What is the primary focus of NCERT Class 7 Maths Chapter 8: Working with Fractions?

This chapter primarily focuses on teaching students how to perform multiplication and division of fractions, including proper fractions, improper fractions, and mixed fractions. It builds upon earlier concepts of fractions and their types.

NCERT Solutions Class 7 Maths Chapter 8

For each of the questions below, choose the expression that describes the solution. Then simplify it. (a) Maria bought 8 m of lace to decorate the bags she made for school. She used

\frac{1}{4} m

for each bag and finished the lace. How many bags did she decorate? (i)

8 \times \frac{1}{4}

(ii)

\frac{1}{8} \times \frac{1}{4}

(iii)

8 \div \frac{1}{4}

(iv)

\frac{1}{4} \div 8

(b)

\frac{1}{2}

meter of ribbon is used to make 8 badges. What is the length of the ribbon used for each badge? (i)

8 \times \frac{1}{2}

(ii)

\frac{1}{2} \div \frac{1}{8}

(iii)

8 \div \frac{1}{2}

(iv)

\frac{1}{2} \div 8

(c) A baker needs

\frac{1}{6} kg

of flour to make one loaf of bread. He has 5 kg of flour. How many loaves of bread can he make? (i)

5 \times \frac{1}{6}

(ii)

\frac{1}{6} \div 5

(iii)

5 \div \frac{1}{6}

(iv)

5 \times 6

Sol. (a) (i) Given, the total length of lace

=

8 m and lace used for each bag

= \frac{1}{4} m

Now, number of bags she decorated

= 8 \div \frac{1}{4}

(b) (ii) Given, total length of ribbon

= \frac{1}{2}

metre and total number of badges

= 8

Now, length of ribbon used for each badge

= \frac{1}{2} \div 8

(c) (iii) Given, the total weight of flour

=

5 kg and flour required for one loaf

= \frac{1}{6} kg

. Now, number of loaves

= 5 \div \frac{1}{6}

If

\frac{1}{4} kg

of flour is used to make 12 rotis, how much flour is used to make 6 rotis? Sol. Given flour used to make 12 rotis

= \frac{1}{4} kg

Now, flour used to make

1 roti = \frac{1}{4} \div 12 = \frac{1}{4} \times \frac{1}{12} = \frac{1}{48} kg

And flour used to make 6 rotis

= \frac{1}{48} \times 6 = \frac{1}{8} kg

So, the flour used to make 6 rotis is

\frac{1}{8} kg

.

Pātịganita, a book written by Sridharacharya in the 9th century CE, mentions this problem: "Friend, after thinking, what sum will be obtained by adding together

1 \div \frac{1}{6}, 1 \div \frac{1}{10}, 1 \div \frac{1}{13}, 1 \div \frac{1}{9}

and

1 \div \frac{1}{2}

. What should the friend say? Sol. Here,

1 \div \frac{1}{6} = 1 \times \frac{6}{1} = 6

,

1 \div \frac{1}{10} = 1 \times \frac{10}{1} = 10

,

1 \div \frac{1}{13} = 1 \times \frac{13}{1} = 13

,

1 \div \frac{1}{9} = 1 \times \frac{9}{1} = 9

and

1 \div \frac{1}{2} = 1 \times \frac{2}{1} = 2

Now, total sum

= 6 + 10 + 13 + 9 + 2 = 40

So, the friend should say 40 .

Mira is reading a novel that has 400 pages. She read

\frac{1}{5}

of the pages yesterday and

\frac{3}{10}

of the pages today. How many more pages does she need to read to finish the novel? Sol. Given, total number of pages in a novel = 400 Now, number of pages read by Mira on yesterday

= \frac{1}{5} \times 400 = 80

And number of pages read by Mira today

= \frac{3}{10} \times 400 = 120

So, total pages read in both days

= 80 + 120 = 200

Hence, number of pages remaining to finish the novel

= 400 - 200 = 200

So, Mira needs to read 200 more pages to finish the novel.

A car runs 16 km using 1 litre of petrol. How far will it go using

2 \frac{3}{4}

litres of petrol? Sol. Given, the total distance covered by car in 1 litre of petrol = 16 km So, distance covered by car in

2 \frac{3}{4}

litres of petrol

= 2 \frac{3}{4} \times 16 = \frac{11}{4} \times 16 = \frac{176}{4} = 44 km

So, the car will go 44 km using

2 \frac{3}{4}

litres of petrol.

