Turn real-world situations into proportions, then solve
Setting Up the Proportion
Step 1: Identify the two pairs of related values. Step 2: Write them as two fractions with matching units (same type on top, same type on bottom). Step 3: Cross multiply and solve.
The golden rule: Keep units consistent. If miles are on top in the first fraction, miles must be on top in the second fraction.
Examples
A car travels 150 miles on 5 gallons. How far on 8 gallons?
Set up: miles/gallons = miles/gallons
150/5 = x/8
Cross multiply: 5x = 1,200
x = 1,200 ÷ 5 = 240 miles
If 4 workers can paint a fence in 6 hours, how long for 3 workers?
⚠️ This is an inverse proportion — more workers = less time. Don't set it up the same way.
Total work: 4 × 6 = 24 worker-hours
3 workers: 24 ÷ 3 = 8 hours
Common Setup Mistakes
💡 Watch for:
• Mixing up which values pair together
• Putting different units on the same side of the fraction
• Using direct proportion when the situation is inverse (more workers = less time)
• Forgetting to include units in your answer
🎯 Practice Problems
1. If 3 books cost $24, how much do 7 books cost?
A) $42
B) $56
C) $72
D) $48
2. A recipe needs 2 cups of flour for 12 cookies. How much for 30 cookies?
A) 3 cups
B) 4 cups
C) 5 cups
D) 6 cups
3. A car goes 200 miles on 8 gallons. How many gallons for 350 miles?
A) 10
B) 12
C) 14
D) 16
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🎯 Bonus Practice
1. If 5 machines produce 200 units in a day, how many units do 8 machines produce?
A) 280
B) 300
C) 320
D) 400
2. A 6-foot person casts a 4-foot shadow. A tree casts a 20-foot shadow. How tall is the tree?
A) 24 feet
B) 30 feet
C) 12 feet
D) 40 feet
3. A map shows 2 inches = 50 miles. If two cities are 7 inches apart, what is the real distance?
A) 100 miles
B) 150 miles
C) 175 miles
D) 350 miles
4. If 15 workers take 4 days to finish a job, how long for 10 workers?
A) 2.7 days
B) 6 days
C) 5 days
D) 8 days
5. A printer prints 80 pages in 10 minutes. How many pages in 25 minutes?