Grade 7 Book 1 Unit 1 and 2

3.2 Division of Fractions

To divide fractions
o Take the reciprocal of the divisor.

o Change the operation into multiplication.

o Apply multiplication.

Given as dividend and as divisor;


÷ = ×



Example 7

Find the quotient of the following;

a. 3 ÷ 7 =? b. ቀ− 4ቁ ÷ 1 1 =? c. 3 ÷ ቀ− 2ቁ =?
7
48 5 9

Solution

a. 3÷7 = 3×8

48 47

= 3×8 = 24 = 6

4×7 28 7

b. ቀ− 45ቁ ÷ 1 1 = ቀ− 45ቁ ÷ 8
7 7

= ቀ− 4ቁ × 7 = −4×7

5 8 5×8

= − 28 = − 7

40 10

c. 3 ÷ ቀ− 2ቁ = 3 × ቀ9ቁ

9 12

= 3×(−9) = − 27

1×2 2

Mathematics Book 1 39

Exercise 2D

1. Solve the following
a. ቀ−4 4ቁ ÷ ቀ−2 1ቁ =

52

b. ቀ1 ÷ 1ቁ × 1 =

23 4

c. [ቀ− 2ቁ ÷ 4] × ቀ− 3ቁ =
55 8

d. ቀ− 9 ቁ ÷ ቀ1 + 2ቁ =

10 6 3

e. ቀ−4 5ቁ ÷ [ቀ− 7ቁ − 3] =

9 84

2. 2 1 dozen eggs cost 67 1 baht. Find the cost of 1 egg.
2 2

3. The thickness of 400 page book, with 200 sheets per book, is 12 1 . Find
2

the thickness of:

a. 1 sheet

b. 100 sheets

40 Mathematics Book 1

4. Decimal

4.1 Place Value of Decimals

Decimals represent numbers that are not whole numbers. We show the
value by using a decimal point. Decimal numbers use the base 10 system.

Place Value

Whole Number Decimal Decimal
Point

Thousands Hundreds Tens Ones Tenths Hundredths Thousandths

103 102 101 1 11 1
10 102 103

1000 100 10 1 11 1
10 100 1000

The place value of each digit for 918.276 is

9 1 8.2 7 6

Hundreds ( 9 x 102) Thousandths ( 6 x1103)
Tens ( 1 x 10) Hundredths ( 7 x1102)

Ones ( 8 x 1) Tenths ( 2 x 1 )

10

The expanded form of 918.276 is

= (9 × 102) + (1 × 10) + (8 × 1) + ቀ2 × 1ቁ + ቀ7 × 1 ቁ + (6 × 1103)
102
10

Mathematics Book 1 41

Example 8

Write the following in expanded form:

a. 1055.5 b. 253.067 c. 0.003

Solution

a. 1055.5 = (1 × 1000) + (5 × 10) + (5 × 1) + (5 × 1 )

10

b. 253.067 = (2 × 100) + (5 × 10) + (3 × 1) + ቀ6 × 1 ቁ + (7 × 1 )

100 1000

c. 0.003 = (3 × 1 )

1000

Exercise 2E

1. Express the following decimals in expanded form.

Decimals Expanded Form
1) 0.34

2) 0.05
3) 95.12
4) 590.012
5) 803.1005

2. Express the following as decimal numbers.

Expanded Form Decimals

1) 3 + ቀ1 × 1ቁ + (2 × 1102)

10

2) ቀ1 × 1ቁ + ቀ2 × 1102ቁ + (4 × 1103)

10

3) ቀ3 × 110ቁ + ቀ4 × 1102ቁ + (4 × 1104)

4) (9 × 102) + (5 × 1) + ቀ3 × 1102ቁ + (1 × 1103)
5) (8 × 102) + (5 × 10) + (2 × 1102)

42 Mathematics Book 1

4.2 Comparing Decimals

1.2.1 Comparing Positive Decimals

We can compare decimals by comparing the digits in the same place.
a. 3.45 and 4.51
We compare the digits in the ones place value 3 and 4.
3 < 4, therefore 3.45 < 4.51

b. 0.49 and 0.47
Digits in the tenths place value are equal so we compare the
hundredths place value 9 and 7.
9 > 7, therefore 0.49 > 0.47

1.2.2 Comparing Negative Decimals

We can compare decimals by considering the absolute value. When
comparing negative numbers, the decimal that has the smaller absolute value
is bigger.

a. −0.51 and −0.59
The absolute value of −0.51 is 0.51.
The absolute value of −0.59 is 0.59.
0.51 < 0.59 therefore −0.51 > −0.59.

b. −5.43 and −3.45
The absolute value of −5.43 is 5.43.
The absolute value of −3.45 is 3.45.
5.43 > 3.35 therefore − 543 < −3.45.

