Chapter 2: Fractions and Decimals

Q51Written answer

To divide a decimal number by 100, we move the decimal point in the number to the left by two places.

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Solution:-

True.

Example: 3.4/100 = 0.034

Q52Written answer

1 is the only number which is its own reciprocal.

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Solution:-

True.

We know that, if the denominator is not given, then we have to assume 1 always.

So, the reciprocal of 1/1 = 1/1

Q53Written answer

2/3 of 8 is same as (2/3) ÷ 8

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Solution:-

False.

2/3 of 8 = (2/3) × 8

Q54Written answer

The reciprocal of 4/7 is 4/7

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Solution:-

False.

The reciprocal of 4/7 is 7/4.

Q55Written answer

If 5 is added to both the numerator and the denominator of the fraction 5/9, will the value of the fraction be changed? If so, will the value increase or decrease?

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Solution:-

If 5 is added to both the numerator and denominator of the fraction 5/9 = 10/14

But, 5/9 ≠ 10/14

Yes, the value of the fraction is changed, and also, the value is increased.

Q56Written answer

What happens to the value of a fraction if the denominator of the fraction is decreased while the numerator is kept unchanged?

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Solution:-

The value of a fraction is increased when the denominator of the fraction is decreased while the numerator is kept unchanged.

Example: ¼ = 0.25

½ = 0.5

Q57Written answer

Which letter comes 2/5 of the way among A and J?

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Solution:-

There are 10 letters from A to J

So, 2/5 of 10 = 2/5 × 10

= 2 × 2

= 4

The 4^th letter from A to J is D.

Therefore, D comes 2/5 of the way among A and J.

Q58Written answer

If 2/3 of a number is 10, then what is 1.75 times of that number?

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Solution:-

From the question, it is given that,

2/3 of a number is 10.

Let us assume the number be ‘P’.

Then,

2/3 of P = 10

2/3 × P = 10

By cross multiplication, we get,

P = 10 × 3/2

P = 5 × 3

P = 15

So, the number is 15

Again it is given in the question that, 1.75 times of that number = ?

= 1.75 of 15

= 1.75 × 15

= 26.25

Q59Written answer

In a class of 40 students, 1/5 of the total number of students like to eat rice only, 2/5 of the total number of students like to eat chapati only, and the remaining students like to eat both. What fraction of the total number of students like to eat both?

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Solution:-

From the question, it is given that,

Number of students in a class = 40 students

1/5 of the total number of students like to eat rice only = 1/5 × 40

= 1 × 8

= 8 students

2/5 of the total number of students like to eat chapati only = 2/5 × 40

= 2 × 8

= 16 students

Then,

Number of students like to eat both = 40 – (8 + 16)

= 40 – 24

= 16 students

Fraction of the total number of students like to eat both = 16/40 = 2/5

Q60Written answer

Renu completed 2/3 part of her homework in 2 hours. How much part of her homework had she completed in 1¼ hours?

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Solution:-

From the question, it is given that,

Renu completed 2/3 part of her homework in 2 hours.

Let us assume the total part of the homework be ‘P’.

Then,

2/3 of P = 2

2/3 × P = 2

By cross multiplication, we get,

P = 2 × 3/2

P = 3 homework

So, part of her homework she had completed in 1¼ hours i.e. 5/4 hours

Let us assume part of the homework she had completed in 5/4 hours be = Q

Then,

Q of 3 = 5/4

Q × 3 = 5/4

By cross multiplication, we get,

Q = (5/4) × (1/3)

Q = 5/12

Therefore, Renu completed 5/12 part of her homework in 5/4 hours.

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