Question

3) What number should be added to 1/4 to get 2/5 ?​

Answer 1

★ How to do :-

Here, we are given with a fraction and the sum of two fractions. But, we are not given with the other number which should be added to the given fraction. We can take the value of other number as x. Then, we can shift the constants and the variables on two different sides, by changing the signs. Then, we can find the value of x by subtracting those two fractions. We also verify the statement by substituting the value of other fraction anf then check it. So, let's solve!!

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➤ Solution :-

${\tt \leadsto \dfrac{1}{4} + x = \dfrac{2}{5}}$

Shift the first number on LHS to RHS, changing it's sign.

${\tt \leadsto x = \dfrac{2}{5} - \dfrac{1}{4}}$

LCM of 5 and 4 is 20.

${\tt \leadsto x = \dfrac{2 \times 4}{5 \times 4} - \dfrac{1 \times 5}{4 \times 5}}$

Multiply the numerator and denominator of both fractions in RHS.

${\tt \leadsto x = \dfrac{8}{20} - \dfrac{5}{20}}$

Write both numerators with one common denominator and subtract them.

${\tt \leadsto x = \dfrac{8 - 5}{20} - \dfrac{3}{20}}$

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Verification :-

${\tt \leadsto \dfrac{1}{4} + x = \dfrac{2}{5}}$

Substitute the value of x.

${\tt \leadsto \dfrac{1}{4} + \dfrac{3}{20} = \dfrac{2}{5}}$

LCM of 4 and 20 is 20.

${\tt \leadsto \dfrac{1 \times 5}{4 \times 5} + \dfrac{3}{20} = \dfrac{2}{5}}$

Multiply the numerator and denominator of first fraction on LHS.

${\tt \leadsto \dfrac{5}{20} + \dfrac{3}{20} = \dfrac{2}{5}}$

Write both numerators on LHS with common denominator.

${\tt \leadsto \dfrac{5 + 3}{20} = \dfrac{2}{5}}$

Add the numerators on LHS.

${\tt \leadsto \dfrac{8}{20} = \dfrac{2}{5}}$

Write the fraction on LHS in lowest form by cancellation method.

${\tt \leadsto \dfrac{2}{5} = \dfrac{2}{5}}$

So,

${\tt \leadsto LHS = RHS}$

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Hence verified !!

Answer 2

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★Solution:-

• Let the number added to 1/4 be x to get 2/5.

According To Question,

$\frac{1}{4} + x = \frac{2}{5} \\ \\ :\implies \: x = \frac{2}{5} - \frac{1}{4} \\ \\ :\implies \: x = \frac{8 - 5}{20} \\ \\ :\implies \: x = \frac{3}{20}$

★Verification:-

$:\implies \frac{1}{4} + \frac{3}{20} = \frac{2}{5} \\ \\ :\implies \frac{5 + 3}{20} = \frac{2}{5} \\ \\ : \implies \frac{ \cancel8 \cancel{\tiny4 } }{ \cancel{20 \tiny \cancel{10} }} = \frac{2}{5} \\ \\ :\implies \frac{2}{5} = \frac{2}{5}$

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All Done! :D