1.2.3 Comparing Decimals with Opposite Signs

We learned that numbers on the right of zero (0) are larger than numbers
on the left of zero.

a. 0.1 > −1.5
b. 0.009 > −2.1

Mathematics Book 1 43

Example 9

Arrange −2.75, −3.56, 0.15 and 0.513 in descending order.

Solution

a. Consider the positive decimals:
0.513 > 0.15

b. Consider the negative decimals:
−2.75 > −3.56

Therefore, 0.513, 0.15, −2.75, −3.56

4.3 Rounding a Decimal

Rounding off a decimal is to end decimals after the specified number of
decimal places. To round off decimals:

o Decide the last digit to keep, and then look at the digit just to the right
of it.

o If the digit is less than 5, do not change the rounding digit but drop
all digits to the right of it.

o If the digit is greater than or equal to 5, add 1 to the rounding digit
and drop all digits to the right of it.

Example 10

a. Rounding a decimal to a whole number:

a. 15.521
To whole number.

Therefore 15.521 ≈ 16
b. Rounding to one decimal place:
a. 2.916
To one decimal place.

Therefor 2.916 ≈ 2.9
c. Rounding off to two decimal places:
a. 15.8385
To two decimal places.

Therefore 15.8385 ≈ 15.84

44 Mathematics Book 1

Exercise 2F

1. Arrange the following decimals in ascending order.
a. 0.12, 0.21. 0.42
b. 15.15, 16.45, 15.76
c. 0.04, 0.05, 0.045, 0.5
d. -5.152, -2.052, -4.612, 5.602
e. -3.1, -2.1, -1.3, -1.2, -1.1

2. Arrange the following decimals in descending order.
a. 2.22, 22.2, 0.0222, 0.22
b. -0.555, -0.0055, -55.5, -5.55
c. -10.1, 0.01, 10.01, 0.11
d. 3.345, -3.11, -3.01, 3.001
e. 28.008, 28.08, 28.8, 28.0008

3. Round off the following decimals to the nearest thousandths.
a. -4.8719
b. -9.2345
c. 0.0076
d. -0.7672
e. 0.8575

4. The weights of four students in the same class are 41.5 kg, 39.7 kg, 40.3 kg
and 42.8 kg. List the weights in ascending order.

5. John is 161.42 cm tall, James is 160.05 cm tall and Joe is 159.98 cm tall. List
their heights in descending order.

Mathematics Book 1 45

5. Addition and Subtraction of Decimals

5.1 Addition of Decimals

To add decimal numbers, follow the steps below:
o Write the numbers such that their decimal points are below one
another.
o Insert zeros in empty decimal place values so that all the number
have the same number of decimal places.
o Add the numbers in the same way as whole numbers.
o Place the decimal point of the result in line with the other decimal
points.

Example 11

Find the sum of the following decimals:
a. 15.6 + 0.837 b. (−0.27) + (−1.3) c. 3.5 + (−0.713)

Solution

a. + 15.6 Align the decimal points vertically.
0.837
Insert zeros to get the same number of
+ 15.600 decimal places.
0.837

+ 15.600 Add the numbers, then place the decimal
0.837 point aligned with the other decimal
point.

16.437

46 Mathematics Book 1

b. + -0.27 Align the decimal points vertically.
-1.3
Insert zero to get the same number of decimal
+ -0.27 places.
-1.30
Add the numbers, then place the decimal
+ -0.27 point aligned with the other decimal point,
-1.30 then copy the sign.

-1.57

Note:
In adding two negative decimals, add their absolute values then copy the
sign.

c. + 3.5 Align the decimal points vertically.
-0.713
Insert zeros to get the same number of
+ 3.500 decimal places.
-0.713

+ 3.500 Subtract the numbers, then place the
-0.713 decimal point aligned with the other decimal
point, and then copy the sign of the number
2.787 with bigger absolute value.

