Fraction questions for class 6

The following questions on fractions have different types of questions that can be practiced by the students to get more ideas to solve the problems based on fractions.

Contents

Fraction questions for class 6 (solved examples)

Example 1: Make equivalent fractions by multiplying the numerator and denominator by the given number.

(a) $\frac{2}{3}$ by 4 (b) $\frac{3}{7}$

by 5

Sol. (a) $\frac{2}{3}=\frac{2 \times 4}{3\times 4}=\frac{8}{12}$ Ans. $\frac{2}{3}$

and $\frac{8}{12}$ are equivalent fractions.

(b) $\frac{3}{7}=\frac{3\times 5}{7\times 5}=\frac{15}{35}$

Ans. $\frac{3}{7}$ and $\frac{15}{35}$

are equivalent fractions.

Example 2 : Make equivalent fractions by dividing the numerator and denominator by the given number.

(a) $\frac{12}{36}$ by 3 (b) $\frac{6}{14}$

by 2

Sol. (a) $\frac{12}{36}=\frac{12/3}{36/3}=\frac{4}{12}$ Ans. $\frac{12}{36}$

and $\frac{4}{12}$ are equivalent fractions.

(b) $\frac{6}{14}=\frac{6/2}{14/2}=\frac{3}{7}$

Ans. $\frac{6}{14}$ and $\frac{3}{7}$

are equivalent fractions.

Example 3: Fill in each box to make equivalent fractions.

(a) $\frac{1}{2}=\frac{\square }{10}$ (b) $\frac{6}{14} =\frac{\square }{7}=\frac{9}{\square }=\frac{15}{\square }$

Sol. (a) $\frac{1\times 5}{2\times 5}=\frac{\left [ 5 \right ]}{10}$

(b) $\frac{6}{14}=\frac{6/2}{14/2}=\frac{\left [ 3 \right ]}{7}, \, \, \frac{3\times 3}{7\times 3}=\frac{9}{\left [ 21 \right ]},\, \, \, \frac{3\times 5}{7\times 5}=\frac{15}{\left [ 35 \right ]}$

. Thus $\frac{6}{14} =\frac{\left [ 3 \right ] }{7}=\frac{9}{\left [ 21 \right ]}=\frac{15}{\left [ 35 \right ] }$

Example 4: Write $\frac{6}{10},\frac{5}{10},\frac{2}{10}\, \, and\, \frac{7}{10}$

in ascending order.

Sol. The fractions $\frac{6}{10},\frac{5}{10},\frac{2}{10}\, \, and\, \frac{7}{10}$ are like fractions. Let us compare their numerators.

Since 2<5<6<7. Therefore $\frac{2}{10}< \frac{5}{10}< \frac{6}{10}< \frac{7}{10}$

Example 5: Arrange the following fractions in descending order. $\frac{3}{2}, \frac{1}{2}, \frac{7}{10}, \frac{5}{6}$

Sol. The given fractions are unlike fractions. So we shall change them into equivalent fractions with common denominator, which is the LCM of 5, 2, 10,6 .

LCM of 5, 2, 10, 6 are 30 .

Changing each of the given fractions into equivalent fraction with denominator 30, we get

$\frac{3}{5} =\frac{3\times 6}{5\times 6}=\frac{18}{30}$

, $\frac{1}{2}=\frac{1\times 15}{2\times 15}=\frac{15}{30}$ , $\frac{7}{10}=\frac{7\times 3}{10\times 3}=\frac{21}{30}$

, $\frac{5}{6}=\frac{5\times5}{6\times 5}=\frac{25}{30}$

Clearly , $\frac{25}{30}>\frac{21}{30}>\frac{18}{30}>\frac{15}{30}$

Hence , the given fractions in descending order are $\frac{5}{6}>\frac{7}{10}>\frac{3}{5}>\frac{1}{2}$

Example 6: Add $3\frac{1}{2}$

and $4\frac{1}{5}$ .

Sol. Change mixed numbers to improper fractions, $3\frac{1}{2}=\frac{7}{2}$

and $4\frac{1}{5}=\frac{21}{5}$ .

Now Convert unlike fractions to like fractions with the same denominator 10 (LCM of 2 and 5) and add them

$\frac{7\times 5}{2\times 5}=\frac{35}{10},\, \, \, \, \frac{21\times 2}{5\times 2}=\frac{42}{10}$

Hence $3\frac{1}{2}+4\frac{1}{5}=\frac{7}{2}+\frac{21}{5}=\frac{35}{10}+\frac{42}{10}=\frac{77}{10}=7\frac{7}{10}$ Ans. $7\frac{7}{10}$

Example 7: Aditya mixed $2\frac{1}{8}$ L of green paint with $3\frac{5}{16}$

L of red paint. How much paint does he have now?

Sol. Quantity of green paint = $2\frac{1}{8}$ L

quantity of red paint= $3\frac{5}{16}$

Total quantity of paint= $2\frac{1}{8}$ L + $3\frac{5}{16}$

L = $\frac{17}{8}$ L + $\frac{53}{16}$

L

The LCM of 8 and 16 =16, $\frac{17}{8}=\frac{17\times 2}{8\times 2}=\frac{34}{16}$

So, $\frac{17}{8}$

+ $\frac{53}{16}$ = $\frac{34}{16}+\frac{53}{16}=\frac{34+53}{16}=\frac{87}{16}=5\frac{7}{6}$

Ans. Aditya has $5\frac{7}{16}$ L of paint.

