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# Multiplication of Fractions

In fractions help , We have several Multiplication Of Fractions examples here , which will help us to understand , how diffetent kind of fractions can be multiplied with each other.

Example for Multiplication Of Fractions

One-quarter of one-seventh of a land is sold for Rs 30,000. What is the value of an eight thirty-fifths of land?

Solution.

One-quarter of one-seventh = $\frac{1}{4}$ × $\frac{1}{7}$ = $\frac{1}{28}$

Now, $\frac{1}{28}$ of a land costs = Rs 30,000

... $\frac{8}{35}$ of the land will cost $\frac{30,000 × 28 × 8}{35}$ = Rs 1,92,000

## Fraction Multiplication Example

After taking out of a purse $\frac{1}{5}$ of its contents, $\frac{1}{12}$ of the remainder was found to be Rs 7.40. What sum did the purse contain at first?

Solution.

After taking out $\frac{1}{5}$ of its contents, the purse remains with $\frac{4}{5}$ of contents. Now, $\frac{1}{12}$ of $\frac{4}{5}$ = Rs 7.40 or, $\frac{1}{15}$ = Rs 7.40 ... 1 = Rs 111

similarly we can do Division Of Fractions as well.

## Example on Fractions

108 + ? $\frac{1}{3}$ + $\frac{2}{5}$ × 3$\frac{3}{4}$ = 10$\frac{1}{2}$

Solution.

Let x be the missing number

= 108 ÷ x of $\frac{1}{3}$ + $\frac{2}{5}$ × 3$\frac{3}{4}$ = 10$\frac{1}{2}$

= 108 ÷ $\frac{1}{3}$x + $\frac{2}{5}$ × $\frac{15}{4}$ = $\frac{21}{2}$

= 3 × $\frac{108}{1}$x + $\frac{3}{2}$ = $\frac{21}{2}$

= 3 × $\frac{108}{1}$x = $\frac{21}{2}$ – $\frac{3}{2}$

= 3 × $\frac{108}{1}$x = 9

= x = 3 $\frac{108}{9}$

x = 36

## Multiplying Fractions Example

This problems is from operations in fractions.

How many $\frac{1}{8}$s are there in 37$\frac{1}{2}$ ?

Solution.

Number of $\frac{1}{8}$’s

= $\frac{75}{2}$ ÷ $\frac{1}{8}$

= $\frac{75}{2}$ × 8

= 300

## Example 1

a person was go multiply a fraction by $\frac{6}{7}$. Instead, he divided and got an answer which exceeds the correct answer by $\frac{1}{7}$. The correct answer was

Solution.

Let x be the fraction

$\frac{7}{6}$x – $\frac{6}{7}$x = $\frac{1}{7}$ ]x = $\frac{6}{13}$

Correct answer = $\frac{6}{7}$x = $\frac{6}{7}$ × $\frac{6}{3}$

= $\frac{36}{91}$

## Example 2

$\frac{? ÷ 12}{0.2 × 3.6}$ = 2

Solution.

Putting x in place of ?

$\frac{1 ÷ 12}{0.2 × 3.6}$ = 2 or, x ÷ 12 = 2 × 0.2 × 3.6

] x = 2 × 0.2 × 3.6 × 12 or,

x = 17.28

## Example 3

?? × 7 × 18 = 84

Solution.

Substituting x for ?, we get

? x × 7 × 18 = 84

or, ?x × 7 = $\frac{84}{18}$ or, (?x × 7)2 = ($\frac{84}{18}$)2

or, x × 7 = $\frac{84 × 84}{18 × 18}$ or, x = $\frac{84 × 84}{18 × 18 × 7}$

= 3.11

## Example 4

2$\frac{3}{1}$ x × y$\frac{1}{2}$ = 7$\frac{3}{4}$, find the values of x and y.

Solution.

Taking the quotient 2, y and 7, we get 2y = 7, which gives the quotient as 3

... y = 3. Substituting the value of y. we get

2$\frac{3}{1}$x × 3$\frac{1}{2}$ = 7$\frac{3}{4}$

Now, [{7$\frac{3}{4}$}{3$\frac{1}{2}$} = 2$\frac{3}{1}$x ] 2$\frac{3}{14}$ = 2$\frac{3}{1}$x

... x = 14, y = 3

## Example 5

A boys was asked to multiply a given number by $\frac{8}{17}$. Instead, he divided the given number by $\frac{8}{17}$ and got the result 225 more than what he should have got if he had multiplied the number by $\frac{8}{17}$.

Solution.

x × $\frac{17}{8}$ – x × $\frac{8}{17}$ = 225

or, $\frac{225}{136}$x = 225

... x = 136

## Example 6

If we multiply a fraction by itself and divide the product by its reciprocal, the fraction thus obtained is 18$\frac{26}{27}$. The original fraction is

Solution.

x × x, $\frac{1}{1}$x = 18$\frac{26}{27}$ or,

x3 = $\frac{512}{27}$

... x3 = ($\frac{8}{3}$)3 and so x = $\frac{8}{3}$

= 2$\frac{2}{3}$