Let's consider the following fraction:
We can generate equivalent fractions by multiplying the numerator and denominator by any whole number.
For example, multiplying the numerator and denominator by we get
Similarly, by multiplying the numerator and denominator by we get
Therefore, the following fractions are all equivalent:
We can check that these fractions are equivalent using fraction models:
All three models have the same shape and the same shaded area. Therefore, they represent equivalent fractions.
Create a fraction equivalent to with a denominator of
To make an equivalent fraction with a denominator of we multiply the numerator and the denominator of by
Therefore,
$\dfrac{1}{4} = $
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$\dfrac{5}{12}$ |
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$\dfrac{6}{12}$ |
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$\dfrac{3}{12}$ |
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$\dfrac{7}{12}$ |
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$\dfrac{8}{12}$ |
Create a fraction equivalent to $\dfrac{1}{2}$ that has a denominator of $10.$
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Create a fraction equivalent to $\dfrac{2}{3}$ that has a denominator of $6.$
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We can also divide the numerator and denominator of a fraction by the same number to give an equivalent fraction.
For example, let's consider the following fraction:
Let's create some equivalent fractions by dividing:
- Notice that and both have as a factor. Therefore, we can divide our fraction by to create an equivalent fraction:
- Similarly, and both have as a factor. Therefore, we can divide our fraction by to create an equivalent fraction:
- Finally, and also have as a factor. Therefore, we can divide our fraction by to create an equivalent fraction:
Therefore, the following fractions are all equivalent:
Create a fraction equivalent to with a denominator of
To make a denominator of , we divide the numerator and the denominator of by
Therefore,
Create a fraction equivalent to $\dfrac{8}{20}$ that has a denominator of $5.$
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$\dfrac{21}{18} =$
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$\dfrac{5}{6}$ |
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$\dfrac{7}{6}$ |
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$\dfrac{4}{6}$ |
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$\dfrac{9}{6}$ |
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$\dfrac{8}{6}$ |
To express a whole number as a fraction, we use the number itself as the numerator and put it over a denominator of
For example, the number can be written as a fraction in the following way:
We can now find some equivalent fractions. For example:
multiplying our fraction by we get
multiplying our fraction by we get
Therefore, the following numbers are all equivalent:
What is the missing digit in the following equality?
Let's write as a fraction with denominator :
To make a denominator of we multiply the numerator and the denominator of by
Therefore, the missing number is
What is the missing digit in the following equality? \[ 7 = \dfrac{21}{\,\fbox{$\phantom{0}$}} \]
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$6$ |
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$4$ |
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$9$ |
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$12$ |
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$3$ |
$6 = $
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$\dfrac{20}{4}$ |
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$\dfrac{22}{4}$ |
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$\dfrac{24}{4}$ |
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$\dfrac{18}{4}$ |
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$\dfrac{28}{4}$ |
Create a fraction equivalent to the number $7$ that has a denominator of $4.$
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b
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