Mathematics: 1. if the same number is added to the numerator and subtracted from the denominator of 23/12, the resulting fraction is equivalent to the reciprocal of 2/3. what is the number?

Convert into fractions with equivalent denominators.Hope this helps.頑張って!...

1. if the same number is added to the numerator and

Ответ:

Epicbuildzz

07.01.2022

Mathematics

The number is -2

Step-by-step explanation:

step 1

Find the reciprocal of 2/3

Remember that when multiply a number by its reciprocal, the result is 1

The reciprocal of 2/3 is 3/2

step 2

Let

x-----> the number added to the numerator and denominator

$\frac{23+x}{12-x}=\frac{3}{2}$

Solve for x

$2(23+x)=3(12-x)\\46+2x=36-3x\\2x+3x=36-46\\5x=-10\\x=-2$

step 3

verify

$\frac{23+x}{12-x}$

substitute x=-2

$\frac{23-2}{12+2}$

$\frac{21}{14}$

Simplify

$\frac{3}{2}$ ----> is ok

therefore

The number is -2

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Ответ:

EsiahJohnson

05.06.2022

Mathematics

Convert into fractions with equivalent denominators.

$\frac{5}{8}=\frac{45}{72}$

$\frac{3}{9}=\frac{24}{72}$

$y+\frac{24}{72}=\frac{45}{72}$

$y=\frac{21}{72}$

$y=\frac{7}{24}$

Hope this helps.

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1. if the same number is added to the numerator and subtracted from the denominator of 23/12, the resulting fraction is equivalent to the reciprocal of 2/3. what is the number?

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