Gujarat Board GSEB Textbook Solutions Class 6 Maths Chapter 7 Fractions InText Questions and Answers.

## Gujarat Board Textbook Solutions Class 6 Maths Chapter 7 Fractions InText Questions

Try These (Page 137)

Question 1.

Show \(\frac { 3 }{ 5 }\) on a number line.

Solution:

We divide the length between 0 and 1 on a number line into 5 equal parts. The point A represents \(\frac { 3 }{ 8 }\)

Question 2.

Show \(\frac { 1 }{ 10 }\) , \(\frac { 0 }{ 10 }\) , \(\frac { 5 }{ 10 }\) and \(\frac { 10 }{ 10 }\) on a number line.

Solution:

We draw a number line. Divide the length between 0 and 1 into 10 equal parts.

The point B represents \(\frac { 1 }{ 10 }\)

The point A represents \(\frac { 0 }{ 10 }\)

The point C represents \(\frac { 5 }{ 10 }\)

The point D represents \(\frac { 10 }{ 10 }\)

Question 3.

Can you show any other fraction between 0 and 1? Write five more fractions that you can show and depict them on the number line.

Solution:

Yes, we can show any number of fractions that are greater than 0 and less than 1.

Five other fractions, i.e. \(\frac { 2 }{ 3 }\) , \(\frac { 6 }{ 7 }\) , \(\frac { 1 }{ 8 }\) , \(\frac { 4 }{ 9 }\) and \(\frac { 4 }{ 5 }\) can be shown on a number line between 0 and 1. Direct these numbers on the number line by yourself.

Question 4.

How many fractions lie between 0 and 1? Think, discuss and write your answer.

Solution:

An infinite number of fractions lie between 0 and 1.

Try These (Page 138)

Question 1.

Give a proper fraction:

(a) Whose numerator is 5 and denominator is 7.

(b) Whose denominator is 9 and numerator is 5.

(c) Whose numerator and denominator add up to 10. How many fractions of this kind can you make?

(d) Whose denominator is 4 more than the numerator.

(Give any five. How many more can you make?)

Solution:

∴ Fractions whose numerator and denominator add up to 10 are: \(\frac { 0 }{ 10 }\) , \(\frac { 1 }{ 9 }\) , \(\frac { 2 }{ 8 }\) , \(\frac { 3 }{ 7 }\) and \(\frac { 4 }{ 6 }\).

(d) There can be infinite number of fractions whose denominator is 4 more than the numerator. Some of them are: \(\frac { 1 }{ 5 }\) , \(\frac { 2 }{ 6 }\) , \(\frac { 3 }{ 7 }\) , \(\frac { 4 }{ 8 }\) , \(\frac { 5 }{ 9 }\), etc.

Question 2.

A fraction is given. How will you decide, by just looking at it, whether, the fraction is (a) less than 1? (b) equal to 1?

Solution:

Question 3.

Fill up using one of these: ‘>’ , ‘<‘ or ‘=’

Solution:

Try These (Page 142)

Question 1.

Are \(\frac { 1 }{ 3 }\) and \(\frac { 2 }{ 7 }\);\(\frac { 2 }{ 5 }\) and \(\frac { 2 }{ 7 }\);\(\frac { 2 }{ 9 }\) and \(\frac { 6 }{ 27 }\) equivalent? Give reason.

Solution:

(i) \(\frac { 1 }{ 3 }\) and \(\frac { 2 }{ 7 }\) ∵ 1 × 7 = 7, 3 × 2 = 6

and 7 ≠ 6, i.e. 1 × 7 ≠ 3 × 2

∴ \(\frac { 1 }{ 3 }\) and \(\frac { 2 }{ 7 }\) are not equivalent fractions.

(ii) \(\frac { 2 }{ 5 }\) and \(\frac { 2 }{ 7 }\) ∵ 2 × 7 = 14, 5 × 2 = 10

and 14 ≠ 10, i.e. 2 × 7 ≠ 5 × 2

∴ \(\frac { 2 }{ 5 }\) and \(\frac { 2 }{ 7 }\) are not equivalent fractions.

