# Fractions Class-6 ML Aggarwal ICSE APC Maths Solutions

Fractions Class-6 ML Aggarwal ICSE APC Mathematics Solutions Chapter-6. We provide step by step Solutions of Exercise / lesson-6 Fractions ICSE Class-6th ML Aggarwal Mathematics.

Our Solutions contain all type Questions with Exe- 6.1, Exe-6.2, Exe- 6.3, Exe-6.4, Exe- 6.5, Exe-6.6, Exe- 6.7, Objective Type Questions  (includes: Mental Maths, Multiple Choice Questions, HOTS ), and Check Your Progress to develop skill and confidence. Visit official Website CISCE for detail information about ICSE Board Class-6 Maths.

## Fractions Class-6 ML Aggarwal ICSE APC Mathematics Solutions Chapter-6

–: Select Topic :–

Exe- 6.1,

Exe-6.2,

Exe- 6.3,

Exe-6.4,

Exe- 6.5,

Exe-6.6,

Exe- 6.7,

Objective Type Questions

Mental Maths,

Multiple Choice Questions,

HOTS

### Exercise – 6.1,Fractions Class-6 ML Aggarwal ICSE APC Mathematics Solutions

Question 1

Write the following division as fractions:
(i) 3 ÷ 7
(ii) 11 ÷ 78
(iii) 113 ÷ 128
(i) 3 ÷ 7 = $\frac{3}{7}$
(ii) 11 ÷ 78 = $\frac{11}{78}$
(iii) 113 ÷ 128 = $\frac{113}{128}$

Question 2

Write the following fractions in words.
(i) $\frac{2}{7}$
(ii) $\frac{3}{10}$
(iii) $\frac{15}{28}$

(i) $\frac{2}{7}$ = Two – Seventh
(ii) $\frac{3}{10}$ = Three – Tenth
(iii) $\frac{15}{28}$ fifteen – Twenty eighth

Question 3

Write the following fractions in number form:
(i) one – sixth
(ii) three – eleventh,
(iii) seven-fortieth
(iv) thirteen – one hundred twenty fifth
(i) One – sixth = $\frac{1}{6}$
(ii) Three-eleventh = $\frac{3}{11}$
(iiii) seven-fortieth = $\frac{7}{40}$
(iv) Thirteen-one hundred twenty fifth = $\frac{13}{125}$

Question 4

What fraction of each of the following is shaded part?

Question 5

Shade the parts of the following figures according to given fractions:

Question 6.

In the adjoining figure, if we say that the shaded region is $\frac{1}{4}$ of the whole region, then identify the error in it.

The whole rectangle is not divided into four equal parts.

Question 7.
Write the fraction in which
(i) numerator = 5 and denominator = 13
(ii) denominator = 23 and numerator = 17
Solution:
(i) $\frac{5}{13}$
(ii) $\frac{17}{23}$

Question 8.
Shabana has to stitch 35 dresses. So, ar she has stitched 21 dresses. What fraction of dresses has she stitched?

Number of dresses she had to stiches = 35
Number of dresses she has finished = 21
∴ Fraction of dresses she has finished = $\frac{21}{35}=\frac{3}{5}$

Question 9.
What fraction of a day is 8 hours ?

Number of hours in a day = 24 hours
∴ Required fraction = $\frac{8}{24}$

Question 10.
What fraction of an hour is 45 minutes ?

An hour (1 hour) = 60 minutes
∴ Required fraction = $\frac{45}{60}$

Question 11.
How many natural numbers are there from 87 to 97? What fraction of them are prime numbers?

The natural numbers from 87 to 97 are 87, 88, 89, 90, 91, 92, 93, 94, 95, 96 and 97. Total number of natural number = 11 Out of these, the prime numbers are 87 and 97
Total number of these prime numbers = 2
∴ Required fraction = $\frac{2}{11}$

### Fractions Class-6 ML Aggarwal ICSE Maths Solutions Exe-6.2

Question 1

Show the fractions $\frac{2}{5}, \frac{3}{5}, \frac{4}{5} \text { and } \frac{5}{5}$ on a number line.

Question 2.
Show $\frac{1}{8}, \frac{2}{8}, \frac{3}{8} \text { and } \frac{7}{8}$ on a number line.

Question 3.
Show $\frac{0}{10}, \frac{1}{10}, \frac{3}{10}, \frac{5}{10}, \frac{7}{10} \text { and } \frac{10}{10}$ on a number line.

### Fractions Exe-6.3 Class-6 ML Aggarwal ICSE Maths Solutions

Question 1

State which of the following fractions are proper, improper or mixed:

Question 2

Convert the following improper fractions into mixed numbers:

Question 3

Convert the following mixed number into improper fractions:

Question 4.
Write the fractions representing the shaded regions. Are all these fractions equivalent?

