Sixty is 5/6 of what number

Sixty is 5/6 of what number

The Correct Answer and Explanation is :

The correct answer is: 72.

To find out what number sixty is ( \frac{5}{6} ) of, we can set up a simple equation. Let ( x ) be the unknown number. The relationship can be expressed as:

[
\frac{5}{6} x = 60
]

To solve for ( x ), we need to isolate it on one side of the equation. We can do this by multiplying both sides by the reciprocal of ( \frac{5}{6} ), which is ( \frac{6}{5} ):

[
x = 60 \times \frac{6}{5}
]

Next, we perform the multiplication:

[
x = 60 \times \frac{6}{5} = \frac{60 \times 6}{5}
]

Calculating the numerator:

[
60 \times 6 = 360
]

Now we divide this by 5:

[
x = \frac{360}{5} = 72
]

Therefore, sixty is ( \frac{5}{6} ) of 72.

Explanation

The solution process involves understanding the concept of fractions and their relationships to whole numbers. The fraction ( \frac{5}{6} ) signifies that we are dealing with five parts out of a total of six. To find the whole number from which these parts are taken, we essentially reverse the operation implied by the fraction.

When we set up the equation ( \frac{5}{6} x = 60 ), it clearly states that if we take ( \frac{5}{6} ) of some number ( x ), the result will be 60. By multiplying both sides of the equation by the reciprocal of ( \frac{5}{6} ), we can effectively solve for ( x ).

The use of reciprocals is a fundamental aspect of algebra. By multiplying by ( \frac{6}{5} ), we counteract the ( \frac{5}{6} ) on the left side, thus allowing us to solve for the unknown ( x ) easily.

This method highlights the importance of understanding how to manipulate equations and fractions to isolate variables. In this case, we find that ( 72 ) is the complete whole number from which ( 60 ) is derived as ( \frac{5}{6} ).