We can use models to multiply fractions by whole numbers. But can we do this without using models?
As it turns out, models give us vital clues on how this should be done!
To demonstrate, let's take a look at the fraction model for
In the answer, we end up with parts, and the denominator remains the same. This is always the case.
Therefore, to multiply a fraction by a whole number, we follow the following steps:
Step 1: We multiply the numerator by the whole number.
Step 2: We keep the denominator the same.
Using these steps, we can figure out the answer without using models:
Find the value of
To multiply a fraction by a whole number, we multiply the fraction's numerator by the whole number and keep the denominator the same:
Expressed as an improper fraction in its lowest terms, $4 \times \dfrac 7 {15} =$
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$2\times \dfrac 2 {9} =$
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$\dfrac{4}{3}$ |
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$\dfrac{1}{9}$ |
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$\dfrac{2}{9}$ |
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$\dfrac{4}{9}$ |
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$\dfrac{1}{4}$ |
$\dfrac 2 {11} \times 3 =$
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$ \dfrac{5}{11}$ |
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$ \dfrac{6}{11}$ |
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$ \dfrac{6}{33}$ |
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$ \dfrac{2}{33}$ |
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$ \dfrac{23}{11}$ |
Multiply
To multiply a fraction by a whole number, we multiply the fraction's numerator by the whole number and keep the denominator the same:
Finally, we simplify this fraction by interpreting as a division:
$3\times\dfrac 1 3=$
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$3$ |
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$1$ |
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$2$ |
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$\dfrac 1 3$ |
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$\dfrac 2 3$ |
Expressed as a whole number, $\dfrac{1}{2} \times 2 =$
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Expressed as a whole number, $\dfrac 1 7\times 28=$
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Multiply
To multiply a fraction by a whole number, we multiply the fraction's numerator by the whole number and keep the denominator the same:
To simplify this fraction, we can divide the numerator and denominator by
$3\times\dfrac 1 {6}=$
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$\dfrac{1}{2}$ |
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$3$ |
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$\dfrac{1}{3}$ |
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$2$ |
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$\dfrac{1}{6}$ |
Expressed as a fraction in its lowest terms, $ 2\times\dfrac 3 {8} =$
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Expressed as a fraction in its lowest terms, $\dfrac 2 {9} \times 3=$
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Find the value as a mixed number.
To multiply a fraction by a whole number, we multiply the fraction's numerator by the whole number and keep the denominator the same:
We now convert this to a mixed number:
Expressed as a mixed number in its lowest terms, $6\times\dfrac 7 {8}=$
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Expressed as a mixed number in its lowest terms, $\dfrac 3 {8}\times 4 =$
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