Question 5

Write the fractions representing the shaded regions and pair up the equivalent fractions from each row:

Question 6.

(i) Find the equivalent fraction of $\frac{15}{35}$ with denominator 7.
(ii) Find the equivalent fraction of $\frac{2}{9}$ with denominator 63.

(i) $\frac{15}{35}=\frac{ . . .}{7}$
Let the numerator be a
⇒ 15 × 7 = 35 × a
$a=\frac{15 \times 7}{35}$
⇒ a = 3
∴ $\frac{15}{35}=\frac{3}{7}$

(ii) $\frac{2}{9}=\frac{\dots}{63}$
Let the numerator, which needs to be calculated as x
⇒ 2 × 63 = 9 × x
⇒ $x=\frac{2 \times 63}{9}$
⇒ x = 14
∴ $\frac{2}{9}=\frac{14}{63}$

Question 7

Find the equivalent fraction of $\frac{3}{5}$ having
(i) denominator 30
(ii) numerator 27.

(i) $\frac{3}{5}$ having denominator 30
Multiply and divide the fraction by 6, we get
$\frac{3}{5} \times \frac{6}{6}=\frac{18}{30}$

(ii) $\frac{3}{5}$ having numerator 27
Multiply and divide the fraction by 9, we get
$\frac{3}{5} \times \frac{9}{9}=\frac{27}{45}$

Question 8

Replace ‘…..’ in each of the following by the correct number.

Question 9

Check whether the given pairs of fractions are equivalent:

Question 10

Reduce the following fractions to simplest form:

Question 11

Convert the following fractions into equivalent like fractions:

### Exercise – 6.4 Fractions Class-6 ML Aggarwal ICSE Maths Solutions

Question 1

Show the fractions $\frac{1}{6}, \frac{2}{6}, \frac{3}{6}, \frac{4}{6}, \frac{5}{6}, \frac{6}{6}$ and $\frac{8}{6}$ on the number line. Replace ‘……’ by an appropriate sign” between given fractions:

Question 2

Compare the given fractions and replace ‘….’ by an appropriate sign ”

Question 3

Replace ‘…..’ by an appropriate sign ‘<, = or >’ between the given fractions:

Question 4

Write the shaded portions as fractions. Arrange them in ascending order using appropriate sign between fractions:

Question 5

Compare the following pairs of fractions:

Question 6

Fill in the boxes by the symbol < or > to make the given statements true:

Question 7.

Arrange the given fractions in descending order:

Question 8

Arrange the given fractions in the ascending order:

### Fractions Class-6 ML Aggarwal ICSE APC Mathematics Solutions Exercise – 6.5

Question 1

Work out the following :

Question 2

Find in the missing fractions:

Question 3

Work out the following:

Question 4.

Simplify the following:

Question 5.
(i) What number should be added to $\frac{5}{12}$ to get $2 \frac{3}{8}$?
(ii) What number should be subtracted from 5 to get $1 \frac{5}{13}$ ?

### ML Aggarwal Solutions Fractions Exercise – 6.6 for ICSE Class-6

Question 1

Evaluate the following:

Question 2

Evaluate the following:

Question 3.
Find the reciprocal of each of the following
(i) $\frac{9}{13}$
(ii) $2 \frac{3}{8}$

(i) Reciprocal of $\frac{9}{13}$ is $\frac{13}{9}$ = $1 \frac{4}{9}$
(ii) Reciprocal of $2 \frac{3}{8}$ or $\frac{19}{8}$ is $\frac{8}{19}$

Question 4

Evaluate the following:

### Fractions Exercise – 6.7 of ML Aggarwal for ICSE Class-6 APC Mathematics

Question 1

Sarita bought $\frac{2}{5}$ metre of ribbon and Laiita $\frac{3}{4}$ metre of ribbon. What is the total length of the ribbon they bought?

Ribbon bought by Sarita = $\frac{2}{5}$ m
Ribbon bought by Lalita = $\frac{3}{4}$ m
∴ Total length of the ribbon they bought

Question 2

A bamboo of length $2 \frac{3}{4}$ metre broke into two pieces. One piece was $\frac{7}{8}$ metre long. How long is the other piece?

Let of original piece of bamboo = $2 \frac{3}{4}$ = $\frac{11}{4}$ metre
Length of one piece = $\frac{7}{8}$ metre
Length of other piece = $\frac{7}{8}$ metre – $\frac{7}{8}$ metre

Question 3.
Nidhi’s house is $1 \frac{9}{10}$ km from her school. She walked some distance and then took a bus for $1 \frac{1}{2}$ km to reach the school. How far did she walk?

