# Fractions - Class 6 - Mathematics

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## Examples - Fractions | NCERT | Mathematics | Class 6

Express the following as mixed fractions :

(a) $\frac{17}{4}$

(b) $\frac{11}{3}$

(c) $\frac{27}{5}$

(d) $\frac{7}{3}$

To express the given fractions as mixed fractions, we divide the numerator by the denominator to find out how many whole units there are, and then use the remainder as the new numerator of the fraction part. Here are the calculations for each:

(a) $\frac{17}{4}$:

Whole units: $17 \div 4 = 4$, with a remainder of $1$.

Mixed fraction: $4\frac{1}{4}$.

(b) $\frac{11}{3}$:

Whole units: $11 \div 3 = 3$, with a remainder of $2$.

Mixed fraction: $3 \frac{2}{3}$.

(c) $\frac{27}{5}$:

Whole units: $27 \div 5 = 5$, with a remainder of $2$.

Mixed fraction: $5 \frac{2}{5}$.

(d) $\frac{7}{3}$:

Whole units: $7 \div 3 = 2$, with a remainder of $1$.

Mixed fraction: $2 \frac{1}{3}$.

Therefore, the mixed fractions are:

(a) $4\frac{1}{4}$

(b) $3 \frac{2}{3}$

(c) $5 \frac{2}{5}$

(d) $2 \frac{1}{3}$

Express the following mixed fractions as improper fractions:

(a) $2 \frac{3}{4}$

(b) $7 \frac{1}{9}$

(c) $5 \frac{3}{7}$

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Sign up nowFind the equivalent fraction of $\frac{2}{5}$ with numerator 6 .

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Sign up nowFind the equivalent fraction of $\frac{15}{35}$ with denominator 7.

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Sign up nowFind the equivalent fraction of $\frac{2}{9}$ with denominator 63.

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Compare $\frac{4}{5}$ and $\frac{5}{6}$.

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Compare $\frac{5}{6}$ and $\frac{13}{15}$.

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Subtract $\frac{3}{4}$ from $\frac{5}{6}$.

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Add $\frac{2}{5}$ to $\frac{1}{3}$.

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Simplify $\frac{3}{5}-\frac{7}{20}$

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Add $2 \frac{4}{5}$ and $3 \frac{5}{6}$

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Find $4 \frac{2}{5}-2 \frac{1}{5}$

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Simplify: $8 \frac{1}{4}-2 \frac{5}{6}$

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## Exercise 7.1 - Fractions | NCERT | Mathematics | Class 6

Write the fraction representing the shaded portion.

(i) Triangle within a triangle – 2/4 shaded

(ii) 3x3 square grid – 8/9 shaded

(iii) Group of circles – 4/8 shaded

(iv) Circle with a shaded segment – 1/4 shaded

(v) Staircase shape – 3/7 shaded

(vi) Group of flowers – 3/12 shaded

(vii) Group of pencils – 10/10 shaded

(viii) Complex triangle design – 4/9 shaded

(ix) Flower design – 4/8 shaded

(x) Insect design – 1/2 shaded

Draw a circle. Divide it into six parts. colour one part

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Identify the error, if any.

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What fraction of a day is 8 hours? with steps

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What fraction of an hour is 40 minutes? with steps

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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? with steps

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

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

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

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

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What fraction of these circles have X's in them? (There are 8 circles. 4 are covered with X) with steps

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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? with steps

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## Exercise 7.2 - Fractions | NCERT | Mathematics | Class 6

Draw number lines and locate the points on them:

(a) $\frac{1}{2}, \frac{1}{4}, \frac{3}{4}, \frac{4}{4}$

(b) $\frac{1}{8}, \frac{2}{8}, \frac{3}{8}, \frac{7}{8}$

(c) $\frac{2}{5}, \frac{3}{5}, \frac{8}{5}, \frac{4}{5}$

Here are the number lines with the indicated points located on them:

(a) Points: $\frac{1}{2}, \frac{1}{4}, \frac{3}{4}, \frac{4}{4}$

(b) Points: $\frac{1}{8}, \frac{2}{8}, \frac{3}{8}, \frac{7}{8}$

(c) Points: $\frac{2}{5}, \frac{3}{5}, \frac{8}{5}, \frac{4}{5}$

Express the following as mixed fractions : with steps

(a) $\frac{20}{3}$

(b) $\frac{11}{5}$

(c) $\frac{17}{7}$

(d) $\frac{28}{5}$

(e) $\frac{19}{6}$

(f) $\frac{35}{9}$

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Express the following as improper fractions : with steps

(a) $7 \frac{3}{4}$

(b) $5 \frac{6}{7}$

(c) $2 \frac{5}{6}$

(d) $10 \frac{3}{5}$

(e) $9 \frac{3}{7}$

(f) $8 \frac{4}{9}$

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## Exercise 7.3 - Fractions | NCERT | Mathematics | Class 6

Draw number lines and locate the points on them:

a. shaded part 1/2

b. shaded part 2/4

c. shaded part 3/6

d. shaded part 4/8

Here are the number lines with the located points for each shaded part:

a. Shaded part $\frac{1}{2}$:

b. Shaded part $\frac{2}{4}$:

c. Shaded part $\frac{3}{6}$:

d. Shaded part $\frac{4}{8}$:

Note: You'll observe that all the fractions reduce to $\frac{1}{2}$, and hence, the point located on the number line is the same for all four cases.

