 2 kg of flour, 3 kg of sugar
(ii) Bill of 4 kg flour, 2 litres cooking oil, 1 kg of tea
(iii) Bill of 3 kg of pulses, 4 kg of rice, 1 litre cooking oil.
3. a) Let's copy the annual budget of Mr. Gurung given below. Then answer the
following questions.
Income Expenditure
Sources Amounts (Rs) Titles Amount (Rs)
Vegetable farming 1,05,000 Food and 90,000
cloths
Poultry 1,50,000 Education 1,10,000
Fishery 1,80,000
Insurance 45,000
Total
Miscellaneous 25,000
Total
(i) Calculate his total annual income and expenditure.
(ii) How much money is he planning to save?
239Approved by Curriculum Development Centre, Sanothimi, Bhaktapur vedanta Excel in Mathematics - Book 4
Statistics
b) The annual income of Mrs. Sangita Thakuri from different sources and
expenditures on different titles are given below. Prepare her annual
budget.
Sources and income Titles and expenditure
Goat farming Rs 1,25,000 Food and cloths Rs 85,000
Dairy Rs 1,10,000 Education Rs 1,20,000
Bee Keeping Rs 75,000 Health Insurance Rs 35,000
Taxes Rs 15,000
How much money is she planning to save in a year?
It's your time - Project work!
4. a) Let's make groups of your friends. Visit a few number of shops in your
locality and collect the sample of some bills. Discuss about these bills in
your class.
b) Let's ask to your family members whether they have any types of bills
given by shopkeeper. Then, study about the bills.
13.3 Bar graph - Looking back
Classwork - Exercise
1. Let's study this horizontal bar graph and answer the given questions.
Favourite fruits The bars represent the number of students
who like different fruits.
Apple
Mango a) How many students like apple?
Orange b) How many students like orange?
Banana c) Which one is the least favourite
fruit?
0 1 2 3 4 5 6 7 8 9 10 11
Number of students d) How many students participated in the
survey?
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Statistics
2. Let's read this vertical bar graph and answer the questions.
a) What do the bars represent?
b) Let's write the number of students in the given table who got different
grades. 13 Annual result of class 4
Grades 12
'A' Grade 'B' Grade 'C' Grade 11
No. of students 10
9
c) In which grade did the highest number of 8 Number of students
students pass? 7
6
d) How many students appeared in the annual 5
exam of class 4? 4
3
The given graph is called a bar graph. 2
It's a way to show and compare data, or
information. 1
O 'B' 'C'
'A'
Grade Grade Grade
Result
A bar graph has four main parts: a title, labels,
a scale, and bars. Flowers in School Garden
15
1. In the given bar graph, the title is
'Flowers in School Garden'. 14
13
2. Below the graph is the label 'Types of Number of flowers12
Flowers'. Just below the bars, the types 11
flowers are written as 'Rose', 'Lily', and
'Daffodil'. 10
9
3. The scale is the set of numbers along 8
7
the left side of the graph. It shows the 6
number of items. 5
4
4. Bars are the rectangular vertical or 3
horizontal boxes drawn to represent the 2
given information. 1
O Lily Daffodil
Rose
Types of Flowers
241Approved by Curriculum Development Centre, Sanothimi, Bhaktapur vedanta Excel in Mathematics - Book 4
Statistics
Exercise - 13.2
Section A - Classwork Favourite Sports
1. Let's say and write the correct answer Number of students11 Football Cricket Table Tennis
of the following questions. Types of Sports
10
a) What is the title of the bar graph? 9
8
b) What is the label of the bar graph? 7
6
5
c) How many students like cricket? 4
3
d) How many students do not like 2
football? 1
O
e) How many less students like table
tennis than cricket?
f) Which is the most popular sport among the students?
g) Which is the least popular sport among the students?
h) How many students participated in the survey?
