Section 04 · Multiplication and Division · F13

Dividing fractions

I can divide with fractions by asking how many groups fit, and use multiplying by the reciprocal to calculate.

Learn

You have 2 cups of rice and each serving is 1/3 cup. How many servings can you make?

2 ÷ 1/3 asks: how many 1/3s fit into 2? Each whole holds 3 thirds, so 2 wholes hold 6. 2 ÷ 1/3 = 6.

Dividing by a fraction less than 1 gives a bigger answer, because many small groups fit.

To calculate, multiply by the reciprocal (flip the divisor): 2/3 ÷ 4/5 = 2/3 × 5/4 = 10/12 = 5/6.

You can never divide by zero: no number of zero-sized groups ever fills an amount, so 3/4 ÷ 0 is undefined.

Each jump is one group of 1/denominator. Set the line to reach 2 using thirds, then quarters. How many jumps does each take?

Number line from 0 to 2, each whole split into 3 equal parts. A point marks 6 thirds, 6 jumps of one 3th from zero.

Numerator6

Denominator3

Use the hints as much as you like. You can try each question as many times as you need.

0 of 2 solved

How many 1/3s fit into 2? (2 ÷ 1/3)

1/2 ÷ 1/4 = ?

Answers are checked exactly — equivalent fractions count unless a question asks for a particular form.

0 of 4 solved

3/4 ÷ 1/8 = ?

2/3 ÷ 4/5 in simplest form.

A 3/4 m board is cut into pieces 3/8 m long. How many pieces?

What is 3/4 ÷ 0?

Flipping the first fraction instead of the second.

Why it happens: Only the divisor is replaced by its reciprocal.

What to do: Keep, change, flip: keep the first, change ÷ to ×, flip the second.

Expecting division to always make a number smaller.

Why it happens: Dividing by a fraction under 1 counts many small groups.

What to do: Estimate: “how many of these small pieces fit?”

Three practice questions to check your understanding. Hints and retries are allowed, so this counts as practice — not mastery.

0 of 3 solved

3 ÷ 1/4 = ?

5/6 ÷ 5/12 = ?

1/2 ÷ 3 in simplest form.

Ready? Answer 4 new questions with no hints and one try each. This is the only way a lesson is marked as mastered.