Question

by what number should 4 whole 7/8 be multiplied to get 87 whole 3/4?​

Answer 1

Answer:

4.7/8 × 18 = 87.3/4

i.e. the final answer is 18.

Answer 2

★ How to do :-

Here, we are given with a fraction that should be multiplied with an other number. We are also given with the answer that should be obtained while multiplying those two fractions. But, we are not given with the second fraction that the first fractions needs to be multiplied with. We are asked to find the same. Here, we use some other concepts such as shifting of numbers from one hand side to the other, which changes the sign of the appropriate number. So, let's solve!!

$\:$

➤ Solution :-

Let the other number be y,

${\tt \leadsto 4 \dfrac{7}{8} \times y = 87 \dfrac{3}{4}}$

Convert both mixed fractions to improper fractions.

${\tt \leadsto \dfrac{39}{8} \times y = \dfrac{351}{4}}$

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

${\tt \leadsto y = \dfrac{351}{4} \div \dfrac{39}{8}}$

Take the reciprocal of second fraction and multiply both the fractions.

${\tt \leadsto y = \dfrac{351}{4} \times \dfrac{8}{39}}$

We can write those fractions in lowest form by cancellation method.

${\tt \leadsto y = \dfrac{\cancel{351} \times 8}{4 \times \cancel{39}} = \dfrac{117 \times 8}{4 \times 13}}$

Now, cancel the other remaining numbers on numerator and denominator.

${\tt \leadsto y = \dfrac{117 \times \cancel{8}}{\cancel{4} \times 13} = \dfrac{117 \times 2}{1 \times 13}}$

Now, multiply the remaining numbers and write it in lowest form.

${\tt \leadsto y = \cancel \dfrac{234}{13} = 18}$

$\:$

${\red{\underline{\boxed{\bf So, \: the \: other \: number \: is \: \: 18}}}}$

━━━━━━━━━━━━━━━━━━━━━

Verification :-

${\tt \leadsto \dfrac{39}{8} \times y = \dfrac{351}{4}}$

Substitute the value of y.

${\tt \leadsto \dfrac{39}{8} \times 18 = \dfrac{351}{4}}$

Write the second number in fractional form.

${\tt \leadsto \dfrac{39}{8} \times \dfrac{18}{1} = \dfrac{351}{4}}$

Multiply the numbers on LHS.

${\tt \leadsto \dfrac{39 \times 18}{8 \times 1} = \dfrac{351}{4}}$

Write the resulting fraction.

${\tt \leadsto \dfrac{702}{8} = \dfrac{351}{4}}$

Write the obtained answer in lowest form by cancellation method.

${\tt \leadsto \dfrac{351}{4} = \dfrac{351}{4}}$

So,

${\sf \leadsto LHS = RHS}$

$\:$

Hence verified !!