(iii) \(\frac { 2 }{ 9 }\) and \(\frac { 6 }{ 27 }\) ∵ 2 × 27 = 54, 9 × 6 = 54

and 54 = 54, i.e. 2 × 27 = 9 × 6

∴ \(\frac { 2 }{ 9 }\) and \(\frac { 6 }{ 27 }\) are equivalent fractions.

Question 2.

Give an example of four equivalent fractions.

Solution:

The following pairs of fractions are equivalent:

(i) \(\frac { 2 }{ 8 }\) and \(\frac { 1 }{ 4 }\)

(ii) \(\frac { 5 }{ 12 }\) and \(\frac { 15 }{ 36 }\)

(iii) \(\frac { 8 }{ 11 }\) and \(\frac { 16 }{ 22 }\)

(iv) \(\frac { 4 }{ 26 }\) and \(\frac { 2 }{ 13 }\)

Question 3.

Identify the fractions in each. Are these fractions equivalent?

Solution:

(i) The given figure represents the fraction \(\frac { 6 }{ 8 }\)

We have: \(\frac { 6 }{ 8 }\) = \(\frac{6 \div 2}{8 \div 2}\) = \(\frac { 3 }{ 4 }\)

(ii) The given figure represents the fraction \(\frac { 9 }{ 12 }\)

We have: \(\frac { 9 }{ 12 }\) = \(\frac{9 \div 3}{12 \div 3}\) = \(\frac { 3 }{ 4 }\)

(iii) The given figure represents the fraction \(\frac { 12 }{ 16 }\)

We have: \(\frac { 12 }{ 16 }\) = \(\frac{12 \div 4}{16 \div 4}\) = \(\frac { 3 }{ 4 }\)

(iv) The given figure represents the fraction \(\frac { 15 }{ 20 }\)

We have: \(\frac { 12 }{ 16 }\) = \(\frac{12 \div 4}{16 \div 4}\) = \(\frac { 3 }{ 4 }\)

Since, all the fractions represent \(\frac { 3 }{ 4 }\),

i.e., \(\frac { 6 }{ 8 }\) = \(\frac { 9 }{ 12 }\) = \(\frac { 12 }{ 16 }\) = \(\frac { 15 }{ 20 }\) =

Thus, the given figures represent equivalent fractions.

Try These (Page 143)

Question 1.

Find five equivalent fractions of each of the following:

(i) \(\frac { 2 }{ 3 }\)

(ii) \(\frac { 1 }{ 5 }\)

(iii) \(\frac { 3 }{ 5 }\)

(iv) \(\frac { 5 }{ 9 }\)

Solution:

Try These (Page 146)

Question 1.

Write the simplest form of:

(i) \(\frac { 15 }{ 75 }\)

(ii) \(\frac { 16 }{ 72 }\)

(iii) \(\frac { 17 }{ 51 }\)

(iv) \(\frac { 42 }{ 28 }\)

(v) \(\frac { 80 }{ 24 }\)

Solution:

(i) \(\frac { 15 }{ 75 }\)

Factors of 15 are: 1, 3, 5 and 15

Factors of 75 are: 1, 3, 5, 15, 25 and 75

Common factors are: 1, 3, 5 and 15

∴ HCF of 15 and 75 = 15

Now, \(\frac { 15 }{ 75 }\) = \(\frac{15 \div 15}{75 \div 15}\) = \(\frac { 1 }{ 5 }\)

Thus, simplest form of \(\frac { 15 }{ 75 }\) is \(\frac { 1 }{ 5 }\)

(ii) \(\frac { 16 }{ 72 }\)

Factors of 16 are: 1, 2, 4, 6, 8 and 16

Factors of 72 are: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36 and 72

∴ Common factors are: 1, 2, 4, 6 and 8

∴ HCF of 16 and 72 is 8.

