Rewriting Fractions with Common Denominator: One a Factor of the Other
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Title: Rewriting Fractions with Common Denominator: One a Factor of the Other
You already know how to rewrite fractions with a different denominator using the product of the denominators as the common denominator. In this lesson, you’ll learn another method of finding a common denominator that can be used occasionally.
Here’s an example. One-half and three-eighths. In this case, notice that the denominator of the first fraction, 2, is a factor of the second denominator, 8.
Let’s look at what happens when we add these fractions on the number line.
We can add these on the number line for halves by putting them back to back like this.
We see that the end of the combined fractions does not fall on one of the lines for a half.
But now let’s add these on the other number line.
Now, the end of the combined fractions does fall on one of the lines for an eighth.
This means that we can add these fractions using eighths, so eight is a common denominator for these two fractions.
When a common denominator is one of the denominators for one of the fractions, there is no need to rewrite one of the fractions. In this case, we don’t need to rewrite three eighths. We do need to rewrite the other fraction like this.
So this fraction becomes four-eighths.
Another example. Four-thirds and five-sixths. In this example, 3 is a factor of 6, so the common denominator for these fractions is 6. Because the common denominator is 6, we don’t need to rewrite the fraction five-sixths, but we do need to rewrite four-thirds with the common denominator of 6.
So, now we have eight-sixths and five-sixths.
Another example. In this case, the first denominator, 3, is not a factor of the other denominator, 8. This means the common denominator is not one of the denominators of the two fractions. One common denominator is the product of 3 and 8, or 24. In this case, both fractions would need to be rewritten with a common denominator of 24.
This gives us eight twenty-fourths and 18 twenty-fourths.
Last example. Five-fourths and nine-sixteenths. Here, four is a factor of 16, so the common denominator is 16. That means nine-sixteenths is not rewritten, but five-fourths must be rewritten as an equivalent fraction with a denominator of 16.
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