# NCERT Solutions for Class 6 Maths Chapter 7 Fractions InText Questions

These NCERT Solutions for Class 7 Maths Chapter 7 Fractions InText Questions Questions and Answers are prepared by our highly skilled subject experts.

## NCERT Solutions for Class 7 Maths Chapter 7 Fractions InText Questions

NCERT In-text Question Page No. 137

Question 1.
Show $$\frac { 3 }{ 5 }$$ on a number line.
First we write 1 as $$\frac { 3 }{ 5 }$$ and divide the number line into 5 equal parts.

Question 2.
Show $$\frac{1}{10}, \frac{0}{10}, \frac{5}{10}$$ and $$\frac{10}{10}$$ on a number line.
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.
Step-by-step explanation:
To find the fraction between 0 and 1.
We should always remember one thing that “Denominator should be large than the numerator always”.
Thus, the fraction between 0 and 1 is:
$$\frac { 2 }{ 5 }$$ = 0.4 5
$$\frac { 34 }{ 35 }$$ = 0.97
$$\frac { 1 }{ 10 }$$ = 0.4
$$\frac { 51 }{ 65 }$$ = 0.78
$$\frac { 24 }{ 28 }$$ = 0.85

Question 4.
How many fractions lie between 0 and 1?
An infinite number of fractions lie between 0 and 1.

NCERT In-text Question Page No. 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.
A proper fraction whose:
(a) numerator is 5 and denominator is 7 = $$\frac { 5 }{ 7 }$$
(b) denominator is 9 and numerator is 5 = $$\frac { 5 }{ 9 }$$
(c) numerator and denominator add up to 10.
Pairs of numbers having sum 10 ‘ =(1,9), (2, 8), (3, 7), (4, 6) (5, 5)
Therefore, the proper fractions are $$\frac{1}{9}, \frac{2}{8}, \frac{3}{7}, \frac{4}{6}$$
(d) denominator is 4 more than the numerator.
$$=\frac{1}{5}, \frac{2}{6}, \frac{15}{19}, \frac{105}{109}, \frac{199}{203}$$

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?
(a) If the numerator is smaller than the denominator, then the fraction will be less than 1.
(b) If the numerator is equal to the denominator, then the fraction will be equal to 1

Question 3.
Fill up using one of these : “>’, ‘<’ or ‘=’

NCERT In-text Question Page No. 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.
(i) $$\frac { 1 }{ 3 }$$ and$$\frac { 2 }{ 7 }$$ ∵ 1 x 7 = 7, 3 x 2 = 6 and 7 ≠ 6 , i.e. 1 x 7 ≠ 3 x 2
∴ $$\frac { 1 }{ 3 }$$ and$$\frac { 2 }{ 7 }$$ are not equivalent and are not equivalent fractions.

(ii) $$\frac { 2 }{ 5 }$$ and$$\frac { 2 }{ 7 }$$ ∴ 2 x 7 = 14, 5 x 2 = 10 and 14 ≠ 10, i.e. 2 x 7 ≠ 5 x 2

(iii) $$\frac { 2 }{ 9 }$$ and$$\frac { 6 }{ 27 }$$ ∵ 2 x 27 = 54, 9 x 6 = 54
and 54 = 54, i.e. 2 x 27 = 9 x 6
$$\frac { 2 }{ 9 }$$ and$$\frac { 6 }{ 27 }$$

Question 2.
Give example of four equivalent fractions.
Following pairs of fractions are equivalent.
(a) $$\frac { 2 }{ 8 }$$ and $$\frac { 1 }{ 4 }$$
(b) $$\frac { 5 }{ 12 }$$ and $$\frac { 15 }{ 36 }$$
(c) $$\frac { 8 }{ 11 }$$ and $$\frac { 16 }{ 22 }$$
(d) $$\frac { 4 }{ 26 }$$ and $$\frac { 2 }{ 13 }$$

Question 3.
Identify the fractions in each. Are there fractions equivalent?

(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 $$\frac { 4 }{ 26 }$$
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. $$\frac{6}{8}=\frac{9}{12}=\frac{13}{16}=\frac{15}{20}$$ = (each $$\frac { 3 }{ 4 }$$)
Thus, the given figures represent equivalent fractions.