Note:
In adding two decimals with opposite sign, subtract their absolute values
then copy the sign of the number with bigger absolute value.

Mathematics Book 1 47

5.2 Subtraction of Decimals

Subtraction of decimals is carried out in a similar way when adding decimal
numbers.

o Write the numbers such that their decimal points are below one
another.

o Insert zeros in empty decimal place values so that all the numbers
have the same number of decimal places.

o Subtract the numbers in the same way as whole numbers.
o Place the decimal point of the result in line with the other decimal

points.

Example 12

Find the difference of the following decimals:

a. 40.1 − (−11.93) c. −18.397 − 183.97

b. −121.17 − (−0.98)

a.

Solution

a. - 40.10 + 40.10
-11.93 11.93

52.03

b. - -121.17 + -121.17
-0.98 0.98

-120.19

- -18.397 + -18.397
183.97 -183.970
-202.367

48 Mathematics Book 1

Exercise 2G

1. Calculate the following:
a. (−4.2 + 9.8) − 2.5 =

b. (8.5 − 11.9) − 10.8 =

c. (−12.6 − 4.4) − 9.9 =

d. 20.30 − (1 − 19.5) =

e. (−1.7) + [(−10.14) − 0.05] =

2. Find the value of “ x ”.
a. 6.3 + (−1.1) = − 1.5

b. −3.01 + = (2.3) + 11.2

c. 0 + = 4.23 + 5.6 + (−0.92)

d. (−1.09) + = 11.32 + (−7.4) + 4

e. (−9.04) + 16.7 = − 4

Mathematics Book 1 49

3. Jonas purchased a bag for 1,340.60 baht, a book for 328.23 baht and a tie for
480.55 baht. How much is left with him if he had 3,000 baht in all?

4. Mark had 939.50. He gave 135.03 to Lisa, 445.85 to Tina and the remaining
money to Lana. How much did he give to Lana?

5. Felix travelled 280.75 km and Stephen travelled 386.78 km. Who travelled
more and by what distance?

6. Mark and Matthew saved up 1810.75 baht and 1,045.25 baht respectively to
buy a gift for Mother’s Day. How much money in all have the brothers set aside
for the gift?

7. The temperature at 5 a.m. was −7.5⁰c. By 9 a.m., the temperature had risen
to −3.9⁰c.
a. Find the rise in temperature.
b. By 1 p.m., the temperature had risen 5.7⁰c more. What was the
temperature at 1 p.m.?

50 Mathematics Book 1

6. Multiplication and Division of Decimals

6.1 Multiplication of Decimals

To multiply decimals,
o Multiply the numbers as if there is no decimal.
o Count the number of digits after the decimal in each factor.
o Count the same number of digits on the product from right then
place the decimal point.

Example 13

a. 0.78 × 4 =? c. 23.41 × 10 =?
b. 1.03 × 1.6 =? d. 76.34 × 100 =?

Solution 2 decimal places.

a. 0.78 × 4 = 0.78 2 decimal places.
×4 1 decimal place.
3.12 3 decimal places.

b. 1.03 × 1.6 = 1.03

× 1.6

+ 618
103

1.648

c. 23.41 × 10 = 23.41 When multiplying a decimal by 10,
× 10 move the decimal point 1 place to
the right.
234.1

d. 76.34 × 100 = 76.34 When multiplying a decimal by
× 100 100, move the decimal point 2
places to the right.
7634.00

Mathematics Book 1 51

Example 14

A man is 6 times as old as his son. What is the man’s age if his son is 7.75
years old?

Solution

The man = 6 x (his son)
= 6 x 7.75
= 46.5

Therefore, the man is 46.5 years old.

Example 15

Rachel bought 3.5 kilograms of pork at 120.5 baht per kilogram, and 1.25
kilogram of beef at 100 baht per kilogram. If she has 1,000 baht bank note, how
much change will she get?

Solution

a. Rachel bought pork which costs 120.5 baht/kg

She bought x 3.5 kg

So 3.5 kg of pork costs 421.75 baht

b. She bought beef which costs 100 baht/kg

She bought x 1.25 kg

So 1.25 kg of beef costs 125 baht

So, the cost of pork and beef is
. + = . baht.

If she has 1,000 banknote bill, then
, − . = . baht.

