Mathematics- Problems and Solutions: CLASS 6 CHAPTER 7: FRACTIONS

Exercise 7.1

1. Write the fraction representing the shaded portion.

Solution

[There are four equal parts out of which 2 parts are shaded.]

ii)

[There are 9 equal parts out of which 8 parts are shaded.]

iii)

[There are 8 equal parts out of which 4 parts are shaded.]

iv)

[There are 4 equal parts out of which 1 part is shaded.]

[There are 7 equal parts out of which 3 parts are shaded.]

vi)

[There are 12 flowers of the same kind out of which 3 are shaded.]

vii)

[There are 10 pencils out of which 10 are shaded.]

viii)

[There are 9 equal parts out of which 4 parts are shaded.]

ix)

[There are 8 equal parts out of which 4 parts are shaded.]

[There is a shape divided into 2 equal parts, out of which one part is shaded.]

2. Colour the part according to the given fraction:

Solution

ii)

iii)

iv)

3. Identify the error if any:

Solution

The shaded portions do not represent the given fractions as each shape is not divided into equal parts.

4. What fraction of a day is 8 hours?

Solution

In a day there are 24 hours. So, 8 hours in a 24 hour day is represented as

5. What fraction of an hour is 40 minutes?

Solution

One hour is 60 minutes. So, 40 minutes as a fraction of an hour is represented as

.
.

6. Arya, Abhimanyu, and Vivek shared lunch. Arya has brought two sandwiches, one made of vegetable and one of jam. The other two boys forgot to bring their lunch. Arya agreed to share his sandwiches so that each person will have an equal share of each sandwich.

(a) How can Arya divide his sandwiches so that each person has an equal share?

(b) What part of a sandwich will each boy receive?

Solution

a) Arya should divide his sandwiches into 3 equal parts and give 1 part of each sandwich so that each person has an equal share.

b) Each boy will receive

of a sandwich.
.

7. Kanchan dyes dresses. She had to dye 30 dresses. She has so far finished 20 dresses. What fraction of dresses has she finished?

Solution

She has finished 20 dresses out of 30.

So, fraction of dresses she has finished =

8. Write the natural numbers from 2 to 12. What fraction of them are prime numbers?

Solution

Natural numbers from 2 to 12 are 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 and 12

Prime numbers – 2, 3, 5, 7, 11

There are 11 natural numbers from 2 to 12 out of which 5 are prime numbers.

Fraction of numbers that are prime is

9. Write the natural numbers from 102 to 113. What fraction of them are prime numbers?

Solution

Natural numbers from 102 to 113 are 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112 and 113

Prime numbers – 103, 107, 109, 113

There are 12 natural numbers from 102 to 113 out of which 4 are prime numbers.

So, fraction of numbers that are prime is

10. What fraction of these circles have X’s in them?

Solution

There are 8 circles out of which 4 have X’s in them.

So, fraction of circles having X’s is

11. Kristin received a CD player for her birthday. She bought 3 CDs and received 5 others as gifts. What fraction of her total CDs did she buy and what fraction did she receive as gifts?

Solution

Number of CDs Kristin purchased = 3

Number of CDs she received as gifts = 5

So, total number of CDs = 8

Kristin purchased 3 CDs out of a total number of 8 CDs.

Fraction of CDs she purchased =

Kristin received 5 CDs out of a total number of 8 CDs.

Fraction of CDs she received as gifts =

Exercise 7.2

1. Draw number lines and locate the points on them:

Solution

2. Express the following as mixed fractions:

Solution

A mixed fraction has a combination of a whole and a part.

3. Express the following as improper fractions :

Solution

We can express a mixed fraction as an improper fraction as

Exercise 7.3

1. Write the fractions. Are all these fractions equivalent?

Solution

2. Write the fractions and pair up the equivalent fractions from each row.

Solution

The fractions are as follows:

The pairs are as follows:

a) ii)

b) iv)

c) i)

d) v)

e) iii)

3. Replace in each of the following by the correct number:

Solution

To find an equivalent fraction, we may divide both the numerator and the denominator by the same number.

