Bringing fractions to a common denominator – this is the replacement of fractions with different denominators by fractions equal in size to them, but having the same denominators.
In this publication, we will consider how this operation is performed. We will also analyze practical examples for a better understanding of the material presented.
Algorithm for reducing fractions to a common denominator
To reduce fractions to the lowest common denominator, follow these steps:
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- We find both denominators.
- We find an additional factor for each fraction, equal to the result of dividing the LCM by the denominator of this fraction.
- We multiply the numerator and denominator of each fraction by the factor found for it.
Examples
Example 1
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to the lowest common denominator.
Solution
It will not work to reduce these fractions, so we immediately go to step 2 of the algorithm described above.
The least common multiple (LCM) of the denominators of both fractions is 48.
Additional multiplier: for the first fraction with a denominator of 12 it is 4 (48:12), for the second fraction with a denominator of 16 it is 3 (48:16).
Now we multiply the numerator and denominator of each fraction by the additional factor found for them.
First fraction:
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Second fraction:
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Thus, we have reduced different fractions to a common denominator.
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Example 2
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to the lowest common denominator.
Solution
In this case, you can reduce the fractions: the first by – 2, the second – by 6.
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The NOC for both denominators is 35, respectively, for the first fraction the additional factor is 5, for the second – 7.
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