Now \(\frac { 16 }{ 72 }\) = \(\frac{16 \div 8}{72 \div 8}\) = \(\frac { 2 }{ 9 }\)

Thus, the simplest form of \(\frac { 16 }{ 72 }\) is \(\frac { 2 }{ 9 }\)

(iii) \(\frac { 17 }{ 51 }\)

Factors of 17 are: 1 and 17

Factors of 51 are: 1, 3 and 17

The common factor is 17

∴ HCF of 17 and 51 = 17

Now \(\frac { 17 }{ 51 }\) = \(\frac{17 \div 17}{51 \div 17}\) = \(\frac { 1 }{ 3 }\)

Thus, the simplest form of \(\frac { 17 }{ 51 }\) is \(\frac { 1 }{ 3 }\)

(iv) \(\frac { 42 }{ 28 }\)

Factors of 42 are: 1, 2, 3, 6, 7, 14, 21 and 42

Factors of 28 are: 1, 2, 4, 7, 14 and 28

Common factors are: 1, 2, 7 and 14

∴ HCF of 42 and 28 = 14

Now \(\frac { 42 }{ 28 }\) = \(\frac{42 \div 14}{28 \div 14}\) = \(\frac { 3 }{ 2 }\)

Thus, the simplest form of \(\frac { 42 }{ 28 }\) is \(\frac { 3 }{ 2 }\)

(v) \(\frac { 80 }{ 24 }\)

Factors of 80 are: 1, 2, 4, 5, 8, 10, 16, 20, 40 and 80

Factors of 24 are: 1, 2, 3, 4, 6, 8, 12 and 24

Common factors are: 1, 2, 4 and 8

∴ HCF of 80 and 24 = 8

Now, \(\frac { 80 }{ 24 }\) = \(\frac{80 \div 8}{24 \div 8}\) = \(\frac { 10 }{ 3 }\)

Thus, the simplest form \(\frac { 80 }{ 24 }\) is \(\frac { 10 }{ 3 }\)

Question 2.

Is \(\frac { 49 }{ 64 }\) in its simplest form?

Solution:

∵ Factors of 49 are: 1,7 and 49

Factors of 64 are: 1, 2, 4, 8, 16, 32 and 64

The common factor is 1, i.e. 49 and 64 have no common factor other than 1.

∴ 49 and 64 are coprime, i.e. \(\frac { 49 }{ 64 }\) is in its simplest form.

Try These (Page 148)

Question 1.

You get one-fifth of a bottle of juice and your sister gets one-third of a bottle of juice. Who gets more?

Solution:

Let us divide a rectangle into 5 equal parts and shade one of them, i.e. one-fifth is shaded.

Now, divide the same rectangle into 3 equal parts and shade one of them, Le. one-third is shaded, obviously, one third is greater. Thus, your sister gets more juice.

Try These (Page 149)

Question 1.

(a) Which is the larger fraction?

(i) \(\frac { 7 }{ 10 }\) or \(\frac { 8 }{ 10 }\)

(ii) \(\frac { 11 }{ 24 }\) or \(\frac { 13 }{ 24 }\)

(iii) \(\frac { 17 }{ 102 }\) or \(\frac { 12 }{ 102 }\)

(b) Why are these comparisons easy to make?

Solution:

(a) (i) \(\frac { 7 }{ 10 }\) < \(\frac { 8 }{ 10 }\)

Denominators are same and 7 < 8

∴ \(\frac { 7 }{ 10 }\) < \(\frac { 8 }{ 10 }\)

(ii) \(\frac { 11 }{ 24 }\) and \(\frac { 13 }{ 24 }\)

Denominators are same and 11 < 13

∴ \(\frac { 11 }{ 24 }\) < \(\frac { 13 }{ 24 }\)

(iii) \(\frac { 17 }{ 102 }\) and \(\frac { 12 }{ 102 }\)

Denominators are same and 17 > 12

∴ \(\frac { 17 }{ 102 }\) and \(\frac { 12 }{ 102 }\)

(b) These comparisons are easy because these are like fractions.

Question 2.

(a) \(\frac { 1 }{ 8 }\) , \(\frac { 5 }{ 8 }\) , \(\frac { 3 }{ 8 }\)

(b) \(\frac { 1 }{ 5 }\) , \(\frac { 11 }{ 5 }\) , \(\frac { 4 }{ 5 }\) , \(\frac { 3 }{ 5 }\) , \(\frac { 7 }{ 5 }\)

(c) \(\frac { 1 }{ 7 }\) , \(\frac { 3 }{ 7 }\) , \(\frac { 13 }{ 7 }\) , \(\frac { 11 }{ 7 }\) , \(\frac { 7 }{ 7 }\)

Solution:

We can write the like fractions in ascending or in descending order according to the order of their numerators.