Section B
2. Let's draw bar graphs using the information given in the tables.
a) Careers Doctor Teacher Pilot b) Events Quiz Sports Dance Music
No. of 7 94 No. of 20 50 25 10
Students Participants
Career Choices School Day Events
55
50
Doctor Number of participants 45
Teacher
40
35
30
25
20
Pilot 15
O 1 2 3 4 5 6 7 8 9 10 10
Number of students
5
vedanta Excel in Mathematics - Book 4
242 O Quiz Sports Dance Music
Events
Approved by Curriculum Development CentreSanothimi, Bhaktapur
Statistics
3. a) Class 4 students conducted a survey about which cartoon characters
they like. The table given below shows their responses:
Cartoon Characters Mickey Mouse Bugs Bunny Scooby Doo Daffy Duck
59
No. of students 12 8
Draw a bar graph using this information.
b) The table given below shows the number of votes received by the
candidates of school prefect in a school
Candidates A B CD
No. of votes 30 80 50 100
Draw a bar graph using this information.
c) The scores obtained by different houses in a Maths Quiz Contest are
given below in the table. Draw a bar graph using the information.
Houses Green House Red House Yellow House Blue House
Scores 60 40 50 35
It's your time - Project work!
4. a) Let's make a group of 5 students. Conduct a survey and find the number
of students from class 1 to class 5 in your school. Write the numbers in
the table and show the information in a bar graph.
Classes 1 23 45
No. of Students
b) Working on your own, or with a partner, or in a group, investigate the
following for the pupils in your class. Collect the statistics in a table
and then illustrate them in bar graphs.
(i) Their favourite subjects (ii) Their favourite sports
(iii) Their favourite vegetables
(iv) How do they usually come to school, by walking, or by school bus or
by own vehicles?
Vedanta ICT Corner
Please! Scan this QR code or
browse the link given below:
https://www.geogebra.org/m/h9rndjxp
?
243Approved by Curriculum Development Centre, Sanothimi, Bhaktapur vedanta Excel in Mathematics - Book 4
Answers
Answers
Section B 1.1. Number System
5. a) 54 = 5 × 10 + 4 × 1 Exercise – 1.1
b) 270 = 2 × 100 + 7 × 10
c) 1325 = 1 × 1000 + 3 × 100 + 2 × 10 + 5 × 1 d) 3017 = 3 × 1000 + 1 × 10 + 7 × 1
6. a) 63 = 6 × 10 + 3 × 1 b) 542 = 5 × 100 + 4 × 10 + 2 × 1
c) 4507 = 4 × 1000 + 5 × 100 + 7 × 1 d) 20304 = 2 × 10000 + 3 × 100 + 4 × 1
7. a) T O b) H T O c) Th H T O d) T-th Th H T O
8. a) 672 b) 4853 c) 51491
2 × 1 = 2 3 × 1 = 3 1 × 1 = 1
7 × 10 = 70 5 × 10 = 50 9 × 10 = 90
6 × 100 = 600 8 × 100 = 800 4 × 100 = 400
4 × 1000 = 4000 1 × 1000 = 1000
5 × 10000 =50000
9. a) 84 b) 725 c) 408 d) 2077 e) 5346 f) 36187
10. a) 45 b) 180 c) 900
11. a) Nine thousand seventy-five b) Fifteen thousand nine rupees 12. a) Rs 7011 b) 10086
13. a) one b) two c) three d) seven e) nine
Exercise – 1.2
Section B
3. a) L1 T-2th T5h H6 T1 O0 One lakh twenty-five thousand six hund red t en.
b) T-l L T- th Th H T O Twenty-seven lakh eighteen thousand three hundred
2 7 1 8 3 0 9 nine.
c) C T-l L T-th Th H T O Four crore seventeen lakh thirty-six thousand
4 1 7 3 6 0 8 2 eighty-two.
