Math5

Formation of algebraic equation and their solution

While forming an algebraic equation, we have to suppose the unknown quantity as

variables like x, y, z etc. and we have to translate the statement into algebraic equation.

Example : A number means ‘x’
a number + 7 = 11
A number added to 7 equals to 11.
Solution: x + 7 = 11

Let the number be ‘x’

From the given condition,

x + 7 = 11

or, x + 7 - 7 = 11 - 7

or, x = 4

\ The required number is 4.

Example :

5 less than a number y is 13. 5 less than y means (y - 5)
Solution:

y - 5 = 13
y - 5 + 5 = 13 + 5
y = 18
Example :

2 times a number added to 5 is 17. Two times of x = 2x
Solution: two times of x added to 5 is 2x + 5
Let the number be ‘x’.

From the given condition,

2x + 5 = 17 Subtracting 5 from both sides.
or, 2x + 5 - 5 = 17 - 5

or, 2x = 12

or, 2x = 12 Dividing both sides by 2
2 2
or, x = 6

Example :

Area of a rectangle is 24 cm². If its length is 8 cm, find its breadth.
Solution:

Let the breadth of the rectangle be ‘x’.

l = 8 cm, b = x cm, A = 24 cm²

We have,

A = l × x or, 24 = 8x

Oasis School Mathematics Book-5 251

or, 284 cm = 8x or 3cm = x 8 cm
8
or, x = 3 cm
x cm

\ Breadth of the rectangle = 3 cm.

Exercise 13.9

1. Form the equations and solve them:

a. Sum of y and 6 is 11 b. Difference of x and 2 is 9
c. 25 added to y is 30 d. 15 taken away from z is 25
e. y is taken away from 10 is 7 f. Product of x and 5 is 25
g. 3 multiplied to x gives 18 h. x divided by 3 is 6

2. Make the equation and solve the following problems:

a. 2 times a number added to 6 is 20.

b. 3 times a number added to 4 is 25.

c. If 7 is subtracted from 3 times a number the result is 8.
d. If 4 is subtracted from 2 times a number, the result is 2.
e. If a number is divided by 4, the result is 3.

3. a. Area of a rectangle is 15 cm². If the length is 5 cm, find the breadth.

b. The product of two numbers is 21. If one of them is 7, find the other
number.

4. Write the algebraic expression for the following:

a. Select a number: x
Multiply it by 4: .....................
Add 7 to the result: .....................
b. Select a number: y
Multiply it by 4: .....................
Subtract 7 to the result: .....................

Mathematical fun

- Think of a number x 5 10 15 20 100

- Add 50 to it x + 50 55

- Double it 2x + 100 110

- Add 48 to it 2x + 148 158

- Divide it by 2 x + 74 79

- Take away the number you 74 74
thought of

Try this with other numbers and compare the result. It's interesting! Every
time the result is 74.

252 Oasis School Mathematics Book-5

Worksheet

Let's check Aadhya's copy. Tick the correct answer. Cross the wrong one and

do the correction. Name : Aadhya Sharma

Class : V

1. Write the expression for the statement 'Two times x is added to 7".

Solution: Correction

Two times x added to 7 is

2x + 7

2. Add: 5x² – 3xy + 2y² and 12x² – 10xy + y²
Solution: 5x² – 3xy + 2y²

+ 12x² – 10xy + y²

17x² + 13xy + 3y²

3. Subtract: 3a³ – 4a²b + 5b³ from 2a³ – 6a²b + 10b³
Solution: 2a³ – 6a²b + 10b³

3a³ – 4a²b + 5b³

(–) (+) (–)

– a³ – 2a²b + 5b³

4. Multiply: (5x + 2y) and (x – y)

Solution: 5x + 2y

× x – y

5x² + 2xy

– 5xy – 2y²

5x² – 3xy – 2y²
5. Divide: 15x³y7 + 10x4y² – 2y² by 5x²y²

Solution: 15x³y7 + 10x4y² = 15x³y7 + 10x4y²
5x²y² 5x²y² 5x²y²

= 3x3+2y7+2 + 2x4+2y2+2
= 3x5y9 + 2x6y4
6. Solve: 2x - 4 = 2
5
Solution : 2x -4+4=2+4 or, 2x = 30
5 or, 2x = 30
or, or, x5= 15 2
2x = 6
5
or, 2x × 5 = 6 × 5
5

Oasis School Mathematics Book-5 253

Objective Questions

Colour the correct alternatives:
1. The literal co-efficient of x in 2xy is

21 y

Ax + 2y3x - yPerimeter of the given DABC is

2. C 6x 6x + 2y 2y

B 2x + y

3. The product of x²y³ and 6x³y7 is

6x5y10 6xy4 1
6xy4
4. 24x7y6 ÷ 12x5y4 is equal to
x²y²
2xy² 1 2
2x²y²
4x³y²
5. What should be multiplied to 5xy to make 20x4y³?

