Question

what number should be added to 3 1/2 of 4/5, So that the sum may be 18​

Answer 1

Answer:

17/10

Step-by-step explanation:

1) 3/2 + 4/5 + x = 18

2) (155 + 8+ 10x) 10=8 [takeing LCM of 2 5 and 1 163 + 10 x = 180

10 x = 180 -163

x = 17/10

hence 17/10 must be added to 3/2 and 4/5 to get 18

Answer 2

★ How to do :-

Here, we are given that the product of two numbers becomes the first number that should be added to the other number. We are also given with the answer obtained while adding those two numbers. We are asked to find the second number that the product of two numbers to be added with. So, first we should find the product those two numbers and then, we should shift the answer obtained from LHS to RHS and then we can find the value of that second fraction. We can also verify our answer by the verification method at the last of our answer by substituting the value of the second number. So, let's solve!!

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➤ Solution :-

Let the other number be y

${\sf \leadsto \bigg( 3 \dfrac{1}{2} \times \dfrac{4}{5} \bigg) + y = 18}$

Convert the given mixed fraction to improper fraction.

${\sf \leadsto \bigg( \dfrac{7}{2} \times \dfrac{4}{5} \bigg) + y = 18}$

Write both numerators and denominators in a common fraction.

${\sf \leadsto \bigg( \dfrac{7 \times 4}{2 \times 5} \bigg) + y = 18}$

Multiply the fractions now.

${\sf \leadsto \dfrac{28}{10} + y = 18}$

Write the fraction in lowest form by cancellation method.

${\sf \leadsto \dfrac{14}{5} + y = 18}$

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

${\sf \leadsto y = 18 - \dfrac{14}{5}}$

LCM of 1 and 5 is 5.

${\sf \leadsto y = \dfrac{18 \times 5}{1 \times 5} - \dfrac{14}{5}}$

Multiply the numerators and denominators of first fraction on RHS.

${\sf \leadsto y = \dfrac{90}{5} - \dfrac{14}{5}}$

Write both numerators with a common denominator.

${\sf \leadsto y = \dfrac{90 - 14}{5}}$

Subtract the numbers to get the value of y.

${\sf \leadsto y = \dfrac{76}{5}}$

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${\red{\underline{\boxed{\bf So, \: the \: other \: number \: is \: \dfrac{76}{5}.}}}}$

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Verification :-

${\sf \leadsto \dfrac{14}{5} + y = 18}$

Substitute the value of y.

${\sf \leadsto \dfrac{14}{5} + \dfrac{76}{5} = 18}$

Write both numerators with a common denominator.

${\sf \leadsto \dfrac{14 + 76}{5} = 18}$

Add the numerators now.

${\sf \leadsto \dfrac{90}{5} = 18}$

Write the fraction on LHS in lowest form.

${\sf \leadsto 18 = 18}$

So,

${\sf \leadsto LHS = RHS}$

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Hence verified !!