Compute Unit Rates with Fraction Ratios

A unit rate can use fractions in both parts.

The unit rate is the first quantity divided by the second.

Dividing by a fraction multiplies by its reciprocal.

Read it: Unit rates with fractions

2/3 ÷ 1/6 asks how many 1/6 pieces fit in 2/3. In sixths, 2/3 is 4/6, and 4 sixths hold 4 pieces of 1 sixth: 2/3 ÷ 1/6 = 4. As a rate: 2/3 of a mile in 1/6 of an hour is 4 miles in 1 hour.

1. Write both fractions in one piece size.
2. Count how many of the second fit in the first.
3. That count is the amount for 1 whole of the second thing: the unit rate.

Dividing by a piece smaller than 1 counts how many pieces fit, so the answer is more than you started with.

A unit rate is how much for 1: 2/3 of a mile every 1/6 of an hour is 4 miles every hour.

Multiplying instead, 2/3 × 1/6 = 2/18, gives a smaller amount, the wrong way.

To divide fractions, write them in one piece size and count the groups; the count is the rate for 1.

3/8 ÷ 1/8 = ___ — 3. In eighths: 3/8 ÷ 1/8, and 3 ÷ 1 = 3.