Adding Mixed Numbers with the Same Denominator

There are two primary methods for adding and subtracting mixed numbers. The first method is to convert both terms to an improper fraction before adding. The second method is to add the whole numbers together and the fractions together separately.

Adding Mixed Numbers with the Same Denominator

Adding Mixed Numbers with the Same Denominator

There are two primary methods for adding or subtracting mixed numbers, and I’ll demonstrate both in each of these examples here. The first method is to convert both terms to an improper fraction before adding.

We’ll take 3 times 2 is 6, plus 2 is 8 over 3, plus 3 times 3 is 9, plus 2 is 11 over 3. We’ll add these together 8 plus 11 is 19 over 3, and 3 goes into 19, 6 times with the remainder of 1, so our solution is 6 and 1/ 3.

The second method is to add the whole number parts and the fraction parts separately. 2 plus 3 is 5, and 2/3 plus 2/3 is 4/3. Unfortunately, this is not a proper mixed number because the fractional part is greater than 1, so we’ll have to convert this fraction to a mixed number, 1 and 1/3, and then we can add the 5 back in and we get 6 and 1/3.

Now on the second problem we have 4 and 1/6 minus 2 and 5/6. First we’re going to do the improper fraction method 6 times 4 is 24, plus 1 is 25 over 6, minus, 6 times 2 is 12, plus 5 is 17 also over 6, and we will subtract 25 minus 17 is 8 over 6, or 4 over 3, which is equal to 1 and 1/3.

The second method has us subtracting 2 from 4 to get 2, and subtracting 5/6 from 1/6 to get negative 4/6. Now obviously this doesn’t work because we have a positive and a negative part to this number, so what we have to do is we can convert this whole number to 1 and 6 over 6, and then we can subtract the 4 over 6 to get 1 and 2 over 6, or 1 and 1/3.

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by Mometrix Test Preparation | Last Updated: August 15, 2019