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Lesson · Grade 8 · Mathematics

Dividing Fractions: How Many Pieces Fit?

  • Grade 8
  • Mathematics
  • 2 min 2 s
  • British Columbia
  • BC8-MA-15

A bar of 3 wholes cut into quarters shows that exactly 4 pieces of three quarters fit, so 3 ÷ 3/4 = 4. Each whole holds 4/3 of a piece, which is the reciprocal of 3/4, so the same answer comes from 3 × 4/3. A second bar checks the rule with 5/6 ÷ 1/3 = 5/6 × 3/1 = 15/6 = 2 1/2, crosses out the common mistake of flipping the first fraction (which gives 2/5), and ends on the recap "To divide by a fraction, multiply by its reciprocal."

Concept: Dividing fractions: how many groups fit

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In one sentence

The question this lesson answers

What is 3 divided by three quarters? That asks how many three quarter pieces fit into 3.

Draw 3 wholes and cut each one into 4 quarters: 3 times 4 is 12 quarters.

Transcript

What the lesson says

What is 3 divided by three quarters? That asks how many three quarter pieces fit into 3.

Draw 3 wholes and cut each one into 4 quarters: 3 times 4 is 12 quarters.

Now mark off 3 quarters at a time: 1, 2, 3, 4.

Exactly 4 pieces fit, with nothing left over. So 3 divided by three quarters is 4.

Why? Look at just 1 whole. One full piece fits, with 1 quarter left over.

That quarter is one third of a piece. So 1 whole holds 1 plus one third, or four thirds.

Four thirds is the reciprocal of three quarters: you get it by swapping the top and bottom numbers.

So 3 wholes hold 3 times four thirds, which is twelve thirds, or 4. That matches our count.

So dividing by three quarters is the same as multiplying by four thirds, its reciprocal.

Try another: five sixths divided by one third. How many thirds fit into five sixths?

Cut 1 whole into sixths and shade 5 of them. One third is the same as 2 sixths.

Mark off 2 sixths at a time: 1, 2, and half of a third. So two and a half thirds fit.

Check with the rule: five sixths times 3 over 1 is fifteen sixths, or two and a half.

A common mistake is flipping the first fraction: six fifths times one third is six fifteenths, only two fifths.

That cannot be right, because more than 2 thirds fit. Flip only the divisor, the number you divide by.

To divide by a fraction, multiply by its reciprocal.

Curriculum

Where this fits

British Columbia, Grade 8

Mathematics, Number: operations with fractions (addition, subtraction, multiplication, division, and order of operations)BC8-MA-15

Previous: Multiplying Fractions: A Fraction of a FractionNext: Order of operations with fractions and brackets

The outcomes and strands follow the British Columbia curriculum.

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