What you’ll learn
Compute unit rates involving fractions.
Key idea
When both quantities are fractions, divide the amount by the number of units. Dividing by a fraction is equivalent to multiplying by its reciprocal, but the units still tell you which quantity is per one.
For example, a recipe uses three-fourths cup for one-half batch. The rate is (3/4 cup) ÷ (1/2 batch), so the batch units cancel to give cups per batch. A rate is meaningful only with its direction and units: cups per batch differs from batches per cup.
Worked example
Enter the exact value or ordered values in the format requested below.
A runner covers 1/2 mile in 4/5 hour at constant speed. Enter exact numerical miles-per-hour rate.
- Miles per hour divide miles by hours: (1/2)/(4/5).
- Use the time's reciprocal to obtain exact rate 5/8; then rate×time=1/2 miles.
Answer: 5/8
Quick Check
Evaluate a worked attempt at compute unit rates involving fractions, identify the first invalid step, and provide the correction.
For 1/3 mile in 3/8 hour, a student writes Step 1: speed=(1/3)÷(3/8). Step 2: multiply (1/3)×(3/8)=1/8. Locate the first invalid step and correct the rate.