4. Find the equivalent fraction of

having

(a) denominator 20 (b) numerator 9 (c) denominator 30 (d) numerator 27

Solution

a) We have the fraction

Numerator is 3 and denominator is 5.

We know that 5 × 4 = 20. So, we have multiply both the numerator and denominator by 4 to find the equivalent fraction having denominator 20.

So,

b) We have the fraction

Numerator is 3 and denominator is 5.

As the numerator should be 9 and 3 × 3 = 9, we have to multiply both the numerator and denominator by 3 to find the equivalent fraction having numerator 9.

So,

c) We have the fraction

Numerator is 3 and denominator is 5.

As the denominator should be 30 and 5 × 6 = 30, we have to multiply both the numerator and denominator by 6 to find the equivalent fraction having denominator 30.

So,

d) We have the fraction

Numerator is 3 and denominator is 5.

As the numerator should be 27 and 3 × 9 = 27, we have to multiply both the numerator and denominator by 9 to find the equivalent fraction having numerator 27.

So,

5. Find the equivalent fraction of

with (a) numerator 9 (b) denominator 4.

Solution

a) We have the fraction

.

Numerator is 36 and denominator is 48.

As the numerator should be 9 and 36 ÷ 4 = 9, we have to divide both the numerator and denominator by 4 to find the equivalent fraction having numerator 9.

So,

b) We have the fraction

Numerator is 36 and denominator is 48.

As the denominator should be 4 and 48 ÷ 12 = 4, we have to divide both the numerator and denominator by 12 to find the equivalent fraction having denominator 4.

So,

6. Check whether the following fractions are equivalent:

Solution

We see that the numerator and the denominator are multiplied by the same number 6.

Hence the fractions are equivalent,

b) If we multiply the numerator and denominator by 4, we get

If we multiply the numerator and denominator by 5, we get

So, we see that the fractions are not equivalent.

c) The numerators 7 and 5, and the denominators 13 and 11 are all prime numbers and hence they cannot be equivalent fractions.

7. Reduce the following fractions to simplest form:

Solution

To reduce a fraction into its simplest form, find the HCF of the numerator and the denominator and divide both by the HCF.

8. Ramesh had 20 pencils, Sheelu had 50 pencils and Jamaal had 80 pencils. After 4 months, Ramesh used up 10 pencils, Sheelu used up 25 pencils and Jamaal used up 40 pencils. What fraction did each use up? Check if each has used up an equal fraction of her/his pencils?

Solution

Fraction of pencils used by Ramesh =

Fraction of pencils used by Sheelu =

Fractions of pencils used by Jamaal =

Yes, they have all used up an equal fraction of his/her pencils.

9. Match the equivalent fractions and write two more of each:

Solution

Exercise 7.4

1. Write shaded portion as fraction. Arrange them in ascending and descending order using correct sign ‘<’, ‘=’, ‘>’ between the fractions:

c) Show

on the number line. Put appropriate signs between the fractions given below:

Solution

The fractions represented by the shaded portions are as follows:

The above fractions in a) and b) are like fractions as they have the same denominator.

When comparing fractions with same denominator, the fraction with the greater numerator is greater.

So, arranging the fractions in ascending order, we have:

c)Let us represent the fractions

on the number line.

2. Compare the fractions and put the appropriate sign:

Solution

a) When the denominators are the same, the fraction with the greater numerator is a greater fraction.

As 3 < 5,

b) When we compare two unlike fractions, we first get their equivalent fractions with a denominator which is the L.C.M of the denominators of both the fractions.

c) The denominators are the same. So, the fraction with the greater numerator is a greater fraction.

d) When we compare two unlike fractions, we first get their equivalent fractions with a denominator which is the L.C.M of the denominators of both the fractions.

3. Make five more such pairs and put appropriate signs.

Solution

4. Look at the figures and write <, >, or = between the given pairs of fractions.

Solution

5. How quickly can you do this? Fill appropriate sign. ( ‘<’, ‘=’, ‘>’)

Solution

6. The following fractions represent just three different numbers. Separate them into three groups of equivalent fractions, by changing each one to its simplest form.

