4E Percent Word Problems Study Guide

Key Vocabulary

Percent Increase — how much a value goes UP, written as a percent. (aumento porcentual)

Percent Decrease — how much a value goes DOWN, written as a percent. (disminución porcentual)

Original Amount — the starting value before the change. (cantidad original)

New Amount — the value after the increase or decrease. (cantidad nueva)

Change — the difference between the new and original amounts. (cambio)

Key Words in Word Problems

Look for these words to decide what to do:

Key Word	What It Means	Operation
"what percent"	Find the percent	Divide part by whole, then × 100
"percent of"	Find the part	Multiply whole × percent (as decimal)
"increased by"	Goes up	Add
"decreased by"	Goes down	Subtract
"how much more / less"	Find the change	Subtract to find the difference

Step-by-Step

1 Read the problem carefully. Underline the numbers and key words.
2 Identify what is the WHOLE (100%) and what is the PART.
3 Set up the equation: Part = Percent × Whole, or Percent = (Part ÷ Whole) × 100.
4 Solve and check: does the answer make sense?

Example: A school had 400 students last year. This year it has 480. What is the percent increase?

Change = 480 − 400 = 80
Percent = (80 ÷ 400) × 100 = 20% increase

Formula Box

Percent Change = (Change ÷ Original) × 100

Change = New Amount − Original Amount

Watch Out!

Always divide by the ORIGINAL amount, not the new amount, when finding percent change.
Increase vs. Decrease: If the new number is bigger, it is an increase. If it is smaller, it is a decrease.
Read carefully! "What percent OF 50 IS 10" means 10 ÷ 50 = 20%.
"IS" = equals, "OF" = multiply. Use these clues to set up equations.

Practice Problems

1. A bike costs $120. The price increases by 25%. What is the new price?

2. A class had 30 students. Now it has 24 students. What is the percent decrease?

3. Maria scored 45 out of 60 on a test. What percent did she score?