(a) \(\frac { 1 }{ 8 }\) , \(\frac { 5 }{ 8 }\) , \(\frac { 3 }{ 8 }\)

∵ 1 , 3 and 5 are in ascending order.

∴ \(\frac { 1 }{ 8 }\) , \(\frac { 3 }{ 8 }\) and \(\frac { 5 }{ 8 }\) are in ascending order and \(\frac { 5 }{ 8 }\) , \(\frac { 3 }{ 8 }\) and \(\frac { 1 }{ 8 }\) are in descending order.

(b) \(\frac { 1 }{ 5 }\) , \(\frac { 11 }{ 5 }\) , \(\frac { 4 }{ 5 }\) , \(\frac { 3 }{ 5 }\) , \(\frac { 7 }{ 5 }\)

∵ 1, 3, 4, 7 and 11 are in ascending order and 11, 7, 4, 3 and 1 are in descending order.

∴ Fractions in ascending order.

\(\frac { 1 }{ 7 }\) , \(\frac { 3 }{ 7 }\) , \(\frac { 7 }{ 7 }\) , \(\frac { 11 }{ 7 }\) , \(\frac { 13 }{ 7 }\)

Try These (Page 151)

Question 1.

Arrange the following in ascending and descending order:

(a) \(\frac { 1 }{ 12 }\) , \(\frac { 1 }{ 23 }\) , \(\frac { 1 }{ 5 }\) , \(\frac { 1 }{ 7 }\) , \(\frac { 1 }{ 50 }\) , \(\frac { 1 }{ 9 }\) , \(\frac { 1 }{ 17 }\)

(b) \(\frac { 3 }{ 7 }\) , \(\frac { 3 }{ 11 }\) , \(\frac { 3 }{ 5 }\) , \(\frac { 3 }{ 2 }\) , \(\frac { 3 }{ 13 }\) , \(\frac { 3 }{ 4 }\) , \(\frac { 3 }{ 17 }\)

(c) Write 3 more similar examples and arrange them in ascending and descending order.

Solution:

We know that in ‘unlike’ fractions having, same numerator, the greater the value of the denominator, the smaller the value of the fractional number.

(a) ∵ 50, 23, 17, 12, 9, 7 and 5 are in descending order

∴ Fractions in ascending order are:

\(\frac { 1 }{ 50 }\) , \(\frac { 1 }{ 23 }\) , \(\frac { 1 }{ 17 }\) , \(\frac { 1 }{ 12 }\) , \(\frac { 1 }{ 9 }\) , \(\frac { 1 }{ 7 }\) , \(\frac { 1 }{ 5 }\)

(b) ∵ 17, 13, 11, 7, 5, 4 and 2 are in descending order

∴ Ascending order of the given fractions is

\(\frac { 3 }{ 17 }\) , \(\frac { 3 }{ 13 }\) , \(\frac { 3 }{ 11 }\) , \(\frac { 3 }{ 7 }\) , \(\frac { 3 }{ 5 }\) , \(\frac { 3 }{ 4 }\) , \(\frac { 3 }{ 2 }\)

And descending order of the given fractions is

\(\frac { 3 }{ 2 }\) , \(\frac { 3 }{ 4 }\) , \(\frac { 3 }{ 5 }\) , \(\frac { 3 }{ 7 }\) , \(\frac { 3 }{ 11 }\) , \(\frac { 3 }{ 13 }\) , \(\frac { 3 }{ 17 }\)

(c) Three more examples of unlike fractions with the same numerator are:

(i) \(\frac { 2 }{ 13 }\) , \(\frac { 2 }{ 25 }\) , \(\frac { 2 }{ 6 }\) , \(\frac { 2 }{ 8 }\) , \(\frac { 2 }{ 10 }\) , \(\frac { 2 }{ 17 }\)

(ii) \(\frac { 5 }{ 6 }\) , \(\frac { 5 }{ 17 }\) , \(\frac { 5 }{ 14 }\) , \(\frac { 5 }{ 7 }\) , \(\frac { 5 }{ 12 }\) , \(\frac { 5 }{ 8 }\) , \(\frac { 5 }{ 11 }\)

(iii) \(\frac { 4 }{ 11 }\) , \(\frac { 4 }{ 13 }\) , \(\frac { 4 }{ 5 }\) , \(\frac { 4 }{ 7 }\) , \(\frac { 4 }{ 19 }\) , \(\frac { 4 }{ 17 }\) , \(\frac { 4 }{ 15 }\)

