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 answer 15 See the solution.







SAMPLE PROBLEM #2:

10 is 2/3 of what number?

Look at the set-up.

Check answer 15 See the solution.







What is 20% of 60?

Answer 12 12 is 75% of what number?

Answer 16 6 is what percent of 8?

Answer 75% 8 is 40% of what?

Answer 20 33 1/3% of what number is 24?

Answer 72 Find 12.5% of 400.

Answer 50 What is 5/8 of 32?

Answer 20 12 is 2/5 of what?

Answer 30 What is 87 1/2% of 150?

Answer 131.25 or 131 1/4 25 is what percent of 30?

Answer 83 1/3% 60 is 3/8 of what number?

Answer 160 12 is what fractional part of 20?

Answer 3/5 12 is what percent of 20?

Answer 60 9 is 37 1/2% of what?

Answer 24 What is 0.25% of 30?

Answer 0.075 or 3/40 15 is what percent of 40?

Answer 37.5% or 37 1/2% What percent of 60 is 75?

Answer 125% 45 is 60% of what?

Answer 75 Find 150% of 30

Answer 45 Find 7/8 of 20.6

Answer 18.025 or 18 1/40

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