6 is 75% of what number?

Explanation

We will look for the key words is, of, and what number in the percent sentence and translate them to mathematical symbols to form a percent equation.  Then we can solve the equation to find the unknown number.

First, we translate

6 is 75% of what number?

6 = 75% • x

• Write 75% as a decimal: 75% = 0.75
  • 6 = 0.75 • x
• To undo the multiplication by 0.75 and isolate x on the right side, divide both sides of the equation by 0.75.
  • \(\frac{6}{\color{red}{0.75}} = \frac{0.75 \cdot x}{\color{red}{0.75}}\)
• To simplify the fraction on the right side of the equation remove the common factor of 0.75.  On the left side, divide 6 by 0.75.
  • \(\require{cancel} 8 = \frac{\cancel{0.75}^1 \cdot x}{\cancel{0.75}_1}\)
• 8 = x

Thus, 6 is 75% of 8.