Conversion Ratios

What Is a Conversion Ratio?

A conversion ratio (or conversion factor) is a fraction where the numerator and denominator are equal amounts in different units. Because the top and bottom are equal, the fraction equals 1 — so multiplying by it changes the unit without changing the value.

Since 1 foot = 12 inches, these are both conversion ratios:

12 inches / 1 foot = 1

1 foot / 12 inches = 1

Pick whichever one cancels the unit you want to get rid of.

How to Use Them

Convert 5 feet to inches

Start: 5 feet

Multiply by: 12 inches / 1 foot

5 × 12 = 60 inches

"Feet" cancels out, "inches" remains

Convert 36 inches to feet

Start: 36 inches

Multiply by: 1 foot / 12 inches

36 ÷ 12 = 3 feet

Choosing the Right Orientation

Put the unit you want on top and the unit you want to cancel on the bottom. The old unit appears in both the starting value and the bottom of the fraction, so it cancels out.

💡 Chain conversions: You can multiply by more than one conversion ratio. To go from inches to yards: multiply by (1 foot / 12 inches) then by (1 yard / 3 feet). Both intermediate units cancel.

🎯 Practice Problems

1. To convert feet to inches, which conversion ratio do you use?

A) 1 foot / 12 inches

B) 12 inches / 1 foot

C) 1 inch / 12 feet

D) 12 feet / 1 inch

2. Convert 3 yards to feet. (1 yard = 3 feet)

A) 1 foot

B) 3 feet

C) 6 feet

D) 9 feet

3. Convert 48 inches to feet. (12 inches = 1 foot)

A) 4 feet

B) 5 feet

C) 36 feet

D) 576 feet

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🎯 Bonus Practice

1. Convert 2 miles to feet. (1 mile = 5,280 feet)

A) 2,640 feet

B) 5,280 feet

C) 10,560 feet

D) 5,282 feet

2. Why does a conversion ratio equal 1?

A) Because both numbers are small

B) Because the numerator and denominator are equal amounts in different units

C) Because you always get 1 when dividing

D) It doesn't equal 1

3. Convert 5 pounds to ounces. (1 pound = 16 ounces)

A) 3.2 ounces

B) 21 ounces

C) 80 ounces

D) 160 ounces

4. Convert 2,000 meters to kilometers. (1 km = 1,000 m)

A) 0.2 km

B) 2 km

C) 20 km

D) 2,000,000 km

5. Convert 90 minutes to hours. (60 minutes = 1 hour)

A) 0.67 hours

B) 1.5 hours

C) 9 hours

D) 5,400 hours