How can I explain how you can add two fractions with denominators of 10 and end up with a sum whose denominator is 5?

If the two numerators add to an even number (x) then that number and the denominator (10) can both be divided by two leaving you with x/2 over 5 because (x/2)/5 is equivalent to x/10

Answered by KBreithaupt | 2024-06-10

To explain how you can add two fractions with denominators of 10 and end up with a sum whose denominator is 5, you need to understand that when adding fractions, the denominators must be the same. When the fractions involved have different denominators, you must find a common denominator. In this case, since 5 is a factor of 10, you can use 5 as the common denominator.
First, you need to rewrite each fraction so that they both have a denominator of 5. To do this for a fraction with a denominator of 10, you divide the denominator by 2, and do the same to the numerator to maintain the value of the fraction. For example, if you have "1/10", when you divide the numerator and denominator by 2, you get a fraction of "1/5".
Once both fractions have the same denominator, you can simply add the numerators together. You never add the denominators. The result will be a sum with a denominator of 5, which might need simplification if common factors are present in the numerator and denominator.

Answered by BetteDavis | 2024-06-24

To add two fractions with a denominator of 10 and end up with a denominator of 5, you can first add the fractions normally, then simplify the result. For example, 10 3 ​ + 10 2 ​ = 10 5 ​ ; simplifying gives 2 1 ​ . The key is in recognizing that both numerator and denominator can be reduced based on common factors.
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Answered by KBreithaupt | 2024-12-26