4x²y² 4x³y³

6. The value of 'x' in the equation 2x + 5 = 11 is

53 –3

7. The equation of the statement '2 times x added to 7 is equal to 19' is

2x + 7 = 19 2x + 19 = 7 7 – 2x = 19

8. Formula of volume of a cube is l × b × h. Volume of the cube having length,
breadth and height (x + 2), (x – 2) and x is

x² – 4 x² + 2x x³ – 4x

9. The value of x in the equation 3x + 3 = 6 is
4

12 4 15

Number of correct answers
254 Oasis School Mathematics Book-5

Unit Test Full marks: 25

1. Write the expression for each of the following statements: 2

a. x is increased by 3 b. z is decreased by 5

2. If a = 1, b = 2, c = 3, d = 0, x = 4, y = 5 and z = 6, find the value of: 1.5×2=3

a. 3a + b - 4d b. (2x + y - 2z) × a

3. Add: 1.5×2=3
a. 2a + 3b + 5c and a - 2b + 3c
b. a² - ab + 2b², 4a² + 3ab + b² and 5a² - 2ab + b²

4. Subtract: 1.5×2=3
a. m + n - 2p from 4m - 2n + 3p
b. 8x + 6y - 4z from 9x + 8y + 2z

5. Multiply: 2
a. 6b×2b×4b b. (-2x³y7) × (-7x4y³)

6. Using the formula A = l × b, find the area of the following figures: 2

l = 2x + 3

b=x+1

7. Divide: b. (12x4y³ - 8xy + 4x²y³) ÷ 2xy 1.5×2=3
a. 12y5 ÷ 3y² 1.5×2=3

8. Solve: b. 5x + 3 = 23 2×2=4
a. x + 1 = 6

9. Make the equation and solve the following problems:
a. If 7 is subtracted from 3 times a number the result is 8.

b. If a number is divided by 4, the result is 3.

Oasis School Mathematics Book-5 255

Model Test Paper

Full Marks : 100

1. Choose the correct alternatives: [20 × 1 = 20]

a. The name of given angle is P
(i) ∠PQR (ii) ∠QPR (iii) ∠RQP

b. I am an angle. My magnitude is more QR
than 180° and less than 360°. Who am I?
(i) Acute angle (ii) reflex angle (iii) obtuse
angle

c. Which of following pairs are complementary angles?

(i) 15° and 75° (ii) 45° and 65° (iii) 55° and 20°

d. The smallest number formed by the digits 2, 3, 1, 0, 8 and 6 is

(i) 012368 (ii) 102368 (iii) 863210

e. One more than the greatest number of five digits is equal to

(i) Smallest number of six digits (ii) Greatest number of six digits

(iii) Smallest number of five digits.

f. The number that is 25728 less than 38637 is

(i) 64365 (ii) 11909 (iii) 12909
g. 5 × 6 + 25÷ 5 – 2 × 3 is equal to

(i) 29 (ii) 6 (iii) 39

h. If a number is divisible by both 2 and 3 then it is divisible by

(i) 5 (ii) 6 (iii) 4

i. Highest common factor of 12 and 18 is

(i) 9 (ii) 3 (iii) 6

j. A number multiplied by itself gives 625 then the number is

(i) square of 625 (ii) cube of 625 (iii) square root of 625

k. The value of 3 5 + 4 1 is equal to: (i) 6 7 (ii) 781 (iii) 743
8 8 8

256 Oasis School Mathematics Book-5

l. Reciprocal of the fraction 3 18 is equal to: (i) 8 (ii) 25 (iii) 31
25 8 8

m. 0.625 × 100 is equal to: (i) 6.25 (ii) 625 (iii) 62.5

n. 23.6 ÷ 100 is equal to: (i) 0.236 (ii) 2.36 (iii) 236

o. 20m cloth costs Rs 1400, then the cost of 1 m cloth is

(i) RS 1400 (ii) Rs 70 (iii) Rs 7

p. 6m 27cm is equal to: (i) 6027 cm (ii) 627cm (iii) 6270cm

q. In 7x8

(i) 7 is base, x is co-efficient and 8 is power

(ii) 8 is base, x is power and 7 is co-efficient

(iii) 7 is co-efficient, x is base and 8 is power

r. Which one of the following groups contains like terms?

