Finding the Whole

Part of the Decimals, Percents & Ratios section of Coddy's Pre-Algebra journey. Lesson 31 of 56.

Sometimes the part is known and the whole is not. 9 members of a club play chess, and they are 20% of the club. How many members does the club have? The part is 20% of the whole, so 0.2 times the whole is 9.

Which number times 0.2 gives 9? Dividing undoes multiplying, the same fact family as 3 times 4 is 12 and 12 divided by 3 is 4. So the whole is the part divided by the percent as a decimal: w = 9 / 0.2. Shift both points one place, as you did for dividing by a decimal, to get 90 / 2, which is 45.

Always check by going forward again: 20% of 45 is 9, exactly the part from the story. A whole is bigger than any part of it under 100%, so if your answer comes out smaller than the part, you have multiplied where you meant to divide.

Challenge

On a bus trip, 12 seats are filled, and that is 30% of all the seats on the bus. How many seats w does the bus have? Write w equal to the calculation, then work it out.