4. a) H-th T-th Th H T O One hundred fifty-seven thousand
1 5 7 3 20 three hundred twenty.
b) M H-th T-th Th H T O Three million two hundred seventy-one thousand
3 2 7 1 0 6 8 sixty-eight
c)
T-m M H-th T-th Th H T O Twenty-one million forty-nine thousand three
21 0 4 9 3 5 5 hundred fifty-five
5. a) 7,560 – Seven thousand five hundred sixty
b) 26,908 – Twenty-six thousand nine hundred eight
vedanta Excel in Mathematics - Book 4 244 Approved by Curriculum Development CentreSanothimi, Bhaktapur
Answers
c) 1,25,043 – One lakh twenty-five thousand forty-three
125,043 – One hundred twenty-five thousand forty-three
d) 38,04,100 – Thirty-eight lakh four thousand one hundred
3,804,100 –Three million eight hundred four thousand one hundred
e) 5,06,09,050 – Five crore six lakh nine thousand fifty
50,609,050 – Fifty million six hundred nine thousand fifty
6. a) Lakh (Hundred thousand), 200000, 2 b) Ten-lakh (Million), 4000000, 4
c) Crore (Ten-million), 10000000,1
7. a) 1 million b) 2 million c) 3 million d) 4 million e) 5 million f) 9 million
8. a)10 million b) 20 million c) 30 million d) 50 million e) 80 million
9. a) 10 lakh b) 60 lakh c) 70 lakh 10. a) 1 crore b) 4 crore c) 7 crore
11. a) 347000, three hundred forty-seven thousand
b) Rs 2580500, two million five hundred eighty thousand five hundred rupees
c) 29192480, twenty-nine million one hundred ninety-two thousand four hundred eighty
12. a) 147516 sq. km, one lakh forty-seven thousand five hundred sixteen sq. km
b) Rs 4750300, forty-seven lakh fifty thousand three hundred rupees
c) Rs 99580000, nine crore ninety-five lakh eighty thousand rupees
13. a) 740, 407 b) 8652, 2568 c) 96310, 10369 d) 875420, 204578 14. Please perform the given
project work. Compare your answers with your friends.
Exercise – 1.3
Section B
3. a) 40 b) Rs 230 c) 260 km d) 4,610
4. a) 500 km b) 700 c) Rs 15,900 d) 19,900 litres
5. a) 220, 200 b) 570, 600 c) 1,660 , 1,700 d) 34,850 , 34,900
Exercise – 1.4
Please complete your classwork yourself.
3S.e cat)io..n. B 147, 149, ... Exercise – 1.5
145,
4. a) ... , 304, 306, 308, ... b) ... ,267, 269, 271, 273, ... c) ... , 591, 593, ... , 597, ...
b) ... , 406, 408, 410, 412, ... c) …,798, 800, 802, 804, ...
5. Please perform the given activities. Discuss about your investigation in your class.
6. Please perform the given activities.
2. Fundamental Operations - I
Exercise – 2.1
Section B b) 1,220 kg c) 1,051 students d) 4,345 people e) Rs 465
8. a) Rs 840 g) 986 girls h) 2,288 men i) Rs 285 j) Rs 535
f) 376 l
9. a) 175, 320 b) 229, 407 c) 387, 712 d) 881, 1580 e) 2880, 5005 f) 3687, 8250
10. a) 941 b) 485 c) 60,550 d) 10,700 e) 203 kg 11. a) Rs 925 b) Rs 850
12. a) (i) 634 (ii) 1,090 b) (i) 456 (ii) 1,090 c) (i) Rs 3,035 (ii) Rs 4,820
13. a) Rs 4,000 b) Rs 2,535 c) Rs 6,740 d) Rs 650 e) Rs 165 f) Rs 150 g) Rs 195
h) Rs 165 i) Rs 1,035 j) Rs 2050 14. and 15. Please perform the given activities
individually or in group. Discuss the outcomes of the activities in the class.
