Fractions

Adding and subtracting mixed numbers

Over the last few pages, you've practiced adding and subtracting different kinds of fractions. But some problems will need one extra step. For example, can you add the fractions below?

In Introduction to Fractions, you learned about mixed numbers. A mixed number has both a fraction and a whole number. An example is 2 1/2, or two-and-a-half. Another way to write this would be 5/2, or five-halves. These two numbers look different, but they're actually the same.

5/2 is an improper fraction. This just means the top number is larger than the bottom number. Even though improper fractions look strange, you can add and subtract them just like normal fractions. Mixed numbers aren't easy to add, so you'll have to convert them into improper fractions first. 

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  Let's add these two mixed numbers: 2 3/5 and 1 3/5.

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  We'll need to convert these mixed numbers to improper fractions. Let's start with 2 3/5.

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  As you learned in Lesson 2, we'll multiply the whole number, 2, by the bottom number, 5.

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  2 times 5 equals 10.

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  Now, let's add 10 to the numerator, 3.

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  10 + 3 equals 13.

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  Just like when you add fractions, the denominator stays the same. Our improper fraction is 13/5.

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  Now we'll need to convert our second mixed number: 1 3/5.

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  First, we'll multiply the whole number by the denominator. 1 x 5 = 5.

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  Next, we'll add 5 to the numerators. 5 + 3 = 8. 

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  Just like last time, the denominator remains the same. So we've changed 1 3/5 to 8/5.

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  Now that we've changed our mixed numbers to improper fractions, we can add like we normally do.

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  13 plus 8 equals 21. As usual, the denominator will stay the same. So 13/5 + 8/5 = 21/5.

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  Because we started with a mixed number, let's convert this improper fraction back into a mixed number.

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  As you learned in the previous lesson, divide the top number by the bottom number. 21 divided by 5 equals 4, with a remainder of 1.

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  The answer, 4, will become our whole number.

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  And the remainder, 1, will become the numerator of the fraction.

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  So 2 3/5 + 1 3/5 = 4 1/5.
  

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