Arrange the following fraction in descending order 3 4 , 7 8 , 7 12 , 17 24

The given fractions are 3 4 , 7 8 , 7 12 , 17 24 These are unlike fractions. So, for arranging them in descending order, we need to first convert them into the like fractions. For that we need to take the LCM of denominators. Thus, by prime factorization of denominators we get 4 = 2 × 2 8 = 2 × 2 × 2 12 = 2 × 2 × 3 24 = 2 × 2 × 2 × 3 Since the maximum number of times the prime factor 2 occurs is three; this happens for 8 and 24 , and the maximum number of times the prime factor 3 occurs is one. ∴ LCM 4 , 8 , 12 , 24 = 2 × 2 × 2 × 3 = 24 Now, let us change each of the given fractions into an equivalent fraction having 24 as its denominator. 3 4 = 3 × 6 4 × 6 = 18 24 7 8 = 7 × 3 8 × 3 = 21 24 7 12 = 7 × 2 12 × 2 = 14 24 17 24 Now arranging the fraction from the highest value to the lowest value of numerator, we get 21 24 > 18 24 > 17 24 > 14 24 ⇒ 7 8 > 3 4 > 17 24 > 7 12 It is the required arrangement of the given fractions in descending order.

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?

Given, Fraction of wall painted by Shubham = 2 3 Fraction of wall painted by Madhavi = 1 3 Total painting by both of them = 2 3 + 1 3 ⇒ Total painting by both of them = 2 + 1 3 ⇒ Total painting by both of them = 3 3 = 1 Hence, they painted the complete wall together.

Find 7 6 + 11 12 + 9 24 .

Given, 7 6 + 11 12 + 9 24 First, we need to take the LCM of denominators 6 = 2 × 3 12 = 2 × 2 × 3 24 = 2 × 2 × 2 × 3 Since the maximum number of times the prime factor 2 occurs is three; and the maximum number of times the prime factor 3 occurs is one. ∴ LCM ( 6 , 12 , 24 ) = 2 × 2 × 2 × 3 = 24 Consider 7 6 + 11 12 + 9 24 = 7 × 4 + 11 × 2 + 9 24 [ ∵ 24 ÷ 6 = 4 and 24 ÷ 12 = 2 ] = 28 + 22 + 9 24 = 28 + 22 + 9 24 = 59 24 Hence, the required sum of the given fractions is 59 24 .

Find the sum of 7 4 + 5 6 .

Given, to find the sum of 7 4 + 5 6 First, we need to find the LCM of denominators 4 = 2 × 2 6 = 2 × 3 Since the maximum number of times the prime factor 2 occurs is two; this happens for 4 . And, the maximum number of times the prime factor 3 occurs is one. ∴ LCM 4 , 6 = 2 × 2 × 3 = 12 Consider 7 4 + 5 6 = ( 7 × 3 ) + ( 5 × 2 ) 12 [Since 12 ÷ 4 = 3 and 12 ÷ 6 = 2 ] = 21 + 10 12 = 31 12 = 2 7 12 Hence, the required sum of fractions is 2 7 12 .

Arrange the following fraction in descending order 2 3 , 3 5 , 7 10 , 8 15

The given fractions are 2 3 , 3 5 , 7 10 , 8 15 These are unlike fractions. So, for arranging them in descending order, we need to first convert them into the like fractions. For that we need to take the LCM of denominators. Thus, by prime factorization of denominators we get 3 = 3 × 1 5 = 5 × 1 10 = 2 × 5 15 = 3 × 5 Since maximum one time each of the prime factor 2 , 3 , 5 has occurred. ∴ LCM ( 3 , 5 , 10 , 15 ) = 2 × 3 × 5 = 30 Now, let us change each of the given fractions into an equivalent fraction having 30 as its denominator. 2 3 = 2 × 10 3 × 10 = 20 30 3 5 = 3 × 6 5 × 6 = 18 30 7 10 = 7 × 3 10 × 3 = 21 30 8 15 = 8 × 2 15 × 2 = 16 30 Now arranging the fraction from the highest value to the lowest value of numerator, we get 21 30 > 20 30 > 18 30 > 16 30 ⇒ 7 10 > 2 3 > 3 5 > 8 15 It is the required arrangement of the given fractions in descending order.

