## Finding the whole

 This is 30% of the apples in the barrel. How many apples are in the entire barrel?   To solve this question, we need to remember that 100% represents the "whole" or "the entire thing". In this problem, we do not know how many apples represent 100%, but we do know that 6 apples are equal to 30%.

There are many ways to solve the above problem. Here are a few of them:

 Method 1 Method 2 Method 3 Since 6 apples equals 30%, each apple is 5%. 5 x 20 = 100, so there are 20 apples. NOTE: This proportion was set up by putting 6 and 30% on top, since 6 apples equals 30%.

All three methods will lead to the same answer  - there are 20 apples in the entire barrel.

Example 2

Jennifer scored 12 points for her basketball team. If this was 40% of the total points scored, how many points did her team score altogether?

 Method 1 Method 2 Method 3 Method 4 12 points can be broken into four groups of 3. This means every 3 points is equal to 10%. Using a table, we can scale the ratio of 12 to 40 up and down. Eventually, we can add 80% and 20% to find the number of points in 100%. This proportion follows the format of $\frac{part}{whole}=\frac{part}{whole}$ . 12 points and 40% are the "parts", so they go on top. Since 40% can be partially reduced to $\frac{12}{30}$, this shows that there were 30 points scored altogether.

# Self-Check

Question 1

This is 60% of the band. How many musicians are in the whole band?

Question 2

These are 8% of the cars in the parking lot. How many cars are in the parking lot?

Question 3

This is 40% of the birds in the cage. How many birds are in the cage?