7.RP.A.3
7th Grade
Ratios & Proportional Relationships
Percent Problems
Use proportional relationships to solve multistep ratio and percent problems, including simple interest, tax, markups, markdowns, and percent change.
How to explain it
The anchor students hold onto: Change the percent to a decimal, then multiply by the whole. For an increase multiply by 1 plus the rate; for a decrease, 1 minus the rate. Percent change divides by the ORIGINAL amount.
The new amount = whole times (1 plus or minus the rate) idea becomes percent-as-coefficient work in 7.EE.A.2, and percent reasoning carries forward into consumer math and scaling.
Worked examples
Example 1
Percent Of
Find 30% of 80.
Step 1Change the percent to a decimal: 30% = 0.30.
Step 2Multiply by the whole: 0.30 × 80 = 24.
Answer24
Example 2
Increase
Increase 50 by 20%.
Step 1A 20 percent increase multiplies by 1.20.
Step 250 × 1.20 = 60.
Answer60
Example 3
Percent Change
From 40 to 50: % change?
Step 1Find the change: 50 - 40 = 10.
Step 2Divide by the original: 10 ÷ 40 = 0.25.
Answer25% increase
Common mistakes
What students write
Multiplies by the percent number instead of its decimal.
The fix
Convert first: 25% = 0.25, then 0.25 × 80 = 20.
What students write
Finds the increase but forgets to add it to the original.
The fix
Increase means original + change, or just × (1 + rate).
Teacher tip
Head off the two predictable errors before they happen. First: Convert first: 25% = 0.25, then 0.25 × 80 = 20. Second: Increase means original + change, or just × (1 + rate).