Is a mix of 3:5 stronger than 4:7? Which store has the better price per unit? Comparing ratios answers these questions.
Method 1: Make the Second Terms Equal
Like comparing fractions with a common denominator — find a common second term, then compare the first terms.
Compare 2:3 vs 5:6
Common second term: LCM of 3 and 6 = 6
2:3 → ×2 → 4:6
5:6 stays 5:6
Compare first terms: 4 vs 5 → 5:6 is larger
Method 2: Convert to Unit Rates
Divide to get a "per 1" value, then compare the decimals directly.
Which is better: $12 for 5 items or $10 for 4 items?
$12 ÷ 5 = $2.40 per item
$10 ÷ 4 = $2.50 per item
$2.40 is cheaper → $12 for 5 is the better deal
Method 3: Cross Multiply
Write the ratios as fractions and cross multiply. The side with the larger product has the larger ratio.
Compare 3:4 vs 5:7
3/4 vs 5/7
3 × 7 = 21 (left side)
4 × 5 = 20 (right side)
21 > 20 → 3:4 is larger
💡 Which method? Unit rates are best for real-world comparisons (prices, speeds). Cross multiplication is fastest for pure number comparisons. Common second term builds intuition.
🎯 Practice Problems
1. Which ratio is larger: 3:5 or 4:7?
A) 3:5
B) 4:7
C) They're equal
D) Can't compare
2. Which is the better deal: $15 for 6 or $20 for 9?
A) $15 for 6
B) $20 for 9
C) Same price
D) Can't tell
3. Compare 1:3 and 2:6. Which is larger?
A) 1:3
B) 2:6
C) They're equal
D) 1:3 by a little
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🎯 Bonus Practice
1. Which ratio is larger: 5:8 or 7:12?
A) 5:8
B) 7:12
C) Equal
D) Can't compare
2. Store A: 3 lbs for $9. Store B: 5 lbs for $14. Which is cheaper per pound?
A) Store A ($3/lb)
B) Store B ($2.80/lb)
C) Same price
D) Need more info
3. Which mixture is stronger: 2 parts concentrate to 5 parts water, or 3 parts to 8 parts water?
A) 2:5
B) 3:8
C) Same strength
D) Can't compare
4. Which car is faster: 240 miles in 4 hours or 350 miles in 6 hours?