Find the sum of 3 4 5 + 2 3 10 + 1 1 15 .

Given, to find the sum of 3 4 5 + 2 3 10 + 1 1 15 We need to convert the mixed fractions into improper fractions ⇒ 3 4 5 + 2 3 10 + 1 1 15 = ( 3 × 5 ) + 4 5 + ( 10 × 2 ) + 3 10 + 15 + 1 15 = 19 5 + 23 10 + 16 15 Now, we need to take the LCM of the denominators 5 = 5 × 1 10 = 2 × 5 15 = 3 × 5 Since the maximum number of times the prime factors 2 , 3 , and 5 occurs is one. ∴ LCM ( 5 , 10 , 15 ) = 2 × 3 × 5 = 30 Now, we change the unlike fractions to like fractions and then keeping the denominator same, we add the numerator values. 19 5 + 23 10 + 16 15 = 19 × 6 5 × 6 + 23 × 3 10 × 3 + 16 × 2 15 × 2 = 114 30 + 69 30 + 32 30 = 114 + 69 + 32 30 = 215 30 = 43 6 Hence, the required sum of the fractions is 43 6 .

A rectangular sheet of paper is 12 1 2 cm long and 10 2 3 cm wide. Find its perimeter.

Given: Length, l = 12 1 2 = 25 2 cm Breadth, b = 10 2 3 = 32 3 cm Perimeter of the sheet = 2 ( l + b ) = 2 25 2 + 32 3 = 2 75 + 64 6 (since the LCM of the denominators 2 and 3 is 6 ) = 2 × 139 6 = 139 3 = 46 1 3 cm ( 139 ÷ 3 gives quotient 46 and remainder 1 ) Therefore, the perimeter of the rectangular sheet is 46 1 3 cm .

EASY

Earn 100

Identify the missing numerator,

$\frac{5}{8} + \frac{?}{8} = \frac{7}{8}$

The missing numerator is

50% studentsanswered this correctly

Important Questions on Fractions

EASY

Mathematics>Arithmetic>Fractions>Addition and Subtraction of Fractions

What number must be subtracted from both the numerator and the denominator of the fraction

\frac{27}{35}

so that it becomes

\frac{2}{3}

EASY

Mathematics>Arithmetic>Fractions>Addition and Subtraction of Fractions

\frac{1}{4}

of the wall is painted blue,

\frac{1}{2}

is painted yellow and remaining

3 m

is painted white, what is the length of the wall?

EASY

Mathematics>Arithmetic>Fractions>Addition and Subtraction of Fractions

Simplify:

(\frac{2}{9} + \frac{3}{5}) \div (\frac{2}{9} + \frac{2}{5})

EASY

Mathematics>Arithmetic>Fractions>Addition and Subtraction of Fractions

Two-third number of the employees of a company are males and the rest of females. If

\frac{3}{8}

of the male employees and

\frac{2}{5}

of the female employees are temporary employees and the total number of permanent employees is

740

, then

\frac{7}{15}

of the total number of employees exceeds the number of temporary female employees by:

EASY

Mathematics>Arithmetic>Fractions>Addition and Subtraction of Fractions

Simplify

[2 \frac{1}{3} - 1 \frac{1}{2}]

\frac{3}{5} + 1 \frac{2}{5} \div 2 \frac{1}{3}

MEDIUM

Mathematics>Arithmetic>Fractions>Addition and Subtraction of Fractions

In an office,

\frac{5}{8}

of the total number of employees are males and the rest are females,

\frac{2}{5}

of the number of males are non-technical workers while

\frac{2}{3}

of the number of females technical workers. What fraction of the total number of employees are technical workers?