Amritpal decides on a destination for his vacation. If he takes a train, it will take him

5 \frac{1}{6}

hours to get there. If he takes a plane, it will take him

\frac{1}{2}

hour . How many hours does the plane save? Sol. Given, time taken by train to reach the destination

= 5 \frac{1}{6} = \frac{31}{6}

hours and time taken plane to reach the destination

= \frac{1}{2}

hour Now, total time saved =

\frac{31}{6} - \frac{1}{2} = \frac{31 - 3}{6} = \frac{28}{6} = \frac{14}{3}

hours So, the plane saves

\frac{14}{3}

hours .

Mariam's grandmother baked a cake. Mariam and her cousins finished

\frac{4}{5}

of the cake. The remaining cake was shared equally by Mariam's three friends. How much of the cake did each friend get? Sol. Given, Mariam and her cousins finished

\frac{4}{5}

of the cake. Now, fraction of cake left

= 1 - \frac{4}{5} = \frac{1}{5}

and cake shared by 3 friends

= \frac{1}{5} \div 3

= \frac{1}{5} \times \frac{1}{3} = \frac{1}{15}

So, each friend got

\frac{1}{15}

of the cake.

Choose the option(s) describing the product of

(\frac{565}{465} \times \frac{707}{676})

. (a)

> \frac{565}{465}

(b)

< \frac{565}{465}

(c)

> \frac{707}{676}

(d)

< \frac{707}{676}

(e) > 1 (f) < 1 Sol. Compare with options: (a)

> \frac{565}{465} : (✓)

Yes, because

\frac{707}{676} > 1

, so multiplying improper fraction increase the value. (b)

< \frac{565}{465}

: (x) No. (c)

> \frac{707}{676} : (✓)

Yes, because

\frac{565}{465} > 1

, so multiplying improper fraction increases the value. (d)

< \frac{707}{676} : (x)

No. (e) > 1: (

✓

) Yes, both fraction are greater than 1 so the product is greater than 1 . (f)

< 1

: (x) No.

∴ (a), (c), (e)

are correct options.

What fraction of the whole square is shaded?

Sol. The whole square is divided into 4 equal smaller squares. Focus on the bottom right square - it's subdivided further: It is split into 8 equal triangles using diagonal lines. Of those 8 parts, 3 triangles are shaded.

Fraction of the whole taken by one small square

= \frac{1}{4}

Fraction of the small triangle that is shaded

= \frac{3}{8}

Fraction of whole square which is shaded Now,

\frac{1}{4} \times \frac{3}{8} = \frac{3}{32}

∴ \frac{3}{32}

of the whole square is shaded.

A colony of ants set out in search of food. As they search, they keep splitting equally at each point (as shown in the fig.) and reach two food sources, one near a mango tree and another near a sugarcane field. What fraction of the original group reached each food source?

Sol. From the figure, the first split i.e., at branch A , the colony divides into 2 equal parts.

∴

Each part represents a fraction

= \frac{1}{2}

So,

\frac{1}{2}

of whole ants reaches to the mango tree. Again, the branch B divides into 2 parts.

∴

Each part represents a fraction

= \frac{1}{2} \div 2 = \frac{1}{4}

So,

\frac{1}{4}

of

\frac{1}{2}

ants reaches to the mango tree. Again, the branch C divides into 4 parts.

∴

Each part represents a fraction

= \frac{1}{4} \div 4 = \frac{1}{16}

So,

\frac{2}{16}

of

\frac{1}{4}

ants reaches to mango tree and

\frac{1}{16}

of

\frac{1}{4}

ants reaches to sugarcane. Again, the branch D divides into 2 parts.

∴

Each part represents a fraction

= \frac{1}{16} \div 2 = \frac{1}{32}

. So,

\frac{1}{32}

of

\frac{1}{16}

ants reaches to mango tree and

\frac{1}{32}

of

\frac{1}{16}

ants reaches to sugarcane.

∴

Total fraction of the original colony who reached mango tree

= \frac{1}{2} + \frac{1}{4} + \frac{2}{16} + \frac{1}{32} = \frac{16 + 8 + 4 + 1}{32} = \frac{29}{32}

and total fraction of the original colony who reached sugarcane field

= \frac{1}{16} + \frac{1}{32} = \frac{2 + 1}{32} = \frac{3}{32}

What is

1 - \frac{1}{2}

?

(1 - \frac{1}{2}) \times (1 - \frac{1}{3})

?

(1 - \frac{1}{2}) \times (1 - \frac{1}{3}) \times (1 - \frac{1}{4}) \times (1 - \frac{1}{5})

?

