We can use fraction models to multiply unit fractions by whole numbers.
For example, let's consider the following product:
First, we represent using a model:
Multiplication by a whole number is simply a repeated addition. And, since we need to multiply by we repeat the fraction model times, as shown below.
There are shaded pieces in total. Therefore, we conclude that
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 fraction model 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 $4 \times \dfrac{1}{5}.$
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a
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$\dfrac{2}{5}$ |
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b
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$\dfrac{3}{5}$ |
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c
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$\dfrac{4}{5}$ |
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d
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$\dfrac{1}{5}$ |
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e
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$\dfrac{6}{5}$ |
Use the model above to calculate $3 \times \dfrac{1}{2}.$
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$\dfrac16$ |
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b
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$\dfrac22$ |
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c
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$\dfrac42$ |
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d
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$\dfrac45$ |
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e
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$\dfrac32$ |
There's another way we can use fraction models to multiply unit fractions by whole numbers.
To demonstrate, let's consider the multiplication problem below:
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 piece. So, the resulting model must have shaded pieces:
Therefore, we conclude that
What multiplication problem is represented by the model above?
We have on the left and on the right.
Therefore, we have
Note: We can swap the factors on the left-hand side. So, the following would be a correct answer too:
What multiplication problem is represented by the model above?
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$\dfrac{4}{5} \times 4 = \dfrac{1}{5}$ |
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b
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$\dfrac{4}{6} \times 4 = \dfrac{1}{6}$ |
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c
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$\dfrac{5}{6} \times 4 = \dfrac{2}{6}$ |
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d
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$\dfrac{1}{6} \times 4 = \dfrac{4}{6}$ |
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$\dfrac{1}{5} \times 4 = \dfrac{4}{5}$ |
What multiplication problem is represented by the model above?
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$\dfrac{1}{3} \times 3 = \dfrac{2}{4}$ |
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b
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$\dfrac{3}{4} \times 3 = \dfrac{1}{4}$ |
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c
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$\dfrac{1}{4} \times 3 = \dfrac{3}{4}$ |
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d
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$\dfrac{1}{4} \times 3 = \dfrac{2}{4}$ |
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e
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$\dfrac{1}{3} \times 3 = \dfrac{3}{4}$ |
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 piece, and the shape on the right has shaded pieces. So the number of shaded pieces has increased by a factor of
Therefore, we have
So, the missing number is
What number is missing from the multiplication problem above?
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a
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$3$ |
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b
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$4$ |
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c
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$6$ |
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d
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$2$ |
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e
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$5$ |
What number is missing from the multiplication problem above?
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a
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$3$ |
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b
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$5$ |
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c
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$1$ |
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d
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$2$ |
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e
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$4$ |