245Approved by Curriculum Development Centre, Sanothimi, Bhaktapur vedanta Excel in Mathematics - Book 4
Answers
3. Fundamental Operations - II
Exercise – 3.1
Section B
8. a)160 b) 1600 c) 2100 d) 21000 e) 24000
f) 1100 g) 22000 h) 6000 i) 4500 j) 4800
9. a) 192 b) 322 c) 765 d) 216 e) 900 f) 1998
g) 4048 h) 1740 i) 6075 j) 13056 k) 31360 l) 560500
10. a) Rs 1,250 b) Rs 1,620 c) Rs 5,700 11. a) 300 eggs b) 144 pencils
c) 240 balls d) Rs 4,800 e) Rs 1,95,000 12. a) 5,000 kg b) 7,000 kg c) 11,340 ml
d) 306 g protein e) 2,160 calories f) 1,50,000 l g) 240 km h) 448 km i) 1,320 km
13. a) 364 days b) 144 months c) 5,475 days 14. a) 400 students b) 270 chairs
15. and 16. Please perform the given project works. Discuss about your outcomes in the class.
Exercise – 3.2
Section B
9. a) 4 b) 40 c) 400 d) 40 e) 2 f) 20 g) 200 h) 20
i) 3 j) 5 k) 4 l) 70 m) 80 n) 80 o) 90 p) 90
10. a) Q =11, R = 3 b)Q = 12, R = 2 c) Q = 16, R = 1 d) Q = 12, R = 0
e) Q = 12, R = 0 f) Q = 106, R = 1 g) Q = 108, R = 2 h) Q = 104, R = 0
i) Q = 106, R = 0 j) Q = 103, R = 0 k) Q = 214, R = 1 l) Q = 212, R = 2
m) Q = 213, R = 1 n) Q = 153, R = 2 o) Q = 142, R = 0
11. a) Q = 1150, R = 2 b) Q = 1192, R = 3 c) Q = 1132, R = 0 d) Q = 1122, R = 2
e) Q = 1092, R = 0 f) Q = 1022, R = 2 g) Q = 1003, R = 0 h) Q = 449, R = 1
i) Q = 588, R = 0 j) Q = 751, R = 0
12. a) Q = 12, R= 0 b) Q = 12, R = 5 c) Q = 10, R = 6 d) Q = 15, R = 0
e) Q = 17, R = 6 f) Q = 9, R = 8 g) Q = 8, R = 2 h) Q = 42, R = 0
i) Q = 62, R = 10 j) Q = 73, R = 5 13. a) Rs 85 b) 5 kg c) Rs 96 d) 8 l
14. a) 15 dozens b) 25 crates c) 24 boxes 15. a) 100 kg b) 1000 kg c) 500 ml
16. a) 11 players b) 14 teams 17. a) 30 students b) 15 columns
18. a) 52 weeks b) 25 years c) 12 years
19. and 20. Please perform the given project works. Discuss about your outcomes in the class.
Exercise – 3.3
Section B
3. a) 153 is divisible by 3 and 9 b) 276 is divisible by 3 c) 387 is divisible by 3 and 9
d) 489 is divisible by 3 e) 5967 is divisible by 3 and 9.