(i) 3x²y, 7x²y and 10x²y (ii) 4x²y, 4xy²
and 4xy

(iii) 5x²y, 5xyz and 10xyz²

s. If 4 is subtracted from the number the result is 12, the number is

(i) 16 (ii) 8 (iii) 12 A
3.8cm
t. Perimeter of the given triangle ABC is

(i) 9cm (ii) 10cm (iii) 11cm 2cm

B 4.2cm C

2. a. Draw the given angles with the help of a protractor. A 2

(i) 96° (ii) 78°

b. In the given figure, write a pair of adjacent

angles. 2 B

c. In the given figure, write the vertically OC
AD
opposite angle of: 2
O
(i) ∠AOD (ii) ∠AOC

CB

d. Three angles of a triangle are given below. Mention their type on the

basis of angles. 2

(i) 25°, 78° and 77° (ii) 120°, 20° and 40°

e. What is the sum of four angles of a quadrilateral? 1

Oasis School Mathematics Book-5 257

3. a. Use comma according to Nepali place value system and write the

number name of: 23064934 2

b. Use comma according to international place value system and write

the number name of: 46984120 2

c. Write the greatest number formed by the digits. 1

3, 6, 4, 8, 0, 1, 2

4. a. Add: 4 8 6 0 2 9 6 3 b. Subtract: 4 6 2 3 9 0 1 4
+ 7 5 9 6 4 8 2 –3864834
+16948231

c. Multiply: 3 0 6 5 1 d. Divide: 93264 ÷ 45 4
× 26

d. Simplify: 25 × 3 – 20 × 3 + 60 ÷ 15 2

5. a. Separate the prime numbers. 2

11, 10, 13, 18, 15, 21, 23, 27, 29 2

b. Test whether the given numbers are divisible 2
2
(i) 523 (by 6) (ii) 716 (by 4) 2

c. Find the prime factors of 48.

d. Find the L.C.M. of: 24 and 36

e. Find the square root of 225.

6. a. Add: 3 1 + 5 2 + 7 14 . 2
2 3
2 13 1 2
b. Find the product of × 6 × 3 . 2

c. A girl has 2 m long ribbon. How many pieces of ribbons each having
3
1
the length of 6 m can be made from her ribbon? 2

7. a Simplify: 5.46 + 3.92 – 1.63 2

b. Multiply: 6.25 × 3.4 2

c. Divide: (i) 63.24 ÷ 10 (ii) 127.8 ÷ 100. 2

258 Oasis School Mathematics Book-5

8. a. In a class, 25 students out of 40 are girls. Find the percentage of girls in

the class. 2

b. If the cost of 5 articles is Rs 140, what is the cost of an article? 2

c. An article is bought for Rs 1560 and sold at Rs 1800. Find the profit or

loss. 2

9. Convert as indicated: 2
a. 3 months 15 days into days 4
b. Rs 125 and 60 Paise into Rs

10. Add or subtract:
a. 15kg 650gm 200mg – 12kg 800gm 450mg
b. 13l 450ml + 25l 840ml

11. a. Find the perimeter of the given figure. 2

4cm

2cm 8cm

9cm
7cm

13cm

b. A rectangular ground has length 5m and breadth 4m. Find its area. 1

c. Find the volume of a cuboid whose length, breadth and height are

6cm, 5 cm and 4cm respectively. 1

d. Find the area of shaded part in the given figure. 2

12cm

6cm 10cm3cm

12. The number of students in different sections of Class V are given below.

Represent this data in the bar graph. 3

Section A B CDE

Number of students 20 25 25 30 20

Oasis School Mathematics Book-5 259

13. Plot the following points on the graph paper. 1

(i) A(2, 4) (ii) B(3, 7)

14. a. List he elements of following set in listing method. 2

(i) A set of even numbers from 1 to 10

(ii) A set of prime numbers from 1 to 10

b. If A = {1, 3, 5, 7, 9}, then put ∈ or ∉ 1

1 ........... A 4 ........... A

15. a. Write the algebraic expression for 2.

(i) three times x is added to 2 2
b. 1
c. (ii) 7 is subtracted from 5 times y 1
d. 1
e. Add: 3x – 5y + 6z and 4x – 7y – 2z 2
f.
Subtract: 2a² – 3ab + 5b² from 3a² + 2ab – 6b²

Multiply: 2x²y × 3xy²

Divide: (15a³b² – 10ab²) ÷ 5ab

Solve: 3x + 2 = 2x + 1

260 Oasis School Mathematics Book-5