Dividing Fractions

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Dividing Fractions: meaning, method and solved example (6th Grade) – Maths PDF

In short: Dividing fractions answers “how many of these fit in that” when both amounts are parts of a whole, and it turns into a multiplication once the second fraction is flipped.

6th GradeNumbers and Operations6.NS.A.1

What is Dividing Fractions?

When you start dividing fractions, ask how many pieces of one size fit inside a length of another size. How many strips of \(\frac{3}{4}\) foot can be cut from a ribbon \(\frac{9}{2}\) feet long?

Precisely, for fractions with \(b, c, d \neq 0\), \(\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c} = \frac{ad}{bc}\). Division by a fraction equals multiplication by its reciprocal.

How to spot it

  • A story cuts a length, a pan or a quantity into equal servings that are themselves fractions.
  • A question asks how many portions of a given size fit in a given amount.
  • The expression has the division sign between two fractions or mixed numbers.
  • A problem gives an area or volume and one fractional side, and asks for the missing side.

The method

  1. Convert every mixed number to a fraction with a top larger than its bottom.
  2. Leave the first fraction alone, swap the division sign for a times sign, and turn the second fraction upside down.
  3. Multiply the numerators together and the denominators together.
  4. Simplify the product and check it with a quick estimate.
Ribbon: 9/2 feet, cut into pieces of 3/4 foot3/43/43/43/43/43/49/2 x 4/3 = 36/6 = 6 pieces
Six pieces of 3/4 foot fill a ribbon that is 4 1/2 feet long.

Dividing Fractions: solved example

Problem

A florist in Savannah has \(\frac{15}{4}\) pounds of rose petals and packs them into sachets of \(\frac{5}{12}\) pound each. How many sachets can she make?

Solution

Flip the second fraction and multiply: \(\frac{15}{4} \times \frac{12}{5}\).

Cancel 5 into 15 and 4 into 12: \(\frac{3}{1} \times \frac{3}{1} = 9\). She can make 9 sachets.

Try it

Question 1

Compute \(\frac{2}{3} \div \frac{8}{9}\).

Show the answer

\(\frac{2}{3} \times \frac{9}{8} = \frac{18}{24} = \frac{3}{4}\).

Question 2

A path is \(2\frac{1}{4}\) miles long. A runner covers \(\frac{3}{8}\) mile per lap. How many laps is the path?

Show the answer

\(\frac{9}{4} \times \frac{8}{3} = \frac{72}{12} = 6\) laps.

Dividing Fractions vs. Reciprocal

Dividing fractions is the whole operation that answers how many times one fraction fits in another. The reciprocal is only one tool inside it: the second fraction turned upside down, which turns the division into a multiplication.

Reciprocal

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