Dividing fractions

Discover

How many $\tfrac{1}{4}$ -cup scoops are in 3 cups?

12
$\tfrac{3}{4}$

Key idea

Divide by a fraction: multiply by its reciprocal.

\dfrac{a}{b} \div \dfrac{c}{d} = \dfrac{a}{b} \cdot \dfrac{d}{c}

. Division answers “how many groups?” or “how much in one group?”. Dividing by a number less than 1 gives a result larger than the starting number.

Worked example

$\tfrac{2}{3} \div \tfrac{4}{5}$ .

\tfrac{2}{3} \cdot \tfrac{5}{4}

Reciprocal of 4/5.

\tfrac{10}{12} = \tfrac{5}{6}

Multiply.

Your turn, guided

Your turn: $\tfrac{3}{4} \div \tfrac{1}{2}$ .

\tfrac{3}{2}

3/4 · 2.

Practice ★

How many $\tfrac{ 1 }{ 2 }$ -cup servings are in 7 cups of rice?
How many $\tfrac{ 1 }{ 4 }$ -cup servings are in 2 cups of rice?

Compute $\tfrac{ 7 }{ 8 } \div \tfrac{ 5 }{ 9 }$ .

Watch out!

Practice ★★

$\tfrac{ 5 }{ 9 }$ of a bag of flour weighs 30 kg. How much does the whole bag weigh (kg)?
$\tfrac{ 2 }{ 5 }$ of a bag of flour weighs 6 kg. How much does the whole bag weigh (kg)?

Boss problem. A ribbon is 4 yards long. It is cut into pieces $\tfrac{ 2 }{ 4 }$ yard long.

Exit ticket

Three questions to check you have got it.

Compute $\tfrac{ 7 }{ 8 } \div \tfrac{ 5 }{ 9 }$ .
Compute $\tfrac{ 1 }{ 6 } \div \tfrac{ 4 }{ 6 }$ .
Compute $\tfrac{ 2 }{ 3 } \div \tfrac{ 4 }{ 5 }$ .

Summary card

Dividing fractions

Multiply by the reciprocal of the divisor.

Watch out: flip the second fraction, not the first.

End of the lesson

Next lesson: Area and volume with fractional lengths Back to the chapter

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