Arrange the above in ascending and descending order by yourself

Solution:

(i) Ascending order:

\(\frac { 2 }{ 25 }\) , \(\frac { 2 }{ 17 }\) , \(\frac { 2 }{ 13 }\) , \(\frac { 2 }{ 10 }\) , \(\frac { 2 }{ 8 }\) , \(\frac { 2 }{ 6 }\)

Descending order:

\(\frac { 2 }{ 6 }\) , \(\frac { 2 }{ 8 }\) , \(\frac { 2 }{ 10 }\) , \(\frac { 2 }{ 13 }\) , \(\frac { 2 }{ 17 }\) , \(\frac { 2 }{ 25 }\)

(ii) Ascending order:

\(\frac { 5 }{ 17 }\) , \(\frac { 5 }{ 14 }\) , \(\frac { 5 }{ 12 }\) , \(\frac { 5 }{ 11 }\) , \(\frac { 5 }{ 8 }\) , \(\frac { 5 }{ 7 }\) , \(\frac { 5 }{ 6 }\)

Descending order:

\(\frac { 5 }{ 6 }\) , \(\frac { 5 }{ 7 }\) , \(\frac { 5 }{ 8 }\) , \(\frac { 5 }{ 11 }\) , \(\frac { 5 }{ 12 }\) , \(\frac { 5 }{ 14 }\) , \(\frac { 5 }{ 17 }\)

(iii) Ascending order:

\(\frac { 4 }{ 19 }\) , \(\frac { 4 }{ 17 }\) , \(\frac { 4 }{ 15 }\) , \(\frac { 4 }{ 13 }\) , \(\frac { 4 }{ 11 }\) , \(\frac { 4 }{ 7 }\) , \(\frac { 4 }{ 5 }\)

Descending order:

\(\frac { 4 }{ 5 }\) , \(\frac { 4 }{ 7 }\) , \(\frac { 4 }{ 11 }\) , \(\frac { 4 }{ 13 }\) , \(\frac { 4 }{ 15 }\) , \(\frac { 4 }{ 17 }\) , \(\frac { 4 }{ 19 }\)

Try These (Page 155)

Question 1.

My mother divided an apple into 4 equal parts. She gave me two parts and my brother one part. How many apples did she give to both of us together?

Solution:

On dividing an apple into 4 equal parts, each part of the apple will be 1/4. My mother gave me two parts, i.e., 2/4 parts, and my brother one part, i.e., 1/4 part. The part she gave us together

Question 2.

Mother asked Neelu and her brother to pick stones from the wheat. Neelu picked one-fourth of the total stones in it and her brother also picked up one-fourth of the stones. What fraction of the stones did both pick up together?

Solution:

Neelu picked one-fourth of the total stones, i.e., 1/4 stones from the wheat and her brother picked up one-fourth of stones, i.e., 1/4 stones. Fractions of stones picked up together by them

Question 3.

Sohan was putting covers on his notebooks. He put one-fourth of the covers on Monday. He put another one-fourth on Tuesday and the remaining on Wednesday. What fraction of the covers did he put on Wednesday?

Solution:

Sohan put one-fourth of the covers on Monday, i.e., 1/4 covers. He put one-fourth on Tuesday, i.e., 1/4 covers and the remaining on Wednesday. Now, covers put on Monday and Tuesday

So, covers put on Wednesday

Try These (Page 156)

Question 1.

Add with the help of a diagram.

(i) \(\frac { 1 }{ 8 }\) + \(\frac { 1 }{ 8 }\)

(ii) \(\frac { 2 }{ 5 }\) + \(\frac { 3 }{ 5 }\)

(iii) \(\frac { 1 }{ 6 }\) + \(\frac { 1 }{ 6 }\) + \(\frac { 1 }{ 6 }\)

Method I:

Look at the figure. It is divided into 8 equal parts.

