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Elan Coil [88]
3 years ago
6

1. If the same number is added to the numerator and subtracted from the denominator of 23/12, the resulting fraction is equivale

nt to the reciprocal of  2/3. What is the number?
Mathematics
1 answer:
ICE Princess25 [194]3 years ago
8 0

Answer:

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

so

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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