# 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 :–**

Objective Type Questions

**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

Answer

(i) 3 ÷ 7 =

(ii) 11 ÷ 78 =

(iii) 113 ÷ 128 =

Question 2

Write the following fractions in words.

(i)

(ii)

(iii)

#### Answer

(i) = Two – Seventh

(ii) = Three – Tenth

(iii) 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

Answer

(i) One – sixth =

(ii) Three-eleventh =

(iiii) seven-fortieth =

(iv) Thirteen-one hundred twenty fifth =

Question 4

What fraction of each of the following is shaded part?

Answer

Question 5

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

Answer

Question 6.

In the adjoining figure, if we say that the shaded region is of the whole region, then identify the error in it.

#### Answer

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)

(ii)

Question 8.

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

#### Answer

Number of dresses she had to stiches = 35

Number of dresses she has finished = 21

∴ Fraction of dresses she has finished =

Question 9.

What fraction of a day is 8 hours ?

#### Answer

Number of hours in a day = 24 hours

∴ Required fraction =

Question 10.

What fraction of an hour is 45 minutes ?

#### Answer

An hour (1 hour) = 60 minutes

∴ Required fraction =

Question 11.

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

#### Answer

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 =

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

Question 1

Show the fractions on a number line.

#### Answer

Question 2.

Show on a number line.

#### Answer

Question 3.

Show on a number line.

#### Answer

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

Question 1

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

Answer

Question 2

Convert the following improper fractions into mixed numbers:

#### Answer

Question 3

Convert the following mixed number into improper fractions:

#### Answer

Question 4.

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

#### Answer

Question 5

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

Answer

Question 6.

(i) Find the equivalent fraction of with denominator 7.

(ii) Find the equivalent fraction of with denominator 63.

#### Answer

(i)

Let the numerator be a

⇒ 15 × 7 = 35 × a

⇒ a = 3

∴

(ii)

Let the numerator, which needs to be calculated as x

⇒ 2 × 63 = 9 × x

⇒

⇒ x = 14

∴

Question 7

Find the equivalent fraction of having

(i) denominator 30

(ii) numerator 27.

#### Answer

(i) having denominator 30

Multiply and divide the fraction by 6, we get

(ii) having numerator 27

Multiply and divide the fraction by 9, we get

Question 8

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

Answer

Question 9

Check whether the given pairs of fractions are equivalent:

Answer

Question 10

Reduce the following fractions to simplest form:

Answer

Question 11

Convert the following fractions into equivalent like fractions:

Answer

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

Question 1

Show the fractions and on the number line. Replace ‘……’ by an appropriate sign” between given fractions:

Answer

Question 2

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

Answer

Question 3

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

Answer

Question 4

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

Answer

Question 5

Compare the following pairs of fractions:

Answer

Question 6

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

#### Answer

Question 7.

Arrange the given fractions in descending order:

Answer

Question 8

Arrange the given fractions in the ascending order:

Answer

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

Question 1

Work out the following :

Answer

Question 2

Find in the missing fractions:

Answer

Question 3

Work out the following:

Answer

Question 4.

Simplify the following:

Answer

Question 5.

(i) What number should be added to to get ?

(ii) What number should be subtracted from 5 to get ?

Answer

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

Question 1

Evaluate the following:

Answer

Question 2

Evaluate the following:

Answer

Question 3.

Find the reciprocal of each of the following

(i)

(ii)

#### Answer

(i) Reciprocal of is =

(ii) Reciprocal of or is

Question 4

Evaluate the following:

Answer

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

Question 1

Sarita bought metre of ribbon and Laiita metre of ribbon. What is the total length of the ribbon they bought?

#### Answer

Ribbon bought by Sarita = m

Ribbon bought by Lalita = m

∴ Total length of the ribbon they bought

Question 2

A bamboo of length metre broke into two pieces. One piece was metre long. How long is the other piece?

#### Answer

Let of original piece of bamboo = = metre

Length of one piece = metre

Length of other piece = metre – metre

Question 3.

Nidhi’s house is km from her school. She walked some distance and then took a bus for km to reach the school. How far did she walk?

#### Answer

Distance of Nidhi’s house from school

Question 4.

From a rope of length m, a piece of length m is cut off. Find the length of the remaining rope.

#### Answer

Total length of rope = m

Length cut off = m

∴ Length of the remaining rope = m

Question 5.

The weight of three packets are kg. kg. and kg. Find total weight of all the three packets.

#### Answer

Weight of 1st packet =

Weight of 2nd packet =

Weight of 3rd packet =

∴ Total weight

Question 6

Shivani read 25 pages of a book containing 100 pages. Nandni read of the same book. Who read less?

#### Answer

Shivani read pages =

Nandni read pages =

Now, LCM of 4 and 5 = 20

Making as like fractions

∴ Shivani read less pages than Nandni.

Question 7

Rafiq exercised for of an hour, while Rohit, exercised for of an hour. Who exercised for a longer time and by what fraction of an hour?

#### Answer

Rafiq exercised for of an hour

= of an hour

Rohit exercised for of an hour

= 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 of an hour.

** ML Aggarwal** **Class-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) reduced to simplest form is …………..

(vii) + ………… = 12

(viii)

#### Answer

(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) reduced to simplest form is

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) are like fractions.

(vii)

#### Answer

(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) are like fractions. **False**

(vii) . **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 :

#### Answer

Question 4.

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

#### Answer

Question 5

The two consecutive integers between which the fraction lies are

(a) 5 and 7

(b) 5 and 6

(c) 6 and 7

(d) 0 and 1

#### Answer

0 and 1 (d)

Question 6.

Which of the following pairs of fractions are not equivalent?

#### Answer

∵ not same. (d)

Question 7.

The fraction equivalent to is

#### Answer

(d)

(Dividing numerator and denominator by 9)

Question 8.

The fraction which is not equal to is

#### Answer

is not equal to . (b)

∴

Question 9.

Which of the following fractions is not in the lowest form?

#### Answer

The lowest form of this can be written as

Question 10.

A pair of like fraction is

#### Answer

Like fractions are those fractions who have same denominator. (b)

Question 11.

Which of the following fractions is the greatest?

#### Answer

(a)

Question 12.

Which of the following fractions is the smallest?

#### Answer

(c)

Question 13

Which of the following is a false statement?

Answer

Because, if we multiply and divide the fraction with 4, we get

(c)

Question 14.

#### Answer

Question 15.

#### Answer

Question 16

Anshul eats of a pizza. The fraction of the pizza left is

#### Answer

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

#### Answer

#### Higher Order Thinking Skills **( HOTS )**

Question 1.

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

#### Answer

⇒ 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 ?

#### Answer

(i) Total number of students = 540

Ratio of students who prefer coffee =

∴ Number of student prefer coffee

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

(iii) Number of Mango shake drinkers

Number of coffee drinkers

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.

**Check Your Progress**

Question 1

State whether the following statements are true (T) or false (F):

(i) The fraction 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.

#### Answer

(i) False

As 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?

#### Answer

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 =

Question 3

Match the equivalent fractions from each row:

Answer

Question 4

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

Answer

Question 5

Arrange the following fractions in descending order :

Answer

Question 6.

Simplify:

Answer

Question 7

Evaluate the following:

Answer

Question 8

Asha and Samuel have bookshelves of the same size partly filled with books. Asha’s shelf is full and Samuel’s shelf is full. Whose bookshelf is more full and by what fraction?

Answer

Question 9

A farmer uses four out of five equal strips of his land for wheat crop and of his land for cereal crop. What fraction of his land is available for other crops?

Answer

A farmer has 5 equal strips of land

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

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