Multiplying and Dividing Fractions

Stage 7 of 23 Strand 5 of 5 4 lessons

4 illustrated lessons, each teaching the why before the how.

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Multiplying Fractions #

One cut made across another.

Multiplying fractions is one cut made across another

Cut the square into 4 down the side and color 3 of them: 3/4.

Now cut it into 3 the other way and color 2 of those: 2/3.

2/3 OF 3/4 is where they agree: 6 of the 12 small squares.

Now you

2/3 × 1/4

2/3 × 3/4

Share one piece among more people.

Sharing a fraction among people cuts the piece smaller

Half a cake is left, and 3 people share it. That is 1/2 ÷ 3.

Cut the half into 3 equal slices. Each slice is 1/6 of the whole cake.

Sharing by 3 is taking a third: the bottom multiplies, and the pieces shrink.

Now you

2/3 ÷ 2

2/5 ÷ 2

How many of those pieces fit inside.

Dividing by a fraction asks how many of those pieces fit inside

3 whole bars. How many half-bars will fit inside them? That is 3 ÷ 1/2.

Lay the halves in one at a time. 3 of them only fill the first bar and a half.

6 fit altogether: 3 ÷ 1/2 = 6. Small pieces fit many times, so dividing by a half doubles.

Now you

4 ÷ 1/3

4 ÷ 1/2

How many of these fit in that?

Dividing by a fraction still counts fits, and flipping it is the shortcut

2/3 ÷ 1/6 asks how many sixths fit in 2/3. Cut it into sixths: 4 fit.

Flipping gives the same count: 2/3 × 6 = 12/3 = 4.

Any fraction divides this way: flip the second one and multiply across.

Now you

3/5 ÷ 3/10

1/3 ÷ 1/6