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Lesson · Grade 8 · Mathematics

Multiplying Fractions: A Fraction of a Fraction

  • Grade 8
  • Mathematics
  • 2 min
  • British Columbia
  • BC8-MA-14

Two thirds of three quarters is drawn as an area model: 3/4 of a square is shaded one way and 2/3 the other way, and the 6 of 12 parts shaded twice give 6/12 = 1/2, which leads to the rule of multiplying the numerators and multiplying the denominators. The same rule then works out 1 1/2 × 2 2/3 = 3/2 × 8/3 = 24/6 = 4, shows why multiplying the whole numbers and fractions separately (giving 2 1/3) is too small, and ends on a one-line recap.

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In one sentence

The question this lesson answers

What is two thirds of three quarters? Of means multiply.

Let a square be one whole. Cut it into four equal columns and shade three.

Transcript

What the lesson says

What is two thirds of three quarters? Of means multiply.

Let a square be one whole. Cut it into four equal columns and shade three.

Then cut it into three equal rows and shade two.

The part shaded twice is two thirds of the three quarters.

Twelve equal parts. Count those shaded twice: one, two, three, four, five, six.

So two thirds times three quarters is six twelfths.

The rule: multiply the numerators, the top numbers. Two times three is six.

Then multiply the denominators, the bottom numbers. Three times four is twelve.

Divide the top and bottom by six: six twelfths is one half, half the square.

Now mixed numbers, a whole number and a fraction: one and a half times two and two thirds.

First make each an improper fraction, with the numerator at least the denominator.

One and a half is two halves plus one half, or three halves.

Two and two thirds is six thirds plus two thirds, or eight thirds.

Three times eight is twenty four, and two times three is six.

Twenty four sixths is twenty four divided by six, which is four.

A common mistake is multiplying the parts separately: one times two is two, and one half times two thirds is one third.

That gives two and one third, less than two and two thirds. Too small, since we multiplied by more than one.

To multiply fractions, make mixed numbers improper, then multiply the numerators and the denominators.

Curriculum

Where this fits

British Columbia, Grade 8

Mathematics, Number: operations with fractions (addition, subtraction, multiplication, division, and order of operations)BC8-MA-14

Previous: Adding and Subtracting Fractions with Different DenominatorsNext: Dividing Fractions: How Many Pieces Fit?

The outcomes and strands follow the British Columbia curriculum.

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