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# Eight times the reciprocal of a number equals 2 times the reciprocal of 4. What is the number?

how to solve geometry word problems

### 2 Answers by Expert Tutors

Michael F. | Mathematics TutorMathematics Tutor
4.7 4.7 (6 lesson ratings) (6)
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Eight times the reciprocal of a number equals 2 times the reciprocal of 4. What is the number?
8×1/r=8/r=2×1/4=2/4=1/2
8/r=1/2
1/r=1/16
r=16
William B. | Biology, Chemistry and Math tutor in Northern Lake CountyBiology, Chemistry and Math tutor in Nor...
4.9 4.9 (10 lesson ratings) (10)
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To begin this problem, you have to know what the reciprocal of a number means. The reciprocal of a number means one over said number. So the reciprocal of 4 would be 1/4 or .25.

So 2*.25=.5

From the beginning portion of the word problem, we know that 8*(1/x) equals .5.

Divide both sides by 8 and you get (1/x)=.0625 which is 1/16. So x equals 16.

To make sure we are right, we can plug x back into the equation.

8*(1/16)=2*(1/4)
.5=.5 So we are correct.