Class 7 Maths Notes for Fractions And Decimals

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CLASS 7
MATHS

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CHAPTER 2: FRACTIONS AND DECIMALS

I. IMPORTANT CONCEPTS:

- Proper fraction

- Improper fraction

- Multiplication of fractions

- Multiplication of a Fraction by a Whole Number

- Fraction as an operator ‗of‘

- Multiplication of a Fraction by a Fraction

- Division of Fractions

- Division of the Whole Number by a Fraction

- Reciprocal of a fraction

- Division of a Fraction by a Whole Number

- Division of a Fraction by Another Fraction

- Multiplication of Decimal Numbers

- Multiplication of Decimal Numbers by 10, 100 and 1000

- Division of a Decimal Number by a Whole Number

- Division of a Decimal Number by another Decimal Number

II. ILLUSTRATIONS/EXAMPLES:

A) MCQ-TYPE QUESTIONS:

2
(a) 7 × 3 =

6 4 2 5
(i) 7 (ii) 7 (iii) (iv)
21 7

12

Ans. (i)

1
(b) What is 2 × 10?

(ii) 1 (ii) 6 (iii) 5 (iv) 3

Ans. (iii)

( c) 1.8 × 1.2 =

(i) 0.216 (ii) 2.16 (iii) 21.6 (iv) 216

Ans. (ii)

( d) 235.4 ÷ 100 =

(i) 23500 (ii) 23.54 (iii) 2.354 (iv) 0.2354

Ans. (iii)

B) CASE STUDY QUESTION:
3
An online game has 50 levels. A gamer is in the Gold team until he crosses 4 of the total
levels. After that, he is in the Platinum team.
This table shows the rewards unlocked after completing various levels.
LEVELS COMPLETED REWARDS

More than or equal to 4/5 levels Jeep
More than 3/5 levels but less than 4/5 Dress
levels
More than 2/5 levels but less than 3/5 Face mask
levels
More than 1/5 levels but less than 2/5 Badge
levels
Mita completed 37 levels. Which reward she would get? Justify your answer.
Solution: Dress as 37 lies between 30 and 40.
3
× 50 = 30
5
4
× 50 = 40
5

C) SHORT ANSWER TYPES QUESTIONS:

3
(i) Savita is dividing 1 4 kg of sweets equally among her seven friends. How much
does each friend receive?

Ans. Each friend will get

13

3 3 1 7 1 1
14 ÷ 7 = 14 × 7 = 4 × 7 = 4

(ii) Harmeet purchased 3.5 kg of potatoes at the rate of Rs. 13.75 per kg. How much
money should he pay?

Ans. 1 kg potato cost – Rs. 13.75

3.5 kg potatoes cost – Rs. 13.75 × 3.5 = Rs. 48.125

Harmeet will pay Rs. 48.125.

(iii) Three boys earned a total of Rs. 235.50. What was the average amount earned per
boy?

Ans. Each boy on average earns = Rs.235.50 ÷ 3 = Rs. 78.50

D) LONG ANSWER TYPE OF QUESTIONS:

3
(i) If the cost of a notebook is Rs.8 4 , how many notebooks can be purchased for Rs.
1
1314 ?

Ans. Number of notebooks purchased =

1 3
Rs. 1314 ÷ Rs.8 4

525 35
= 4 ÷ 4

525 4
= 4 × 35 = 15

(ii) The length of the rectangle is 7.1 cm and its breadth is 2.5 cm. what is the
perimeter of the rectangle?
Ans. Perimeter of rectangle = 2 × (l + b) = 2 × (7.1 + 2.5)
= 2 × (9.6) = 19.2 cm

III. QUESTIONS FOR PRACTICE:

(A) MCQ Type Questions:

(i) The product of a rational number and its reciprocal is always equal to

(a) 0 (b) 1 (c) -1 (d) None of these

1
(ii) 38 × 3 =

14

45 75 54 62
(a) 8 (b) 8 c) 8 d) 8

1
(iii) What is 4 of 16?

a)3 b) 4 c) 2 d) 5

2 4
(iv) ×5=
3

8 10 6 2
𝑎) 15 b) 12 𝑐) 8 d)15

12 3
(v) ÷5 =
5

a)1 b)2 c) 3 d) 4

(vi) 67.8 × 1.2 =

(a) 81.36 b) 8.136 c) 0.8136 d) 813.6

(vii) 74.55 × 100 =

(a) 745.5 b) 7455 c) 74.55 d) 7.455

(viii) 70.5 ÷ 1.5 =

(a) 47 b) 4.7 c) 470 d) 0.47

(ix) 547.8 ÷ 1000 =

(a) 54.78 b) 5.478 c) 5478 d)0.5478

(x) 7m 4 cm =

(a) 74 cm b) 740 cm c) 7400 cm d)704 cm

(B) SHORT ANSWER TYPE QUESTIONS:

1 3
(i) Find: 2 × 2 4

(ii) Which is greater?