NCERT In-text Question Page No. 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) $$\frac { 5 }{ 9 }$$

NCERT In-text Question Page No. 146

Question 1.
Write the simplest form of:
(i) $$\frac{15}{75}$$
(ii) $$\frac{16}{72}$$
(iii) $$\frac{17}{51}$$
(iv) $$\frac{48}{28}$$
(v) $$\frac{80}{24}$$
(i) 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 $$\frac{15}{75} \text { is } \frac{1}{5}$$

(ii) 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
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) Factors of 17 are: 1 and 17
Factors of 151 are: 1, 3 and 17
Common factors 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 ot $$\frac { 17 }{ 51 }$$ is $$\frac { 1 }{ 3 }$$.

(iv) 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 $$\frac{42}{28} \text { is } \frac{3}{2}$$

(v) 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 torm $$\frac{80}{24} \text { is } \frac{10}{3}$$

Question 2.
Is $$\frac{49}{64}$$ in its simplest form?
Steps to simplifying fractions. Find the HCF of numerator and denominator GCD of 42 and 64 is 2. Divide both the numerator and denominator by the GCD 21
Reduced fraction: $$\frac { 21 }{ 32 }$$ .Therefore, 42/64
21 32 simplified is $$\frac { 21 }{ 32 }$$.

NCERT In-text Question Page No. 148

Question 1.
You get one-fifth of a bottle of juice and your sister gets one third of the same size of a bottle of juice. Who gets more?
My sister gets more because $$\frac{1}{3}>\frac{1}{5}$$

NCERT In-text Question Page No. 149

Question 2.
Which is the larger fraction?
(i) $$\frac{7}{10} \text { or } \frac{8}{10}$$
(ii) $$\frac{11}{24} \text { or } \frac{13}{24}$$
(iii) $$\frac{17}{102} \text { or } \frac{12}{102}$$
Why are these comparisons easy to make?
(i) $$\frac{7}{10}<\frac{8}{10}$$
Denominators are same and 7 < 8
∴ $$\frac{7}{10}<\frac{8}{10}$$

(ii) $$\frac{11}{24}<\frac{13}{24}$$
Denominators are same and 11 < 13
∴ $$\frac{11}{24}<\frac{13}{24}$$

(iii) $$\frac{17}{102} \text { and } \frac{12}{102}$$
Denominators are same and 17< 12
∴ $$\frac{17}{102}>\frac{12}{102}$$
(b) These comparisons are easy because these are like fractions.

Question 3.
Write these in ascending and also in descending order:
(a) $$\frac{1}{8}, \frac{5}{8}, \frac{3}{8}$$
(a) $$\frac{1}{5}, \frac{11}{5}, \frac{4}{5}, \frac{3}{5}, \frac{7}{5}$$
(a) $$\frac{1}{7}, \frac{3}{7}, \frac{13}{7}, \frac{11}{7}, \frac{7}{7}$$
Answer: 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 $$\frac{5}{3}, \frac{3}{8}$$ 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 11 are in ascending order and 11, 7, 4, 3 and 1 are in descending order.
∴ Fractions in ascending order:
$$∴$$
∴ Fractions in descending order:
$$\frac{11}{5}, \frac{7}{5}, \frac{4}{5}, \frac{3}{5}, \frac{1}{5}$$

(c) $$\frac{1}{7}, \frac{3}{77}, \frac{13}{7}, \frac{11}{7}, \frac{7}{7}$$
∵ 1, 3, 7, 11 and 13 are in ascending order and 13, 11, 7, 3 and 1 are in descending order.
$$\frac{1}{7}, \frac{3}{7}, \frac{7}{7}, \frac{11}{7}, \frac{13}{7}$$
∴ Fractions in descending order:
$$\frac{13}{7}, \frac{11}{7}, \frac{7}{7}, \frac{3}{7}, \frac{1}{7}$$

NCERT In-text Question Page No. 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.
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:
$$\frac{1}{50}, \frac{1}{23}, \frac{1}{17}, \frac{1}{12}, \frac{1}{9}, \frac{1}{7}, \frac{1}{5}$$ and fractions in descending 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 fraction 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 same numerator are:

