We can use our knowledge of fraction models to multiply fractions by whole numbers.
For example, let's consider the following product:
We start by drawing a fraction model for
Multiplying by means that we need to repeat the fraction times.
Now, we count the number of shaded pieces.
There are shaded pieces in total. Therefore,
Consider the diagram above. Write down this multiplication as a repeated addition of fraction models.
In the model, we have multiplied by This means that we need to make copies of the given fraction model.
So, the missing picture is:
What picture is missing from the multiplication model above?
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What picture is missing from the multiplication model above?
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Use the model above to calculate
Since we need to multiply by , we repeat the fraction model times, as shown below.
There are shaded pieces in total. Therefore:
Use the model above to calculate $2 \times \dfrac{2}{5}.$
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a
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$\dfrac{1}{10}$ |
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b
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$\dfrac{2}{10}$ |
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c
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$\dfrac{2}{5}$ |
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d
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$\dfrac{4}{5}$ |
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e
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$\dfrac{1}{5}$ |
Use the model above to calculate $\dfrac{8}{14} \times 4.$
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$\dfrac{12}{14}$ |
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b
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$\dfrac{24}{14}$ |
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c
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$\dfrac{16}{14}$ |
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d
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$\dfrac{32}{14}$ |
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e
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$\dfrac{28}{14}$ |
There's another way we can use fraction models to multiply fractions by whole numbers.
To demonstrate, let's consider the following multiplication problem:
We start by drawing a fraction model to represent
Now, rather than repeating our model times (which would take a long time), we can instead multiply the number of shaded pieces by
Our model has shaded pieces. So, the resulting model must have shaded pieces:
Therefore, we conclude that
What number is missing from the multiplication problem above?
We have on the left and on the right.
The shape on the left has shaded pieces, and the shape on the right has shaded pieces. So the number of shaded pieces has increased by a factor of (That is, the number of shaded pieces has been multiplied by )
Therefore, the multiplication problem shown is
So, the missing number is
What number is missing from the multiplication problem above?
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a
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$12$ |
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b
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$2$ |
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c
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$3$ |
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d
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$6$ |
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$1$ |
What multiplication problem is represented by the model above?
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$\dfrac{2}{8} \times 2 = \dfrac{5}{8}$ |
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b
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$\dfrac{3}{8} \times 2 = \dfrac{6}{8}$ |
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c
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$\dfrac{2}{6} \times 4 = \dfrac{4}{3}$ |
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d
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$\dfrac{4}{8} \times 2 = \dfrac{6}{8}$ |
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e
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$\dfrac{3}{8} \times 3 = \dfrac{9}{8}$ |
