Algebra & Expressions
Ratios & Proportions
A ratio compares two quantities. A proportion says two ratios are equal. Solve proportions using cross-multiplication: if a/b = c/d, then ad = bc.
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Worked Examples
Follow along with these step-by-step examples. Take your time — there's no rush!
Problem
Solve the proportion: 3/4 = x/20
Step-by-Step Solution
Cross-multiply: 3 × 20 = 4 × x
60 = 4x
Divide by 4: x = 15
Answer
x = 15
Problem
A recipe uses 2 cups of flour for 12 cookies. How much flour for 30 cookies?
Step-by-Step Solution
Set up proportion: 2/12 = x/30
Cross-multiply: 2 × 30 = 12x
60 = 12x → x = 5 cups
Answer
5 cups of flour
Problem
A map uses a scale of 1 inch = 50 miles. How many miles is 3.5 inches?
Step-by-Step Solution
Set up: 1/50 = 3.5/x
Cross-multiply: 1 × x = 50 × 3.5
x = 175 miles
Answer
175 miles
Problem
Solve the proportion: 7/x = 14/10
Step-by-Step Solution
Cross-multiply: 7 × 10 = 14 × x
70 = 14x
x = 5
Answer
x = 5
Problem
A car uses 3 gallons to travel 90 miles. How many gallons for 210 miles?
Step-by-Step Solution
Set up proportion: 3/90 = x/210
Cross-multiply: 3 × 210 = 90x
630 = 90x → x = 7 gallons
Answer
7 gallons
Your Turn — Practice Problems
Try all 5 problems on your own first. Write out your work — that's how it sticks!
💡 Tip: Don't peek at the answers until you've genuinely tried each one.
Solve: 5/8 = x/40
Solve: 3/x = 9/15
A car goes 150 miles on 5 gallons. How far on 8 gallons?
Solve: x/6 = 10/15
A 6-foot person casts a 9-foot shadow. How tall is a tree casting a 24-foot shadow?
Solve: 4/5 = 12/x
A recipe needs 2 eggs for 8 servings. How many eggs for 20 servings?
Solve: x/3 = 8/12
A map scale is 1 cm = 25 km. How many km is 7 cm?
Solve: 6/10 = x/25
A train travels 180 miles in 3 hours. How far in 5 hours at the same rate?
Solve: 9/x = 3/7
Finished all 12? Give yourself a pat on the back — then check your work!
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