Arrange the above in ascending and descending order by yourself

NCERT In-text Question Page No. 155

Question 1.
My mother divided an apple into 4 equal parts. She gave me two parts and my brother one part. How much apple did she give to both of us together?
mother gave to me $$\frac { 1 }{ 2 }$$ part
mother gave to my brother $$\frac { 1 }{ 4 }$$ part
She gave both off us
$$\frac{1}{2}+\frac{1}{4}=\frac{3}{4}$$ part

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?
neelu picked stones = $$\frac { 1 }{ 4 }$$
brother picked up the stones = $$\frac { 1 }{ 4 }$$
The total fraction of the stones they both 1 1 1
pick up together = $$\frac{1}{4}+\frac{1}{4}=\frac{1}{2}$$ of total stones.

Question 3.
Sohan was putting covers on his note books. 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?
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
= $$\frac{1}{4}+\frac{1}{4}=\frac{1+1}{4}=\frac{2}{4}$$
So, covers put on Wednesday

NCERT In-text Question Page No. 156

Question 4.
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. = $$\frac{1}{8}+\frac{1}{8}=\frac{1+1}{8}=\frac{2}{8} \text { or } \frac{1}{4}$$
Method II: We can also represent the above sum in the following manner:

Question 5.
Add $$\frac{1}{12}+\frac{1}{12}$$ How will we show this pictorially and by using paper folding?
We have $$\frac{1}{12}+\frac{1}{12}=\frac{1+1}{12}=\frac{2}{12}=\frac{1}{6}$$
To show $$\frac{1}{12}+\frac{1}{12}$$ pictorially, we have:

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

Question 6.
Make 5 more examples of problems given in 1 and 2 above. Solve them with your friends.
Do it yourself.

NCERT In-text Question Page No. 157

Question 1.
Find the difference between $$\frac { 7 }{ 8 }$$ and $$\frac { 3 }{ 8 }$$ .
$$\frac{7}{8}-\frac{3}{8}=\frac{7-3}{8}=\frac{4}{8}=\frac{1}{2}$$
The difference between $$\frac { 7 }{ 8 }$$ and $$\frac { 3 }{ 8 }$$ is $$\frac { 1 }{ 2 }$$.

Question 2.
Mother made a gud 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?
Seema ate = $$\frac { 1 }{ 5 }$$
1 eat = $$\frac { 1 }{ 5 }$$
Total part eaten is
$$\frac{1}{5}+\frac{1}{5}=\frac{2}{5}$$
The left part would be
= $$1-\frac{2}{5}=\frac{5-2}{5}=\frac{3}{5}$$

Question 3.
My elder sister divided the watermelon into 16 parts. I ate 7 out them. My friend ate 4. How much did we eat between us? How much more of the watermelon did I eat than my friend? What portion of the watermelon remained?
1 ate = $$\frac { 7 }{ 16 }$$
My friend ate = $$\frac { 4 }{ 16 }$$
We both eat $$\frac{7}{16}+\frac{4}{16}=\frac{7+4}{16}=\frac{11}{16}$$
the watermelon more I eat than my friend is $$\frac{7}{16}+\frac{4}{16}=\frac{7-4}{16}=\frac{3}{16}$$
The portion of the watermelon remained $$1-\frac{11}{16}=\frac{16-11}{16}=\frac{5}{16}$$

Question 4.
Make five problems of this type and solve them with your friends.
Do it yourself.

NCERT In-text Question Page No. 159

Question 1.
Subtract $$\frac { 2 }{ 5 }$$ from $$\frac { 5 }{ 7 }$$ .
Subtract $$\frac { 2 }{ 5 }$$ from $$\frac { 5 }{ 7 }$$ .
$$\frac{5}{7}-\frac{2}{5}$$
∴ $$\frac{2}{5}=\frac{2 \times 7}{5 \times 7}=\frac{14}{35}$$
$$\frac{5}{7}-\frac{2}{5}=\frac{25}{35}-\frac{14}{35}=\frac{35-14}{35}=\frac{11}{35}$$