4. a) 16 b) 24 c) 36
2× 8 2 × 12 2 × 18
2 × 2×4 2 × 2×6 2 × 2×9
2 × 2× 2 × 4 2 × 2× 2 × 3 2 × 2× 3 × 3
16 = 2 × 2 ×2 × 2 24 = 2 × 2 ×2 × 3 36 = 2 × 2 × 3 × 3
d) 30 e) 40 f) 54
2 × 20 2 × 27
2 × 15
2 × 2 × 10 2 × 3×9
2 × 3×5
30 = 2 × 3 × 5 2 × 2× 2 × 5 2 × 3× 3 × 3
40 = 2 × 2 × 2 × 5 54 = 2 × 3 × 3 × 3
vedanta Excel in Mathematics - Book 4 246 Approved by Curriculum Development CentreSanothimi, Bhaktapur
Answers
5. b) 12 = 2 × 2 × 3 c) 15 = 3 × 5 d) 18 = 2 × 3 × 3 e) 20 = 2 × 2 × 5
h) 28 = 2 × 2 × 7 i) 30 = 2 × 3 × 5
f) 24 = 2 × 2 × 2 × 3 g) 27 = 3 × 3 × 3
j) 32 = 2 × 2 × 2 × 2 × 2 k) 35 = 5 × 7 l) 36 = 2 × 2 × 3 × 3 m) 40 = 2 × 2 × 2 × 5
n) 42 = 2 × 3 × 7 o) 45 = 3 × 3 × 5 p) 48 = 2 × 2 × 2 × 2 × 3
4 .Order of Operations
Exercise – 4.1
Section B
4. a) 23 b) 25 c) 19 d) 22 e) 15 f) 21 g) 20 h) 1 i) 27 j) 5
5. a) 14 b) 3 c) 32 d) 3 e) 5 f) 40 g) 72 h) 4 i) 32 j) 39 k) 5 l) 8
6. a) (3 + 2) × 5 b) (4 + 3) × 2 c) 4 × (10 – 8) d) 24 ÷ (4 × 2) e) 20 ÷ (7 + 3)
f) (49 – 7) ÷ 7 g) (45 + 18) ÷ 9 h) 3 × ( 6 + 4) ÷2 i) 24 ÷ (6 – 2) × 5
7. a) Rs 7 b) 12 weeks c) 11 students d) 39 chairs e) 12 pencils f) 14 boys
g) 14 m h) Rs 75 8. a) 9 b) 54 c) 4 d) 3 e) 8 9. a) 280 ml b) 48 km
c) 3 km d) Rs 35 e) 35 students f) Rs 2,100 g) 2 sweets
10. Please perform the given project works. Compare your works with your friends.
5. Fraction
Exercise – 5.1
Section B
4. a) 1 b) 1 c) 1 d) 1 e) 1 f) 1 g) 13 h) 13 i) 1 j) 1 k) 1 l) 1
2 3 2 2 3 2 5 4 5 5
1 1 2 2 3 3 4 4 5 6 4 7
5. a) 2 b) 4 c) 3 d) 5 e) 4 f) 5 g) 5 h) 7 i) 6 j) 7 k) 9 l) 8
6. a) 32 b) 3 c) 2 d) 2 e) 3 f) 4 g) 23 h) 3 i) 3 j) 2 k) 3 l) 2
4 3 5 5 5 4 5 3 4 3
2 3 3 4 3 3
m) 3 n) 5 o) 4 p) 5 q) 4 r) 4
7. a) 2 b) 3 c) 2 d) 2 e) 3 f) 4 g) 2 h) 5 i) 2 j) 3 k) 3 l) 4
3 4 3 5 5 5 3 6 3 4 4 5
8. Please complete the given project works and compare your works with your friends.
Exercise – 5.2
Section B
8. a) b) c) d)
9. a) Ascending order : 2 , 3 , 4 , 5 Descending order : 5 , 4 , 3 , 2
7 7 7 7 7 7 7 7
b) Ascending order : 1 , 5 , 6 , 7 Descending order : 7 , 6 , 5 , 1
9 9 9 9 9 9 9 9
c) Ascending order : 130, 4 , 7 , 9 Descending order : 9 , 7 , 4 , 3
10 10 10 10 10 10 10
10. a) 121 b) 221 c) 312 d) 421 e) 113 f) 123 g) 313 h) 114 i) 241 j) 115 k) 225 l) 334