Therefore, she will get a 453.25 baht change.

52 Mathematics Book 1

Exercise 2H

1. Find the product of the following:
a. 0.2 × 0.02 =
b. (−1.5) × (−1.2) =
c. (−0.02) × 100 × 45.5 =
d. (5.8 × 1.2) + (5.7 × 1.5) =
e. 29.992 × 25 × 10 × 100 =

2. Each packet of eggs weighs 0.75 kilogram. What is the weight of 72 packets
of eggs?

3. Larry weighs 7.6 kg. His older brother is 7 times as heavy. How much does his
older brother weigh?

4. Sarah bought 12 meters of fabric to make a patchwork quilt. If the fabric was
on sale for 45.35 per meter, how much did Sarah spend?

5. If the bus fare for a distance of 1 km is 3 baht 25 satang, what is the bus fare
for a distance of 150 km?

6. The Earth takes 365.25 days to travel around the Sun. How many days would
it take for the Earth to travel around the Sun 4.3 times?

Mathematics Book 1 53

6.2 Division of Decimals

6.2.1 If the divisor is a whole number

Place the point right above the Quotient
decimal point of the dividend.

. 1 .083̇ Dividend

3)3.25 3)3.2 50

Divisor 3
25

24

10

9

1 Remainder

Since 3 is repeating and not terminating, the quotient is called Recurring

Decimal.

6.2.2 If the divisor is decimal 5 2.5 Add 0.

0.2)10.5 2)1 0 5.0

Move the decimal point 1 10
place to the right. 05
4
10
10
0

Note:
To divide a decimal by a decimal, convert the divisor to a counting
number by multiplying both the dividend and the divisor by 10 or 100 or 1,000
etc., depending on the number of decimal places of the divisor.

54 Mathematics Book 1

Example 16

There are 6.93 gallons of water in a tank. This water is to be transferred
equally to 3 smaller containers. How much water will each container have?

Solution

The 6.93 gallons of water is to be 2.31
transferred to 3 smaller containers. 3 6.93

So, we need to divide 6.93 by 3; 6
9
9
3
3
0

Therefore, there are 2.31 gallons of water in each container.

Example 17

A motorcycle travels 46.42 kilometers in 2.5 hours. What is the speed of the
motorcycle per kilometer?

Solution

Given the distance = 46.42 km, 18.568
25 464.200
Time= 2.5 hours
25
We need to find the speed. 214
200
speed = distance 142
125
time
170
Thus, we need to divide 46.42km by 2.5 hrs. 150
200
200

0

Therefore, the speed of the motorcycle is 18.568 km/h.

Mathematics Book 1 55

Exercise 2I

1. Solve the following.
a. 18 ÷ 0.9
b. 0.45 ÷ (50)
c. (−30.05) ÷ (−0.5)
d. (−0.7) ÷ 0.8
e. 5.4 ÷ (−0.008)
f. [(−0.5) ÷ 0.02] ÷ 0.4

56 Mathematics Book 1

2. The product of two numbers is 8.1235. One of the numbers is 2.11. What is the
other number?

3. The height of one post is 2.35m. The total of the heights of a bundle of posts is
37.6m. How many posts are there in the bundle?

4. Seven boys were given 100 baht to be divided equally among them. How much
will each receive?

5. 3 dozen of eggs cost 117 baht. Find the cost of each egg.

Mathematics Book 1 57

Summary

• A fraction represents a part of a whole. The top number is called numerator
and the bottom number is called denominator.
• There are 3 types of fraction:

o Proper Fractions are fractions where the numerator is less than
the denominator.

o Improper Fractions are fractions where the numerator is greater
than the denominator.

o Mixed Fractions are fractions where it is a combination of a whole
number and a proper fraction.

• Two fractions are equivalent if they have the same value.
• To write equivalent fractions, we multiply or divide both numerator and

denominator by the same number.
• When comparing two fractions, make the denominator of both fractions

the same and then compare the numerator.
• Decimals represent numbers that are not whole numbers.
• To add or subtract decimals:

o Write the numbers such that their decimal points are below one
another.

o Insert zeros in empty decimal place values so that all the number
has the same number of decimal places.

o Add / subtract the numbers in the same way as whole numbers.
o Place the decimal point of the result in line with the other decimal

points.
• To multiply decimals:

o Multiply the numbers as if there is no decimal.
o Count the number of digit after the decimal in each factor.
o Count the same number of digits on the product from right then

place the decimal point.
• To divide a decimal by a decimal, convert the divisor to a counting

number by multiplying both the dividend and the divisor by 10 or 100 or
1,000 etc., depending on the number of decimal places of the divisor.

