Question

Solve this given equation:
$\: \: \large{3 \frac{1}{x} \times 5 \frac{1}{4} = 17 \frac{1}{2} }$

▪don't spam ​

Answer 1

$\large\underline{\sf{Solution-}}$

Given expression is

$\rm \: 3 \dfrac{1}{x} \times 5 \dfrac{1}{4} = 17 \dfrac{1}{2}$

can be rewritten as

$\rm \: \dfrac{3x + 1}{x} \times \dfrac{20 + 1}{4} = \dfrac{34 + 1}{2}$

$\rm \: \dfrac{3x + 1}{x} \times \dfrac{21}{4} = \dfrac{35}{2}$

$\rm \: \dfrac{3x + 1}{x} = \dfrac{35}{2} \div \dfrac{21}{4}$

$\rm \: \dfrac{3x + 1}{x} = \dfrac{\green{ \cancel{35} \: \: ^{5} }}{ \red{ \cancel2}} \times \dfrac{\red{ \cancel4 \: \: ^{2}} }{\green{ \cancel{21} \: \: ^{3}}}$

$\rm \: \dfrac{3x + 1}{x} = \dfrac{5 \times 2}{3}$

$\rm \: \dfrac{3x + 1}{x} \nearrow= \nwarrow \dfrac{10}{3}$

$\rm \: 10 \times x = 3 \times (3x + 1)$

$\rm \: 10 x = 9x + 3$

$\rm \: 10 x - 9x = 3$

$\bf\implies \:x \: = \: 3$

Verification :-

Consider LHS

$\rm \: 3 \dfrac{1}{x} \times 5 \dfrac{1}{4}$

On substituting the value of x, we get

$\rm \: = \: 3 \dfrac{1}{3} \times 5 \dfrac{1}{4}$

$\rm \: = \: \dfrac{9 + 1}{3} \times \dfrac{20 + 1}{4}$

$\rm \: = \: \dfrac{10}{3} \times \dfrac{21}{4}$

$\rm \: = \: \dfrac{\green{ \cancel{10} \: \: ^{5}}}{\red{ \cancel3}} \times \dfrac{\red{ \cancel{21} \: ^{7} }}{\green{ \cancel{2} \: \: ^{2}}}$

$\rm \: = \: \dfrac{7 \times 5}{2}$

$\rm \: = \: \dfrac{35}{2}$

$\rm \: = \: 17\dfrac{1}{2}$

Hence, Verified

Answer 2

Given:-

• A equation

To find:-

• The value of "x".

Solution:-

$\large\underline{\sf{ \implies3 \times \frac{1}{x} \times 5 \times \frac{1}{4} = 17 \times \frac{1}{2} }}$

We know that to convert a mixed fraction into improper fraction we will multiply and add it in the following order and write the denominator as denominator itself.

We multiply the denominator with the whole and add the numerator.

$\large\underline{\sf{ \implies \frac{3x + 1}{x} \times \frac{21}{4} = \frac{35}{2} }}$

$\large\underline{\sf{ \implies \frac{3x + 1}{x} = \frac{ \red{35}}{ \pink{2}} \div \frac{ \red{21}}{ \pink{4}} }}$

$\large\underline{\sf{ \frac{3x + 1}{x} = \frac{ \red{35}}{ \pink{2}} \times \frac{ \pink4}{ \red{21}} }}$

$\large\underline{\sf{ \implies \frac{3x + 1}{x} = \frac{5 \times 2}{3} }}$

$\large\underline{\sf{ \implies3(3x + 1) = 5 \times 2 \times x}}$

$\large\underline{\sf{ \implies9x + 3 = 10x}}$

$\large\underline{\sf{ \implies3 = 10x - 9x}}$

$\large \blue{\underline{ \green{ \boxed{\sf{ \red{\implies3 = x}}}}}}$

Or,

$\large \blue{\underline{ \green{ \boxed{\sf{ \red{ \implies x = 3}}}}}}$

______________________________________

Basic concept!!

• A mixed fraction is a type of fraction which is formed by a whole, a numerator and a denominator.
• A fraction is a part of the whole.
• A improper fraction is a fraction whose numerator is greater than the denominator.