(1 - \frac{1}{2}) \times (1 - \frac{1}{3}) \times (1 - \frac{1}{4}) \times (1 - \frac{1}{5}) \times (1 - \frac{1}{6})

\times (1 - \frac{1}{7}) \times (1 - \frac{1}{8}) \times (1 - \frac{1}{9}) \times (1 - \frac{1}{10})

? Make a general statement and explain. Sol. We have,

1 - \frac{1}{2} = \frac{1}{2}

Then,

(1 - \frac{1}{2}) \times (1 - \frac{1}{3}) = \frac{1}{2} \times \frac{2}{3} = \frac{1}{3}

Next,

(1 - \frac{1}{2}) \times (1 - \frac{1}{3}) \times (1 - \frac{1}{4}) \times (1 - \frac{1}{5})

= \frac{1}{2} \times \frac{2}{3} \times \frac{3}{4} \times \frac{4}{5} = \frac{1}{5}

And

(1 - \frac{1}{2}) \times (1 - \frac{1}{3}) \times (1 - \frac{1}{4}) \times (1 - \frac{1}{5}) \times (1 - \frac{1}{6})

\times (1 - \frac{1}{7}) \times (1 - \frac{1}{8}) \times (1 - \frac{1}{9}) \times (1 - \frac{1}{10})

= \frac{1}{2} \times \frac{2}{3} \times \frac{3}{4} \times \frac{4}{5} \times \frac{5}{6} \times \frac{6}{7} \times \frac{7}{8} \times \frac{8}{9} \times \frac{9}{10} = \frac{1}{10}

The general expression is

(1 - \frac{1}{2}) \times (1 - \frac{1}{3}) \times (1 - \frac{1}{4}) \times \dots \times (1 - \frac{1}{n})

Now, from above calculations, we have

\frac{1}{2} \times \frac{2}{3} \times \frac{3}{4} \times \dots \times \frac{n - 1}{n}

∴

The value of expression

= \frac{1}{n}

(i)	(ii)	(iii)	(iv)
Row 1	$3 \div \frac{7}{9}$	$\frac{14}{4} \div 2$	$\frac{2}{3} \div \frac{2}{3}$	$\frac{14}{6} \div \frac{7}{3}$
Row 2	$\frac{4}{3} \div \frac{3}{4}$	$\frac{7}{4} \div \frac{1}{7}$	$\frac{8}{2} \div \frac{4}{15}$
Row 3	$\frac{1}{5} \div \frac{1}{9}$	$\frac{1}{6} \div \frac{11}{12}$	$3 \frac{2}{3} \div 1 \frac{3}{8}$

Frequently Asked Questions

What is the primary focus of NCERT Class 7 Maths Chapter 8: Working with Fractions?

How do NCERT Solutions for Chapter 8 help in solving fraction problems?

What types of questions are included in NCERT Solutions for Class 7 Maths Chapter 8?

How are multiplication and division explained in NCERT Solutions for Chapter 8 – Working with Fractions?

In what way do NCERT Solutions for Class 7 Maths Chapter 8 improve conceptual clarity?

How are unlike fractions handled in NCERT Solutions for Chapter 8?

How do NCERT Solutions for Class 7 Maths Chapter 8 support exam preparation?

What is the correct approach to solving mixed fraction problems in the textbook?

What are common mistakes students make in this chapter?

How do step-by-step solutions help in mastering Working with Fractions?

Join ALLEN!

Frequently Asked Questions

What is the primary focus of NCERT Class 7 Maths Chapter 8: Working with Fractions?

How do NCERT Solutions for Chapter 8 help in solving fraction problems?

What types of questions are included in NCERT Solutions for Class 7 Maths Chapter 8?

How are multiplication and division explained in NCERT Solutions for Chapter 8 – Working with Fractions?

In what way do NCERT Solutions for Class 7 Maths Chapter 8 improve conceptual clarity?

How are unlike fractions handled in NCERT Solutions for Chapter 8?

How do NCERT Solutions for Class 7 Maths Chapter 8 support exam preparation?

What is the correct approach to solving mixed fraction problems in the textbook?

What are common mistakes students make in this chapter?

How do step-by-step solutions help in mastering Working with Fractions?

Join ALLEN!

NCERT Solutions Class 7 Maths Chapter 8 Working with Fractions

1.0NCERT Solutions Class 7 Maths Chapter 8 Working with Fractions – Download PDF

2.0Key Concepts in Chapter 8: Working with Fractions

3.0NCERT Solutions for Class 7 Chapter 8 Working with Fractions: All Exercises

4.0NCERT Class 7 Maths Chapter 8 Working with Fractions: Detailed Solutions

FIGURE IT OUT-01

FIGURE IT OUT-02

FIGURE IT OUT-03

FIGURE IT OUT -04

5.0Key Features of NCERT Solutions Class 7 Maths Chapter 8 : Working with Fractions