1 6 2 3
of 7 or 3 of 7
2

15

(iii) The side of a regular hexagon is 3.2 cm. find its perimeter.

(iv) A two-wheeler covers 54.8m in 1 litre of petrol. How much distance will it cover
in 10 litres of petrol?

(v) Find the average of 4.2, 3.6 and 7.8.

(vi) Each side of a polygon is 3.5 cm and its perimeter is 17.5cm. How many sides
does the polygon have?

(vii) (i) Provide the number in the box , such that

3 24
× = 30
5

(ii) The simplest form of the number obtained in is
_____________.

(viii) A car travels 44.4 km in 1.2hours. What is the average distance covered in 1
hour?

(ix) Find the area of the rectangle of length 6.3cm and breadth 3.7cm.

2
(x) Distance between two adjacent saplings is 3 m. There are seven saplings in a row.
Find the distance between the first and the last sapling?

(C) LONG ANSWER TYPE QUESTIONS:

(i) Shade:

2
(a) 3 of the triangles.

3
(b) 5 of the squares.

16

(ii) Ronit and Seema went for a picnic. Their mother gave them water bottle
2
contained 6 litres of water. Ronit consumed 3 of water. Seema consumed
the remaining water.
(a) How much water did Ronit drink?
(b) What fraction of the total quantity of water did Seema drink?
3
(iii) Lipika reads a book for 4hours everyday. She reads the entire book in 6
days. How many hours in all were required by her to read the book?
(iv) A vehicle covers a distance of 43.2 km in 2.4 litres of petrol. How much
distance will it cover in one litre of petrol?
(v) For the celebrating children‘s students of Class VII bought sweets for
Rs.740.25 and cold drink for Rs.70. If 35 students contributed equally
what amount was contributed by each student?
3
(vi) Kajol has Rs. 75. This 8 of the amount she earned. How much did she
earn?

(D) CASE BASED QUESTIONS:

(i) SAVE TREES:

It takes 17 full specific type of trees to make one tonne of paper. If there
are 221 such trees in a forest, then what fraction of forest will be used to
make;

(a) 5 tonnes of paper.

17

7
(b) To save 13 part of the forest how much of paper we
have to save.

(ii) TAKING CARE OF ANIMALS:

The label on a bottle of pet vitamins lists dosage guidelines.

What dosage would you give to each of these animals?

(a) 18 kg adult dog?
(b) A 6 kg cat?

IV. ANSWERS:

A. MCQ-TYPE QUESTIONS:

(i) b ii) b iii) b iv)a v)d vi)a vii)b viii)a ix) d x)d

B. SHORT ANSWER TYPE QUESTIONS:
11 2
(i) ii)7iii)19.2cm iv)548 m v)5.2 vi)5
8

4
vii ) viii)37 km ix) 23.31 sq.cm x) 4 m
3

C. LONG ANSWER TYPE QUESTIONS:

(i) (a) 6 triangles (b) 9 squares
1
(ii) (a) 4 litres (b) 3
(iii) 4.5 hours iv)18 km
v) Rs. 23.15 vi)200

D. CASE BASED QUESTIONS:

(i) SAVE TREES:

5
(a) 13 (b) 119

(ii) TAKING CARE OF ANIMALS:

18

1
(a) 1 tea spoon (b) 1 2 tea spoons

CLASS TEST-1

(CHAPTER 2: FRACTIONS AND DECIMALS)

CLASS: VII MARKS: 20

SNO QUESTION MARKS
SECTION-A 1X 4=4
1. The decimal expression for 8 rupees 8 paise (in Rupees) is

(a) 8.8 (b) 8.08 (c) 8.008 (d) 88.0 1
2. 2
Fraction which is reciprocal of 3 is

−2 3 1
(a) 3 (b) 1 (c) 0 (d) 2

3. 2.4 × 1000 = _________.