58 Mathematics Book 1

Revision Exercise

Part 1 (1-5)

Solve the following:

1. [3 − ቀ− 1ቁ] ÷ ቀ1 − 2 1ቁ =

3 93

2. [11 × (−6)] − ቀ2 × 21ቁ =

12 3 24

3. ቀ−5 1ቁ ÷ ቀ2 1 + 1 1 ቁ =

2 7 14

4. 2 + 0.232 + 4 − 1 1 =

52

5. (3.69 + 0.001) × 1 ÷ 2 1 =

22

Mathematics Book 1 59

Part 2 (6-24) 11. What is 4 months as a fraction of a

Choose the correct answer. year?
6. What is the value of 5 in the decimal
a. 2
23.154? 5
a. 5 1
b. 5 × 10 b. 3
c. 5 ÷ 10
d. 5 ÷ 100 c. 3
4
1
7. Which of the following numbers are d. 4
arranged in ascending order?
a. 1, 0.12, 0.42 12.What is 0.25 of a minute in seconds?
b. −1.15, −2, 0.02 a. 5 seconds
c. 13.3, −10. .3, 0.003 b. 15 seconds
d. −0.10, 1.05, 5.01 c. 20 seconds
d. 40 seconds
8. Which one is correct?
a. 1.5 > −0.5 13. Which is the fraction for 0.21?
b. 1.05 > 10.5
c. 3.2 < −1.3 a. 1
d. −1.4 < −4 21
21
b. 100

9. Which of the following can be c. 21
10
21
expanded as 2 + a + b ? d. 1
10 1000
2ab
a. 1000 14. Which is the decimal for 1 ?
5
(2+a+b)
b. 1000 a. 0.2

c. 2. ab b. 0.45

d. 2. a0b c. 0.8

d. 4.5

10. Which of the following is an 15.What is the decimal form of −1,500
16
improper fraction?

a. 1 ?
5
6 a. −9.375
5
b. b. −90.075

c. 11 c. −90.375

5 d. −93.75
1+1
d.
5

60 Mathematics Book 1

16. What is the fraction form of 20. A box contains 1,000 nails, each nail
weighing 0.75 g. What is the weight,
−0.0604? in grams, of the nails in 15 boxes?
a. 750 g
a. −3

5
−151
b. 2,500 b. 765 g

c. −304 c. 3,750 g
5,000
−150 d. 11,250 g
d. 2,500
21. Sheets of metal 0.025 cm thick are

3 piled one on top of the other until
5
17. There are 250 pupils in a school. they reach the height of 35 1 cm.
2
1
of these pupils walk to school, 10 of How many sheets are there in the

them use the bus and the remainder pile?

use car. How many pupils use the a. 71 sheets

car? b. 111 sheets

a. 25 pupils c. 1,350 sheets

b. 75 pupils d. 1,420 sheets

c. 150 pupils 22. There are 25 students performing

d. 175 pupils in a holiday concert. Of the

18. My mother has 160-meter ball of students, 11 are boys. What decimal

string. She used 0.6 of it on Monday represents the fraction of students

1 that are boys?
4
and of it on Tuesday. What is the a. 0.44

length of the remaining string? b. 0.48

a. 24 meter c. 0.52

b. 40 meter d. 0.56

c. 96 meter 23. A school sold 0.28 of the total books

d. 136 meter at a book fair on the first day. What

fraction of the books was sold on

the first day?

19. The audience for a performance in a. 28 c. 14
100 25
a gymnasium totaled 960. 3 of the 2 1
4 b. 25 d. 4
7
audience were men. 8 of the 24. Brenda jogged 2 of an hour on her
9
remaining were women and the
first day of training for the track
remainder were children. How
team. What decimal represents the
many children were there?
amount of time she spent jogging?
a. 720
a. 0.29 hour
b. 210
b. 0.2 hour
c. 240
c. 0.22 hour

d. 30 d. 0.02 hou

Mathematics Book 1 61