MEDIUM

Mathematics>Arithmetic>Fractions>Addition and Subtraction of Fractions

Arrange the following fraction in descending order

$\frac{3}{4}, \frac{7}{8}, \frac{7}{12}, \frac{17}{24}$

EASY

Mathematics>Arithmetic>Fractions>Addition and Subtraction of Fractions

Shubham painted

\frac{2}{3}

of the wall space in his room. His sister Madhavi helped and painted

\frac{1}{3}

of the wall space. How much did they paint together?

MEDIUM

Mathematics>Arithmetic>Fractions>Addition and Subtraction of Fractions

Find $\frac{7}{6} + \frac{11}{12} + \frac{9}{24}$ .

MEDIUM

Mathematics>Arithmetic>Fractions>Addition and Subtraction of Fractions

Find the sum of $\frac{7}{4} + \frac{5}{6}$ .

EASY

Mathematics>Arithmetic>Fractions>Addition and Subtraction of Fractions

A boy was asked to find

\frac{3}{5}

of a fraction. Instead, he divided the fraction by

\frac{3}{5}

and got an answer which exceeded the correct answer by

\frac{32}{75}

. The correct answer is:

EASY

Mathematics>Arithmetic>Fractions>Addition and Subtraction of Fractions

A number is

18

more than its

\frac{4}{7}

. The number is:

HARD

Mathematics>Arithmetic>Fractions>Addition and Subtraction of Fractions

Find the perimeters of $Δ A B E$ and the rectangle $B C D E$ in this figure. Whose perimeter is greater?

MEDIUM

Mathematics>Arithmetic>Fractions>Addition and Subtraction of Fractions

Arrange the following fraction in descending order

$\frac{2}{3}, \frac{3}{5}, \frac{7}{10}, \frac{8}{15}$

EASY

Mathematics>Arithmetic>Fractions>Addition and Subtraction of Fractions

Cotyledons are also called-

MEDIUM

Mathematics>Arithmetic>Fractions>Addition and Subtraction of Fractions

Find the sum of $3 \frac{4}{5} + 2 \frac{3}{10} + 1 \frac{1}{15}$ .

EASY

Mathematics>Arithmetic>Fractions>Addition and Subtraction of Fractions

A farmer divides

n

cows among his

4

sons in such a way that the first son gets half of the total number of cows, second son gets one-fourth of the whole herd, third l son gets

\frac{1}{5}

of the whole herd and fourth son gets

7

cows. The value of

n

is:

MEDIUM

Mathematics>Arithmetic>Fractions>Addition and Subtraction of Fractions

In a “magic square”, the sum of the numbers in each row, in each column and along the diagonals is the same. Is this a magic square? (Along the first row,

\frac{4}{11} + \frac{9}{11} + \frac{2}{11} = \frac{15}{11}

)

$\frac{4}{11}$	$\frac{9}{11}$	$\frac{2}{11}$
$\frac{3}{11}$	$\frac{5}{11}$	$\frac{7}{11}$
$\frac{8}{11}$	$\frac{1}{11}$	$\frac{6}{11}$

EASY

Mathematics>Arithmetic>Fractions>Addition and Subtraction of Fractions

By adding

1

to numerator as well as to the denominator of a fraction, it becomes

\frac{2}{3}

. What is the original fraction?

MEDIUM

Mathematics>Arithmetic>Fractions>Addition and Subtraction of Fractions

A rectangular sheet of paper is

12 \frac{1}{2} cm

long and

10 \frac{2}{3} cm

wide. Find its perimeter.

Identify the missing numerator, 58+?8=78 The missing numerator is

Important Questions on Fractions

Learn and Prepare for any exam you want !

Identify the missing numerator,

$\frac{5}{8} + \frac{?}{8} = \frac{7}{8}$

The missing numerator is