Example 8: Simplify $\frac{7}{9}-\frac{2}{3}+\frac{5}{6}$

Sol. LCM of 9, 3, 6 is 18

Now $\frac{7}{9}=\frac{7 \times 2}{9\times 2}=\frac{14}{18}$

$\frac{2}{3}=\frac{2\times 6}{3\times 6}=\frac{12}{18}$

$\frac{5}{6}=\frac{5\times 3}{6\times 3}=\frac{15}{18}$

$\frac{7}{9}-\frac{2}{3}+\frac{5}{6}$

= $\frac{14}{18}-\frac{12}{18}+\frac{15}{18}$ = $\frac{14-12+15}{18}=\frac{17}{18}$

Example 9: What must be subtracted from $6\frac{3}{4}$ to get $4\frac{1}{6}$

Sol. The fraction to be subtracted =- $6\frac{3}{4}$ – $4\frac{1}{6}$

= $\frac{27}{4}-\frac{25}{6}$

= $\frac{27\times 3}{4\times 3}-\frac{25\times 2}{6\times 2}$

= $\frac{81}{12}-\frac{50}{12}=\frac{81-50}{12}=\frac{31}{12}=2\frac{7}{12}$

Hence the required fraction to be subtracted is $2\frac{7}{12}$

Example 10: From a rope of 7 meters long, two pieces of length $2\frac{3}{5}$ meters and $3\frac{3}{10}$

meters were cut off. What is the length of the remaining rope?

Sol. Total length of the rope=7 meters

Total length cut off = $2\frac{3}{5} m+3\frac{3}{10} m=\frac{13}{5}m+\frac{33}{10} m$

= $\frac{26}{10}+\frac{33}{10}=\frac{59}{10}m$

Length of the remaining rope= $7-\frac{59}{10}=\frac{70}{10}-\frac{59}{10}=\frac{11}{10}m=1\frac{1}{10}m$

Hence, the length of the remaining rope is $1\frac{1}{10}m$

Multiple Choice Questions(MCQ Fractions questions for class 6 with answers)

Tick the correct answer.

(i)Which of the following is an improper fraction?

(a) $\frac{2}{3}$ (b) $\frac{16}{17}$

(ii) Which fraction is greater than $\frac{1}{2}$ ?

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

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

(d) $\frac{3}{4}$

(iii) Which of the following fractions is the smallest?

(a) $\frac{11}{9}$

(b) $\frac{11}{7}$ (c) $\frac{11}{10}$

(d) $\frac{11}{6}$

(iv) The mixed numeral for the fraction $\frac{37}{8}$

(a) $4\frac{5}{8}$ (b) 3 $\frac{13}{8}$

(v)The fraction which is not equal to $\frac{4}{5}$ is

(a) $\frac{40}{50}$

(b) $\frac{12}{15}$ (c) $\frac{16}{20}$

(d) $\frac{9}{15}$

(vi) Which of the following is not equal to the others?

(a) $\frac{6}{8}$

(b) $\frac{12}{16}$ (c) $\frac{15}{25}$

(d) $\frac{18}{24}$

(vii) Which of the following fractions is the greatest?

(a) $\frac{5}{7}$

(b) $\frac{5}{6}$ (c) $\frac{5}{9}$

(d) $\frac{5}{8}$

(viii) Write $\frac{3}{4}$

as a fraction with denominator 44.

(a) $\frac{33}{44}$ (b) $\frac{5}{44}$

(ix) $4\frac{1}{3}-1\frac{2}{3}+5$

(a) $7\frac{2}{3}$

(b) $\frac{2}{3}$ (c) $5\frac{1}{3}$

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

(x) $4\frac{1}{6}+2\frac{1}{2}+1\frac{1}{3}$

(a) 7 (b) 8 (c) $\frac{2}{3}$ (d) $\frac{5}{4}$

Ans. (i) (c) (ii) (d) (iii) (c) (iv) (a) (v) (d) (vi) (c) (vii) (b) (viii) (a) (ix) (a) (x) (b)

Fractions class 6 extra questions

Fill in the blanks-type questions. (with answers)

(i) A …………………… indicates one or more parts of a whole.

(ii) A fraction obtained by multiplying or dividing the numerator and denominator by the same non-zero number is called an …………………………… of the given fraction.

(iii) A fraction with a numerator less than its denominator is called a ………………………….

(iv) A fraction with a numerator greater than or equal to its denominator is called an ………………………….

(v) Fractions with the same denominators are called ……………………….

(vi) Fractions with different denominators are called ………………………….

(vii) A fraction is said to be in its ………………………….. if the HCF of its numerator and denominator is 1.

(viii) If we compare two fractions with the same denominators, then the one with the greater numerator is ……………….

(ix) If we compare two fractions with the same numerators, then the one with the smaller denominator is ……………….

(x) A combination of a whole number and a proper fraction is a …………………

Ans. (i) Fraction (ii) Equivalent fraction (iii) proper fraction (iv) improper fraction (v) like fractions (vi) unlike fractions (vii) simplest form (viii) greater (ix) greater (x) mixed numeral

Tick the correct answer.

(i) $\frac{1}{3}+\frac{1}{6}=.........$