Its shaded part = \(\frac { 2 }{ 8 }\)

i.e., \(\frac { 1 }{ 8 }\) + \(\frac { 1 }{ 8 }\) = \(\frac{1+1}{8}\) = \(\frac { 2 }{ 8 }\) or \(\frac { 1 }{ 4 }\)

Method II:

We can also represent the above sum in the following manner:

∴ \(\frac { 1 }{ 8 }\) + \(\frac { 1 }{ 8 }\) = \(\frac{1+1}{8}\) = \(\frac { 2 }{ 8 }\)

(ii) \(\frac { 2 }{ 5 }\) + \(\frac { 3 }{ 5 }\)

We have:

Thus, \(\frac { 2 }{ 5 }\) + \(\frac { 3 }{ 5 }\) = \(\frac{2+3}{5}\) = \(\frac { 5 }{ 5 }\) = 1

(iii) \(\frac { 1 }{ 6 }\) + \(\frac { 1 }{ 6 }\) + \(\frac { 1 }{ 6 }\)

We have:

Thus, \(\frac { 1 }{ 6 }\) + \(\frac { 1 }{ 6 }\) + \(\frac { 1 }{ 6 }\) = \(\frac{1+1+1}{6}\) = \(\frac { 3 }{ 6 }\) = \(\frac { 1 }{ 2 }\)

Question 2.

add \(\frac { 1 }{ 12 }\) + \(\frac { 1 }{ 12 }\) How will we show this pictorially and by using paper folding?

Solution:

\(\frac { 1 }{ 12 }\) + \(\frac { 1 }{ 12 }\)

We have:

\(\frac { 1 }{ 12 }\) + \(\frac { 1 }{ 12 }\) = \(\frac { 1+1 }{ 12 }\) + \(\frac { 2 }{ 12 }\) = \(\frac { 1 }{ 16 }\)

To show \(\frac { 1 }{ 12 }\) + \(\frac { 1 }{ 12 }\) pictorially, we have:

Using paper folding (the activity): Do it yourself.

Question 3.

Make 5 more examples of problems given in 1 and 2 above. Solve them with your friends.

Solution:

Do it yourself.

Try These (Page 157)

Question 1.

Find the difference between \(\frac { 7 }{ 8 }\) and \(\frac { 3 }{ 8 }\)

Solution:

∵ \(\frac { 7 }{ 8 }\) – \(\frac { 3 }{ 8 }\) = \(\frac { 7-3 }{ 8 }\) and \(\frac { 4 }{ 8 }\) = \(\frac { 1 }{ 2 }\)

∴ The difference between \(\frac { 7 }{ 8 }\) and \(\frac { 3 }{ 8 }\) is \(\frac { 1 }{ 2 }\).

Question 2.

Mother made a good Patti in a round shape. She divided it into 5 parts. Seema ate one piece from it. If I eat another piece then how much would be left?

Solution:

Total number of equal parts of gud patti = 5

Eaten by Seema = \(\frac { 1 }{ 5 }\)

Eaten by me = \(\frac { 1 }{ 5 }\)

Fraction of gud patti eaten by Seema and me

= \(\frac { 1 }{ 5 }\) + \(\frac { 1 }{ 5 }\) = \(\frac { 1+1 }{ 5 }\) = \(\frac { 2 }{ 5 }\)

∴ Fraction of gud patti left over

Question 3.

My elder sister divided the watermelon into 16 parts. I ate 7 out of them. My friend ate 4. How much did we eat altogether? How much more of the watermelon did I eat than my friend? What portion of the watermelon remained?

Solution:

Total number of parts =16

The fraction of watermelon eaten

∴ \(\frac { 3 }{ 16 }\) parts are eaten by us.

Since,[Fraction of watermelon I ate] – [ Fraction of watermelon my friend ate]

∴ I ate \(\frac { 3 }{ 16 }\) portion of watermelon more than my friend.

Now,

Question 4.

Make five problems of this type and solve them with your friends.

Solution:

Do it yourself.

Try These (page 159)

Question 1.

Add \(\frac { 2 }{ 5 }\) + \(\frac { 3 }{ 7 }\)

Solution:

\(\frac { 2 }{ 5 }\) + \(\frac { 3 }{ 7 }\)

∵ LCM of 5 and 7 = 35

Question 2.

Subtract \(\frac { 2 }{ 5 }\) from \(\frac { 5 }{ 7 }\)

Solution:

\(\frac { 5 }{ 7 }\) – \(\frac { 2 }{ 5 }\)

∵ LCM of 7 and 5 = 35