Draw number lines and locate the points on them:

a. shaded part 4/12

b. shaded part 3/9

c. shaded part 2/6

d. shaded part 1/3

e. shaded part 6/15

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Express the following as mixed fractions :

(a) Shaded part 1/2

(b) Shaded part 4/6

(c) Shaded part 3/9

(d) Shaded part 2/8

(e) Shaded part 3/4

(i) 6/18

(ii) 4/8

(iii) 12/16

(iv) 8/12

(v) 4/16

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Replace $\square$ in each of the following by the correct number :

(a) $\frac{2}{7}=\frac{8}{\square}$

(b) $\frac{5}{8}=\frac{10}{\square}$

(c) $\frac{3}{5}=\frac{\square}{20}$

(d) $\frac{45}{60}=\frac{15}{\square}$

(e) $\frac{18}{24}=\frac{\square}{4}$

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Find the equivalent fraction of $\frac{3}{5}$ having

(a) denominator 20

(b) numerator 9

(c) denominator 30

(d) numerator 27

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Find the equivalent fraction of $\frac{36}{48}$ with

(a) numerator 9

(b) denominator 4

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Check whether the given fractions are equivalent :

(a) $\frac{5}{9}, \frac{30}{54}$

(b) $\frac{3}{10}, \frac{12}{50}$

(c) $\frac{7}{13}, \frac{5}{11}$

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Reduce the following fractions to simplest form :

(a) $\frac{48}{60}$

(b) $\frac{150}{60}$

(c) $\frac{84}{98}$

(d) $\frac{12}{52}$

(e) $\frac{7}{28}$

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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?

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Match the equivalent fractions and write two more for each.

(i) $\frac{250}{400}$ a) $\frac{2}{3}$

(iv) $\frac{180}{360}$ (d) $\frac{5}{8}$

(ii) $\frac{180}{200}$ (b) $\frac{2}{5}$

(v) $\frac{220}{550}$ (e) $\frac{9}{10}$

(iii) $\frac{660}{990}$ (c) $\frac{1}{2}$

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## Exercise 7.4 - Fractions | NCERT | Mathematics | Class 6

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

For both the circle and square grids, we will first list the shaded portions as fractions and then arrange them in both ascending and descending order. Here's how to approach it:

### Circle Grids:

First circle: $3/8$

Second circle: $6/8 = 3/4$

Third circle: $4/8 = 1/2$

Fourth circle: $1/7$

### Square Grids:

First square grid: $8/9$

Second square grid: $4/9$

Third square grid: $3/9 = 1/3$

Fourth square grid: $6/9 = 2/3$

Now, we'll arrange them in ascending and descending order.

### Circle Grids - Ascending Order:

$1/7 < 1/2 < 3/8 < 3/4$

### Circle Grids - Descending Order:

$3/4 > 3/8 > 1/2 > 1/7$

### Square Grids - Ascending Order:

$1/3 < 4/9 < 2/3 < 8/9$

### Square Grids - Descending Order:

$8/9 > 2/3 > 4/9 > 1/3$

These sequences were arranged by comparing the value of each fraction. Fractions with a smaller numerator relative to their denominator are typically smaller. However, to compare fractions accurately, especially when they have different denominators, either find a common denominator or convert them to decimal form. In this scenario, some simplifications were made for fractions with common denominators to facilitate direct comparison.

Compare the fractions and put an appropriate sign.

(a) $\frac{3}{6} \square \frac{5}{6}$

(b) $\frac{1}{7} \square \frac{1}{4}$

(c) $\frac{4}{5} \square \frac{5}{5}$

(d) $\frac{3}{5} \square \frac{3}{7}$

Make five more such pairs and put appropriate signs.

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

(a) $\frac{1}{6} \square \frac{1}{3}$

(b) $\frac{3}{4} \square \frac{2}{6}$

(c) $\frac{2}{3} \square \frac{2}{4}$

(d) $\frac{6}{6} \square \frac{3}{3}$

(e) $\frac{5}{6} \square \frac{5}{5}$

Make five more such problems and solve them with your friends.

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

(a) $\frac{1}{2} \square \frac{1}{5}$

(b) $\frac{2}{4} \square \frac{3}{6}$

(c) $\frac{3}{5} \square \frac{2}{3}$

(d) $\frac{3}{4} \square \frac{2}{8}$

(e) $\frac{3}{5} \square \frac{6}{5}$

(f) $\frac{7}{9} \square \frac{3}{9}$

(g) $\frac{1}{4} \square \frac{2}{8}$

(h) $\frac{6}{10} \square \frac{4}{5}$

(i) $\frac{3}{4} \square \frac{7}{8}$

(j) $\frac{6}{10} \square \frac{3}{5}$

(k) $\frac{5}{7} \square \frac{15}{21}$

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

(a) $\frac{2}{12}$

(b) $\frac{3}{15}$

(c) $\frac{8}{50}$

(d) $\frac{16}{100}$

(e) $\frac{10}{60}$

(f) $\frac{15}{75}$

(g) $\frac{12}{60}$

(h) $\frac{16}{96}$

(i) $\frac{12}{75}$

(j) $\frac{12}{72}$

(k) $\frac{3}{18}$

(1) $\frac{4}{25}$

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

(a) Is $\frac{5}{9}$ equal to $\frac{4}{5}$ ?

(b) Is $\frac{9}{16}$ equal to $\frac{5}{9}$ ?

(c) Is $\frac{4}{5}$ equal to $\frac{16}{20}$ ?

(d) Is $\frac{1}{15}$ equal to $\frac{4}{30}$ ?

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Ila read 25 pages of a book containing 100 pages. Lalita read $\frac{2}{5}$ of the same book. Who read less? with steps

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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? with steps

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In a class A of 25 students, 20 passed with $60 \%$ or more marks; in another class B of 30 students, 24 passed with $60 \%$ or more marks. In which class was a greater fraction of students getting with $60 \%$ or more marks?