(a) 24 (b) 240 (c) 2400 (d) 2.004 1
4. 3
If 4 of a number is 12, the number is

1
(a) 9 (b) 16 (c) 18 (d) 32
SECTION-B 2X2=4
5. 3 4 2
Find: 4 of 7 5
6. Find: 1.3 x 3.1 2
SECTION-C 2X3=6
7. Find:

1 5 2
(a) 3 5 ÷ 4 6
4 2
(b) 7 × 9 1

8. The time taken by Rohan in five different races to run a
distance of 500 m was 3.20 minutes, 3.37 minutes, 3.29
minutes, 3.17 minutes and 3.32 minutes. Find the average 3
time taken by him in the races.

19

SECTION-D 3X2= 6
HURDLE RACE
9. 2
In a hurdle race, Nidhi is over hurdle B and 6 of the way
through the race, as shown in figure.

Then, answer the following:
4
(a) Where will Nidhi be, when she is 6of the way
through the race?
5
(b) Where will Nidhi be when she is 6of the way
through the race?
(c) Give two fractions to tell what part of the race
Nidhi has finished when she is over hurdle C. 2

2

2

ANSWER KEY(TEST-1)
117 96 8
1)b 2) d 3)c 4)b 5) 20 6)4.03 7)(a) 145 (b) 63 8) 3.27 minutes

3 1
9) (a) D (b) E ( c) 6 , 2

20

CLASS TEST-2

(CHAPTER 2: FRACTIONS AND DECIMALS)

SNO QUESTION MARKS

CLASS: VII

MARKS: 30

21

SECTION A(MCQ) 1X10=10
1. 2.5 ÷ 1000 is equal to 1

(a) 0.025 (b) 0.0025 (c) 0.2500 (d) 25000
2. The product of 0.03 × 0.9 is: 1

(a) 2.7 (b) 0.27 (c) 0.027 (d) 0.0027
3. 1 1 1
Which of the following represents 3 of 6 ?

1 1 1 1
(a) 3 + 6 ( c) 3 × 6
1 1 1 1
(b) 3 − 6 (d) 3 ÷ 6

4. The picture interprets

1
(a) 4 ÷ 3
1
(b) 3 × 4 1
3
(c) 4 × 3
1
(d) 3 ÷ 4

5. 8.4 ÷ ______ = 2.1 1

(a) 2 (b) 3 (c ) 1 (d) 4
6. 3 3 1
34 ÷ 4 =

45
(a) 3 (b) 4 (c) 5 (d) 16
7. 2 1
× 25 =
5

(a) 10 (b) 12 (c) 20 (d) 25

8. 3456 ml = _______________litres 1

(a) 34.56 (b) 3.456 (c) 0.3456 (d) 345.6

9. 52.7 ÷ _______ = 0.527 1

(a) 10 (b) 100 (c ) 1000 (d) 1

22

10. 5 10 1
2________3 = 3

(a) × (b) ÷ (c ) + (d) −

SECTION-B 2×4=8
11. 2 2
How many 3 kg pieces can be cut from a cake
of weight 4 kg?
12. A two-wheeler covers a distance of 55.3 km in 2
one litre of petrol. How much distance will it
cover in 10 litres of petrol?
13. Find the average of 4.2, 3.8 and 7.6. 2
14. A car covers a distance of 89.1 km in 2.2 2
hours. What is the average distance covered by
it in 1 hour?
SECTION-C 3×2=6
15. The weight of an object on moon is 1/6 its 3
3
weight on Earth. If an object 5 5kg on Earth,
how much would it weigh on the moon?
16. When 0.02964 is divided by 0.004, what will 3
be the quotient?
SECTION-D 3×2=6
INFLUENCING FOR BUYING CD‘S

23

17. In a survey, 200 students were asked what
influenced them most to buy their latest CD.
The results are shown in the circle graph.

2
(a) How many students said radio influenced
them most? 2

(b) How many more students were influenced
by radio than by a music video

channel?
2
(c) How many said a friend or relative
influenced them or they heard the CD in a
shop?

ANSWERS (TEST-2)

1. B 2) c 3)c 4)b 5)d 6)c 7)a 8)b 9)b 10)a
14
11)6 12)553 km 13)5.2 14)40.5 15)15 kg 14)7.41 15)(a) 90 (b) 74 (c) 50

24

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