Topic A: Ratios & Proportions
Comparing amounts and finding missing values.
01 — Ratios & Unit Rates
Ratios & Unit Rates
A ratio compares two amounts. A unit rate tells you how much for just one.
- Ratio: 3 cats to 5 dogs can be written 3:5 or 3/5.
- Unit rate: divide to get "per 1". $12 for 4 pounds = $3 per pound.
- Best buy: compare unit prices; the smaller price per unit wins.
Example: A car drives 150 miles in 3 hours. 150 ÷ 3 = 50 miles per hour.
Practice — Ratios & Unit Rates
Q1 · Short Answer
Apples cost $6 for 4 pounds. What is the price per pound, in dollars?
Q2 · Multiple Choice
Which is the better buy?
02 — Proportions
Solving Proportions
A proportion says two ratios are equal. Cross-multiply to find the missing number.
- Set up: put matching units in the same spot. miles/hours = miles/hours.
- Cross-multiply: if a/b = c/d, then a × d = b × c.
- Scale drawings: a map scale like 1 inch : 20 miles is a proportion.
Example: 2/5 = x/20 → 5x = 40 → x = 8.
Practice — Solving Proportions
Q3 · Short Answer
Solve: 3/4 = x/12
Q4 · Multiple Choice
On a map, 1 inch = 30 miles. Two towns are 4 inches apart. How many miles apart are they?
Topic B: Percents
Percent of a number, percent change, and interest.
03 — Percent Basics
Percent of a Number
Percent means "out of 100". To find a percent of a number, change the percent to a decimal and multiply.
- Percent → decimal: 25% = 0.25.
- Part = percent × whole: 20% of 50 = 0.20 × 50 = 10.
- Sales tax: add it on. $40 + 8% tax = 40 × 1.08 = $43.20.
- Discount: take it off. $40 with 25% off = 40 × 0.75 = $30.
Example: A $60 jacket is 30% off. 60 × 0.30 = $18 off, so it costs $42.
Practice — Percent of a Number
Q5 · Short Answer
What is 15% of 80?
Q6 · Multiple Choice
A $50 shirt is on sale for 20% off. What is the sale price?
04 — Percent Change & Interest
Percent Change & Simple Interest
Percent change shows how much something grew or shrank compared to where it started.
- Percent change: (new − old) ÷ old × 100.
- Increase vs decrease: positive answer = went up, negative = went down.
- Simple interest: I = P × r × t (principal × rate × time in years). It's on the GED formula sheet!
Example: Price goes from $20 to $25. (25 − 20) ÷ 20 = 0.25 → 25% increase.
Practice — Percent Change & Simple Interest
Q7 · Short Answer
A plant grew from 40 cm to 50 cm. What is the percent increase? (just the number)
Q8 · Multiple Choice
You put $500 in the bank at 4% simple interest for 3 years. How much interest do you earn?