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Subtracting Mixed Numbers

Learn how to subtract mixed numbers using the least common multiple, renaming fractions, and simplifying. Examples and step-by-step explanations provided.

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Subtracting Mixed Numbers

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  1. Subtracting Mixed Numbers Lesson 4-5

  2. Process: • Use the least common multiple to write equivalent fractions if the denominators are not the same. • Subtract numerators. If you cannot subtract numerators, then rename the first mixed number. • Subtract whole numbers. • Simplify.

  3. Borrowing not required: 7 7 3 6 4 8 5 5 5 5 8 8 2 1 8 This answer is in simplest form.

  4. A Picture of Renaming: 3 1 3 1 5 6 • This is a picture of three and one third. • We want to take away one whole and five sixths. • To do this, we need to rename to sixths. • Now we can cross out five of the sixths. • We have subtracted the fractions. Now subtract the wholes. • Take away one whole. • Now we have two sixths, but we need to take away five sixths. We don’t have enough sixths. • Rename one whole to six sixths. • We are left with one whole and three sixths.

  5. Rename Mathematically: 2 3 3 = 1 8 1 2 6 x 2 3 6 6 1 1 5 5 x 1 6 6 1 3 We already had two sixths, and now we have borrowed one whole, which is six more sixths. The LCM of 3 and 6 is 6. 6 We have equivalent fractions, but we don’t have enough sixths to subtract. = Two and six are eight. We now have eight sixths. 1 1 2 Borrow from the whole number. Rename the whole as six sixths. Subtract the fractions, then the whole numbers. Simplify.

  6. Another Example: 8 1 = 14 14 9 9 21 1 7 x 7 14 2 4 4 10 5 x 2 14 7 4 11 The LCM of 2 and 7 is 14. 14 We do not have enough fourteenths, so we must borrow from the 9. This answer is in simplest form.

  7. Subtracting from a whole number: • If you are subtracting a mixed number from a whole number, then rename the whole number. • Borrow one whole and use the denominator from the fraction.

  8. Example: 7 8 1 = 8 8 8 8 3 5 8 We choose eight eighths because the denominator of the fraction is 8. 4 3 8

  9. Homework Time

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