11. a) 3 b) 4 c) 5 d) 5 e) 8 f) 7 g) 13 h) 85 i) 13 j) 16
2 3 3 2 3 4 4 5 5
12. Please complete the given project works and compare your works with your friends.
Section B Exercise – 5.3
3. a) 45 b) 65 c) 68 4. a) 13 b) 37 c) 130 5. a) 35 b) 56 c) 47 d) 78 e) 98
247Approved by Curriculum Development Centre, Sanothimi, Bhaktapur vedanta Excel in Mathematics - Book 4
Answers
6. a) 16 b) 27 c) 58 d) 94 e) 130 7. a) 76, b) 190 c) 38 d) 1
3
8. a) 223 b) 212 c) 253 d) 523 e) 335 f) 1 g) 2 h) 1 i) 115 j) 112
9. a) 85 b) 4 or, 32 c) 34 10. a) 72 b) 85 c) 95 11. a) 3 litre b) 170 c) 421 m d) 3
6 5 7
Exercise – 5.4
Section B 21 c) 112 e) 23 f) 3 g) 123 h) 43
4. a) 21 2 3 i) 3 i) 142 or 121
b) 2 or 1 d) or 1
5. a) 2 b) 3 c) 4 d) 2 e) 3 f) 5 g) 2 h) 4
6. a) Rs 6 b) 3 kg c) Rs 10 d) 5 boys e) 21 students f) 6 l g) 20 km h) Rs 150
c) Rs 300
7. a) 43 b) 170 c) 41 d) 61 8. a) 12 girls b) 30 kg
d) (i) 80 km (ii) 60 km e) (i) 270 girls (ii) 180 boys
6. Decimal and Percent
Exercise – 6.1
Section B
8. a) 0.7 b) 0.4 c) 0.05 d) 0.26
9. a) zero point two b) zero point zero two c) zero point five seven
10. a) 0.5 b) 0.06 c) 0.32
11. a) 2170, 2.7 b) 311060 , 3.16 c) 4150 , 4.5 d) 6110 , 6.1 e) 113090 , 1.39 f) 512040 , 5.24
3 b) 140 170 d) 7 5 f) 1090 g) 13060 81
12. a) 10 c) 100 e) 100 h) 100
13. a) a = 0.7, b = 1.2, c = 2.4, d = 3.1, e = 4.8, f = 5.9, g = 8.3, h = 13.5
14. a) 0.1 5 b) 0.7 6
= 0.1
tenths tenths = 0.7
hundredths = 0.05 d) 0.55 hundredths = 0.06
c) 0.2 8 tenths = 0.5
tenths = 0.2
hundredths = 0.08 hundredths = 0.05
15. a) 0.3 < 0.5 b) 0.3 > 0.05 c) 0.7 > 0.4 d) 0.07 < 0.4 e) 0.26 < 0.28 f) 0.26 > 0.028
16. a) 0.01, 0.02, 0.1 b) 0.08, 0.25, 0.5 17. a) 0.3, 0.2, 0.07 b) 0.09, 0.1, 0.18
18. Please complete the given project works and discuss about the outcomes in the class.
Exercise – 6.2
Section B k) 151 l) 121
7. a) 15 b) 510 c) 52 d) 215 e) 21 f) 210 g) 53 h) 530 i) 54 j) 225 g) 2.2 h) 3.4
m) 221 n) 41 o) 295 8. a) 0.5 b) 0.2 c) 0.4 d) 0.6 e) 0.8 f) 1.5
i) 1.6 j) 2.8 k) 0.25 l) 0.75 m) 0.35 n) 0.45 o) 0.16 p) 0.18 q) 1.12 r) 2.14
9. a) 0.5 b) 0.7 c) 0.7 d) 0.8 e) 1.1 f) 1.2 10. a) 0.07 b) 0.06 c) 0.09 d) 0.13
e) 0.12 f) 0.14 11. a) 0.22 b) 0.33 c) 0.44 d) 0.18 e) 0.33 f) 2.35 g) 5.57 h) 10.54
i) 12.55 12. a) 0.45 b) 0.54 c) 0.63 d) 0.25 e) 0.37 f) 0.34 g) 3.12 h) 4.05 i) 2.59
13. a) 0.93 b) 0.85 c) 0.81 d) 5.6 e) 53.56 f) 82.14 g) 0.25 h) 0.29 i) 3.38
j) 2.82 k) 11.79 l) 19.32 14. a) Rs 60.56 b) 43.215 km c) Rs 101.25
vedanta Excel in Mathematics - Book 4 248 Approved by Curriculum Development CentreSanothimi, Bhaktapur
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