Mrs.D Math · 6th Grade

CROSS
QUEST

Solving Proportions
🏃 Rates
🗺️ Scale Factor
📏 Conversions
⚖️ 3 / 36 = x / 60
✖️ Cross Multiply
🏆 x = 5
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📚 How Cross Quest Works

Solving a Proportion with Cross Multiplication

A proportion is two equal ratios. Keep matching units in the same spots (top with top, bottom with bottom).

1
Set it up: Sharon runs 3 miles in 36 minutes. How far in 60 minutes?
3 mi / 36 min = x mi / 60 min
2
Cross multiply: 3 × 60 = 36 × x
180 = 36x
3
Divide to solve: 180 ÷ 36 = 5 miles

Scale Factor & Conversion Factor

A map scale or a conversion fact is just a ratio — set up a proportion the same way!

✓
Map scale 2 in = 5 mi. The zoo is 3 in away on the map.
2 in / 5 mi = 3 in / x mi  →  2x = 15  →  x = 7.5 mi
✓
Conversion 1 m = 100 cm. How many cm equal 18 m?
1 m / 100 cm = 18 m / x cm  →  x = 1,800 cm

How to Play

🏃
Equivalent Rates — miles per hour, dollars per pound, pages per minute…
🗺️
Scale Factor — map scales, models, and unit conversions.
🎲
Mixed — both types together. Some answers you pick, some you type in!
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