# Two-thirds of a number is five-sixths. How do you find the number?

##### 2 Answers

The number is

#### Explanation:

Let the unknown value be

Multiply both sides by

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Consider just the left hand side

Using the principle (by example) that

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Back to the question

So

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Check

left hand side

#### Explanation:

#"let x represent the number"#

#"then " 2/3" of " x =5/6#

#"replace of by multiplication"#

#rArr2/3 xx x=5/6#

#rArr(2x)/3=5/6#

#color(blue)"cross multiplying"#

#rArr2x xx6=5xx3#

#rArr12x=15#

#"divide both sides by 12"#

#(cancel(12) x)/cancel(12)=15/12#

#rArrx=15/12=5/4larr" in simplest form"#