Solution

The fractions in its simplest form are as follows:

From the simplest forms, we see that there are three groups as

7. Find answers to the following. Write and indicate how you solved them.

Solution

a) No. 5/9 is not equal to 4/5.

b) No, 9/16 is not equal to 5/9.

c) Yes, 4/5 is equal to 16/20

d) No, 1/15 is not equal to 4/30

8. Ila read 25 pages of a book containing 100 pages. Lalita read 2/5 of the same book. Who read less?

Solution

Total number of pages in the book = 100 pages

Number of pages read by Ila = 25 pages

Fraction of pages read by Ila =

Fraction of pages read by Lalita =

Comparing the two fractions, we have

So, Ila read lesser number of pages than Lalita.

9. Rafiq exercised for 3/6 of an hour, while Rohit exercised for ¾ of an hour. Who exercised for a longer time?

Solution

Rohit exercised for a longer time than Rafiq.

10. In a class A of 25 students, 20 passed in first class; in another class B of 30 students, 24 passed in first class. In which class was a greater fraction of students getting first class?

Solution

Total number of students in class A = 25

Number of students passed in first class = 20.

Fraction of students of class A who passed in first class =

Total number of students in class B = 30

Number of students passed in first class = 24.

Fraction of students of class B who passed in first class =

Both class A and B have the same fraction of students who passed in first class.

Exercise 7.5

1. Write these fractions appropriately as additions or subtractions:

Solution

a) The first shaded portion represents the fraction

The second shaded portion represents

and the third portion represents

So, we see that

Hence ‘+’ is the operation involved.

b) The first shaded portion represents the fraction

the second shaded portion represents

and the third portion represents

So, we see that

Hence ‘-’ is the operation involved.

c) The first shaded portion represents the fraction

The second shaded portion represents

and the third portion represents

.
So, we see that

Hence ‘+’ is the operation involved.

2. Solve:

Solution

3. Shubham painted 2/3 of the wall space in his room. His sister Madhavi helped and painted 1/3 of the wall space. How much did they paint together?

Solution

Space painted by them together = Space painted by Shubham + Space painted by Madhavi

Implies, they painted the entire wall.

4. Fill in the missing fractions.

Solution

5. Javed was given 5/7 of a basket of oranges. What fraction of oranges was left in the basket?

Solution

Fraction of oranges given to Javed =

Fraction of oranges left in the basket =

Exercise 7.6

1. Solve

Solution
\

2. Sarita bought 2/5 metre of ribbon and Lalita ¾ metre of ribbon. What is the total

length of the ribbon they bought?

Solution

Length of ribbon Sarita bought = 2/5 meter

Length of ribbon Lalita bought = ¾ meter

Total length of ribbon =

They bought

meters of ribbon together.

3. Naina was given

piece of cake and Najma was given

piece of cake. Find the total amount of cake was given to both of them.

Solution

Total amount of cake both had =

They had

pieces of cake together.

4. Fill in the boxes.

Solution

5. Complete the addition subtraction boxes:

Solution

a) The box shows that the fractions should be added from left to right. So,

The fractions from top to bottom are to be subtracted. So,

So, the completed box is as shown below:

b) The box shows that the fractions should be added from left to right. So,

The fractions from top to bottom are to be subtracted. So,

So the completed box looks as follows:

6. A piece of wire 7/8 metre long broke into two pieces. One piece was 1/4 metre long. How long is the other piece?

Solution

Length of the piece of wire is

Length of one broken piece is

Length of the other broken piece = total length of the wire – length of one broken piece

Length of the piece of wire is

7. Nandini’s house is 9/10 km from her school. She walked some distance and then took a bus for 1/2 km to reach the school. How far did she walk?

Solution

Distance from Nandini’s house to school =

Distance covered by bus = ½ km

Distance she walked = distance from house to school – distance she covered by bus.

Distance walked by Nandhini =

8. Asha and Samuel have bookshelves of the same size partly filled with books. Asha’s shelf is 5/6 th full and Samuel’s shelf is 2/5 th full. Whose bookshelf is more full? By what fraction?

Solution

Fraction of books in Asha’s shelf =