Distance of Nidhi’s house from school
$=1 \frac{9}{10} \mathrm{km}=\frac{19}{10} \mathrm{km}$

Question 4.
From a rope of length $20 \frac{1}{2}$ m, a piece of length $3 \frac{5}{8}$ m is cut off. Find the length of the remaining rope.

Total length of rope = $20 \frac{1}{2}$ m
Length cut off = $3 \frac{5}{8}$ m

∴ Length of the remaining rope = $16 \frac{7}{8}$ m

Question 5.

The weight of three packets are $2 \frac{3}{4}$ kg. $3 \frac{1}{3}$ kg. and $5 \frac{2}{5}$ kg. Find total weight of all the three packets.

Weight of 1st packet = $2 \frac{3}{4}$
Weight of 2nd packet = $3 \frac{1}{3}$
Weight of 3rd packet = $5 \frac{2}{5}$
∴ Total weight

Question 6

Shivani read 25 pages of a book containing 100 pages. Nandni read $\frac{2}{5}$ of the same book. Who read less?

Shivani read pages = $\frac{25}{100}=\frac{1}{4}$
Nandni read pages = $\frac{2}{5}$
Now, LCM of 4 and 5 = 20
Making $\frac{1}{4} \text { and } \frac{2}{5}$ as like fractions

∴ Shivani read less pages than Nandni.

Question 7

Rafiq exercised for $\frac{3}{6}$ of an hour, while Rohit, exercised for $\frac{3}{4}$ of an hour. Who exercised for a longer time and by what fraction of an hour?

Rafiq exercised for $\frac{3}{6}$ of an hour
$\frac{1}{2}$ of an hour
Rohit exercised for $\frac{3}{4}$ of an hour
$\frac{3}{4}$ of an hour
LCM of 2 and 4 = 4

Rafiq’s exercise < Rohit’s exercise
More exercise done by Rohit in fraction

Rohit does exercise more then Rafiq by $\frac{1}{4}$ of an hour.

### ML AggarwalClass-6 ICSE APC Mathematics Solutions Chapter-6 Fractions Objective Type Questions

#### Mental Maths

Question 1

Fill in the blanks:
(i) A fraction is a number which represent a ………… of whole.
(ii) A proper fraction lies between 0 and …………
(iii) A mixed fraction can be converted into ………… fraction.
(iv) Fractions having different denominations are called …………
(v) In two like fractions, the fraction having smaller numerator is …………
(vi) $\frac{144}{180}$ reduced to simplest form is …………..
(vii) $7 \frac{2}{5}$ + ………… = 12
(viii) $\frac{42}{56}=\frac{6}{\dots . .}$

(i) A fraction is a number which represent a part of whole.
(ii) A proper fraction lies between 0 and 1.
(iii) A mixed fraction can be converted into an improper fraction.
(iv) Fractions having different denominations are called unlike fractions.
(v) In two like fractions, the fraction having smaller numerator is smaller.
(vi) $\frac{144}{180}$ reduced to simplest form is $\frac{4}{5}$

Question 2

State whether the following statements are true (T) or false (F):
(i) Two fractions with same numerator are called like fractions.
(ii) A fraction in which the numerator is greater than is denominator is called an improper fraction.
(iii) Every improper fract on can be converted into a mixed fraction.
(iv) Every fraction can be represented by a point on a number line.
(v) In two unlike fractions with same numerator, the fraction having greater denominator is greater.
(vi) $\frac{1}{2}, \frac{1}{3} \text { and } \frac{1}{4}$ are like fractions.
(vii) $5-1 \frac{3}{4}=4 \frac{1}{4}$

(i) Two fractions with same numerator are called like fractions. False
(ii) A fraction in which the numerator is greater than is denominator is called an improper fraction. True
(iii) Every improper fraction can be converted into a mixed fraction. True
(iv) Every fraction can be represented by a point on a number line. True
(v) In two unlike fractions with same numerator, the fraction having greater denominator is greater. False
(vi) $\frac{1}{2}, \frac{1}{3} \text { and } \frac{1}{4}$ are like fractions. False
(vii) $5-1 \frac{3}{4}=4 \frac{1}{4}$.   False

#### Multiple Choice Questions (MCQ)

Question 3

Choose the correct answer from the given four options (3 to 17):
Question 3.
In the given figure, the shaded part is represented by the fraction :

$\frac{3}{7}$

Question 4.
In the given figure, the shaded region is represented by the fraction :

$\frac{5}{24}$

Question 5

The two consecutive integers between which the fraction $\frac{5}{7}$ lies are
(a) 5 and 7
(b) 5 and 6
(c) 6 and 7
(d) 0 and 1

0 and 1 (d)

Question 6.
Which of the following pairs of fractions are not equivalent?

