# Using the Proportion Method to Solve Percent Problems

#### There are a variety of ways to solve percent problems, many of which can be VERY confusing. Fortunately, the PROPORTION METHOD will work for all three types of questions:

What number is 75% of 4?

3 is what percent of 4?

75% of what number is 3?

#### Using the PROPORTION METHOD, the set-up is always the same: PERCENT -- the number with the percent sign (%). PART -- the number with the word is. WHOLE -- the number with the word of.

EXAMPLE #1:
What number is 75% of 4?   (or   Find 75% of 4.)
The PERCENT always goes over 100.
(It's a part of the whole 100%.)
4 appears with the word of:
It's the WHOLE and goes on the bottom. We're trying to find the missing PART (on the top).
In a proportion the cross-products are equal:   So 4 times 75 is equal to 100 times the PART.
The missing PART equals 4 times 75 divided by 100.
(Multiply the two opposite corners with numbers; then divide by the other number.)
 4 times 75 = 100 times the part 300 = 100 times the part 300/100 = 100/100 times the part 3 = the part EXAMPLE #2:
3 is what percent of 4?
3 appears with the word is:     It's the PART and goes on top.
4 appears with the word of:
It's the WHOLE and goes on the bottom. We're trying to find the missing PERCENT (out of the whole 100%).
In a proportion the cross-products are equal:   So 3 times 100 is equal to 4 times the PERCENT.
The missing PERCENT equals 100 times 3 divided by 4.
(Multiply the two opposite corners with numbers; then divide by the other number.)
 3 times 100 = 4 times the percent 300 = 4 times the percent 300/4 = 4/4 times the percent 75 = the percent EXAMPLE #3:
75% of what number is 3?   (or 3 is 75% of what number?)
The PERCENT always goes over 100.
(It's a part of the whole 100%.)
3 appears with the word is:
It's the PART and goes on the top. We're trying to find the missing WHOLE (on the bottom).
In a proportion the cross-products are equal:   So 3 times 100 is equal to 75 times the WHOLE.
The missing WHOLE equals 3 times 100 divided by 75.
(Multiply the two opposite corners with numbers; then divide by the other number.)
 3 times 100 = 75 times the whole 300 = 75 times the whole 300/75 = 75/75 times the whole 4 = the whole #### Even unfriendly-looking problems like this can be solved using the PROPORTION METHOD:

EXAMPLE #4:
Find 83 2/3 % of 12.6   (or   What number is 83 2/3 % of 12.6?)
The PERCENT always goes over 100.
(It's a part of the whole 100%.)
12.6 appears with the word of:
It's the WHOLE and goes on the bottom. We're trying to find the missing PART (on the top).
In a proportion the cross-products are equal:   So 12.6 times 83 2/3 is equal to 100 times the PART.
The missing PART equals 12.6 times 83 2/3 divided by 100.
(Multiply the two opposite corners with numbers; then divide by the other number.)
 12.6 times 83 2/3 = 100 times the part (126/10)(251/3) = 100 times the part 31626/30 = 100 times the part (31626/30)(1/100) = (100/1)(1/100)( the part) 31626/3000 = the part 10542/1000 = the part 10.542 = the part PLEASE NOTE:   There are MANY other ways to do the arithmetic in this problem - hopefully this shows the steps in an understandable manner; it is neither the easiest nor the best approach.

The same method can be used to find the PART or the WHOLE if you are given a fraction instead of a percent. (Remember a percent is simply that amount per 100.).   Solve using cross-products:

SAMPLE PROBLEM #1:
 Find 3/4 of 20. Look at the set-up. Check answer15 See the solution.

SAMPLE PROBLEM #2:
 10 is 2/3 of what number? Look at the set-up. Check answer15 See the solution.

 What is 20% of 60?Answer12 12 is 75% of what number?Answer16 6 is what percent of 8?Answer75% 8 is 40% of what?Answer20 33 1/3% of what number is 24?Answer72 Find 12.5% of 400.Answer50 What is 5/8 of 32?Answer20 12 is 2/5 of what?Answer30 What is 87 1/2% of 150?Answer131.25 or 131 1/4 25 is what percent of 30?Answer83 1/3% 60 is 3/8 of what number?Answer160 12 is what fractional part of 20?Answer3/5 12 is what percent of 20?Answer60 9 is 37 1/2% of what?Answer24 What is 0.25% of 30?Answer0.075 or 3/40 15 is what percent of 40?Answer37.5% or 37 1/2% What percent of 60 is 75?Answer125% 45 is 60% of what?Answer75 Find 150% of 30Answer45 Find 7/8 of 20.6Answer18.025 or 18 1/40