$\frac{6}{14}, \frac{10}{25}$
∵ $\frac{3}{7}, \frac{2}{5}$ not same. (d)

Question 7.
The fraction equivalent to $\frac{45}{81}$ is

$\frac{45,9}{81,9}=\frac{5}{9}$ (d)
(Dividing numerator and denominator by 9)

Question 8.
The fraction which is not equal to $\frac{4}{5}$ is

$\frac{9}{15}$ is not equal to $\frac{4}{5}$. (b)
∴ $\frac{9}{15}=\frac{3}{5}$

Question 9.
Which of the following fractions is not in the lowest form?

The lowest form of this can be written as
$\frac{39}{87}=\frac{13}{29}$

Question 10.
A pair of like fraction is

$\frac{3}{7}, \frac{16}{7}$
Like fractions are those fractions who have same denominator. (b)

Question 11.
Which of the following fractions is the greatest?

$\frac{5}{6}$ (a)

Question 12.
Which of the following fractions is the smallest?

$\frac{11}{10}$ (c)

Question 13

Which of the following is a false statement?

$\frac{3}{4}=\frac{6}{16}$
Because, if we multiply and divide the fraction with 4, we get
$\frac{3}{4} \times \frac{4}{4}=\frac{12}{16}$ (c)

Question 14.

Question 15.

Question 16

Anshul eats $\frac{4}{7}$ of a pizza. The fraction of the pizza left is

Let the total size of pizza be 1

Question 17.
The fraction whose numerator is the smallest odd prime number and denominator is the smallest composite number is

$\frac{3}{4}$

#### Higher Order Thinking  Skills ( HOTS )

Question 1.
Write all proper fractions whose sum of numerator and denominator is 12.

⇒ 1 + 11 = 12
⇒ 2 + 10 = 12
⇒ 3 + 9 = 12
⇒ 4 + 8 = 12
⇒ 5 + 7=12

Question 2

The given figure represents the preferences of the students during breakfast in a hostel mess. If the total number of students in the mess is 540, then with reference to the given figure, answer the following questions:

(i) What is the number of students who prefer coffee?
(ii) Whose number is greater, milk drinkers or orange juice drinkers and by what number?
(iii) What is the total number of students who drink mango shake or coffee? Is it equal to milk drinker?
(iv) Is the sum of all fractions in the given figure equal to 1 ?

(i) Total number of students = 540
Ratio of students who prefer coffee = $\frac{1}{6}$
∴ Number of student prefer coffee

∴ Milk drinkers are more than orange drinkers by number = 45.

(iii) Number of Mango shake drinkers
$=540 \times \frac{1}{6}=90$
Number of coffee drinkers
$=540 \times \frac{1}{6}=90$
Total number of mango shake and coffee drinkers = 90 + 90 = 180
Milk drinkers = 180
Yes, it is equal to milk drinkers.

(iv) Sum of all fraction are:

Yes, the sum of all the fractions are equal to 1.

Question 1

State whether the following statements are true (T) or false (F):
(i) The fraction $\frac{2}{3}$ lies between 2 and 3.
(ii) To find an equivalent fraction to a given fraction, we may add or subtract the same (non-zero) number to its numerator and denominator.
(iii) To add or subtract like fractions, we add or subtract the numerators while keeping the denominator same.

(i) False
As $\frac{2}{3}$ lies between 0 and 1
(ii) False
We should multiply and divide by appropriate numerator keep the denominator same. And that appropriate number is obtained by the LCM of all the denominators.
(ii) True

Question 2.
How many natural numbers are there between 102 and 112? What fraction of them are prime numbers?

The natural numbers from 102 to 112 are: 103, 104, 105, 106, 107, 108, 109, 110, 111 Total number of natural numbers = 9 Out of these prime numbers are:
103, 107, 109 = 3
∴ Total number of these prime numbers = 3
Required fraction = $\frac{3}{9}=\frac{1}{3}$

Question 3

Match the equivalent fractions from each row:

Question 4

Replace by an appropriate symbol ‘< or >’ between the given fractions:

Question 5

Arrange the following fractions in descending order : $\frac{7}{30}, \frac{13}{15}, \frac{9}{10}, \frac{3}{5}$

Question 6.
Simplify: $2 \frac{1}{2}-3 \frac{1}{4}+5 \frac{5}{6}$

Question 7

Evaluate the following:

Question 8

Asha and Samuel have bookshelves of the same size partly filled with books. Asha’s shelf is $\frac{5}{6}$ full and Samuel’s shelf is $\frac{3}{5}$ full. Whose bookshelf is more full and by what fraction?

Question 9

A farmer uses four out of five equal strips of his land for wheat crop and $\frac{1}{7}$ of his land for cereal crop. What fraction of his land is available for other crops?

A farmer has 5 equal strips of land

—: End of Fractions Class-6 ML Aggarwal Solutions  :–