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Differences of Mixed Numbers without Renaming

Subtracting equivalent mixed/improper fractions

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Differences of Mixed Numbers without Renaming
Credit: regan76
Source: https://www.flickr.com/photos/j_regan/7612628332/
License: CC BY-NC 3.0

Matt is making a dress for his sister. He has \begin{align*}7 \frac{2}{3}\end{align*} yards of fabric. He needs \begin{align*}2 \frac{1}{3}\end{align*}  yards to make the dress. How much fabric will Matt have after he makes her dress?

In this concept, you will learn how to subtract mixed numbers. 

Subtracting Mixed Numbers without Renaming

A mixed number is a whole number with a fraction. Just as you can add mixed numbers, you can also subtract mixed numbers in the same way. Subtract the fractions first and then the whole numbers.

Here is a subtraction problem. 

\begin{align*}& \quad \ \ 6\frac{3}{8}\\ & \underline{- \ \ \ 4\frac{1}{8}\;}\end{align*}

Start by subtracting the fractions. These fractions have the same denominator so you can simply subtract the numerators. 

\begin{align*}& \quad \ \ 6\frac{3}{8}\\ & \underline{- \ \ \ 4\frac{1}{8}\;}\\ & \quad \ \ \ \ \frac{2}{8}\end{align*}

Next, subtract the whole numbers.

\begin{align*}& \quad \ \ 6\frac{3}{8}\\ & \underline{- \ \ \ 4\frac{1}{8}\;}\\ & \quad \ \ 2 \frac{2}{8}\end{align*}

Finally, simplify the fraction in  \begin{align*}2\frac{2}{8}\end{align*}

\begin{align*}2\frac{2}{8}=2\frac{1}{4}\end{align*}

The final answer is \begin{align*}2\frac{1}{4}\end{align*}.

If the subtraction problem involves mixed numbers with different denominators, rewrite the fractions of the mixed numbers so they have a common denominator before subtracting.

Here is another subtraction problem. 

\begin{align*}& \quad \ \ 6\frac{3}{4}\\ & \underline{- \ \ \ 3\frac{1}{6}\;}\end{align*}

First, rewrite the fractions with a common denominator. The common denominator is 12. 

\begin{align*}\frac{3}{4} = \frac{9}{12}\quad \quad \frac{1}{6} = \frac{2}{12}\end{align*}

\begin{align*}& \quad \ \ 6\frac{9}{12}\\ & \underline{- \ \ \ 3\frac{2}{12}\;}\end{align*} 

Then, subtract the fractions. 

\begin{align*} & \quad \ \ 6\frac{9}{12}\\ & \underline{- \ \ \ 3\frac{2}{12}\;}\\ & \quad \ \ \ \ \frac {7}{12}\end{align*} Next, subtract the whole numbers. 

\begin{align*}& \quad \ \ 6\frac{9}{12}\\ & \underline{- \ \ \ 3\frac{2}{12}\;}\\ & \quad \ \ 3 \frac {7}{12}\end{align*}

The difference is \begin{align*}3\frac{7}{12}\end{align*}.

Examples

Example 1

Earlier, you were given a problem about Matt making a dress for his sister.

Matt has \begin{align*}7 \frac{2}{3}\end{align*} yards of fabric and uses \begin{align*}2\frac{1}{3}\end{align*}  yards to make his sister a dress. Subtract the amount of fabric he used from the original amount to find how much fabric he has left. 

 \begin{align*}7\frac{2}{3} - 2 \frac{1}{3} = \underline {\;\;\;\;\;\;}\end{align*} 

First, subtract the fractions.

 \begin{align*}\frac{2}{3} - \frac{1}{3} = \frac{1}{3}\end{align*}

Then, subtract the whole numbers.

 \begin{align*}&7-2=5 \\ \\ &7\frac{2}{3} - 2 \frac{1}{3} = 5\frac{1}{3} \end{align*}

Matt will have \begin{align*}5 \frac{1}{3}\end{align*} yards of fabric left over. 

Example 2

Subtract the fractions. Answer in simplest form.

\begin{align*}12\frac{46}{49} - 10\frac{39}{49}=\underline{\;\;\;\;\;\;\;\;\;}\end{align*}

The fractions have a common denominator.

First, subtract the fractions. 

 \begin{align*}\frac{46}{49} - \frac{39}{49}= \frac{7}{49}\end{align*}

Then, subtract the whole numbers.

 \begin{align*}12-10 &=2 \\ \\ 12\frac{46}{49} - 10\frac{39}{49} &= 2\frac{7}{49}\end{align*}

Next, simplify the fraction part of the mixed number.

\begin{align*}2 \frac{7}{49} = 2 \frac {1}{7}\end{align*}

The difference is \begin{align*}2 \frac{1}{7}\end{align*}.

Example 3

Subtract the fractions: \begin{align*}4\frac{4}{5}-3\frac{1}{5}=\underline{\;\;\;\;\;\;\;\;\;}\end{align*}. Answer in simplest form.

First, subtract the fractions.

 \begin{align*}\frac{4}{5}-\frac{1}{5}=\frac {3}{5}\end{align*}

Then, subtract the whole numbers.

\begin{align*}4-3 &=1 \\ \\ 4\frac{4}{5}-3\frac{1}{5} &=1\frac{3}{5}\end{align*}

The difference is \begin{align*}1 \frac{3}{5}\end{align*}.

Example 4

Subtract the fractions: \begin{align*}6\frac{4}{6}-1\frac{2}{6}=\underline{\;\;\;\;\;\;\;\;\;}\end{align*}. Answer in simplest form.

First, subtract the fractions.

 \begin{align*}\frac{4}{6}-\frac{2}{6}=\frac {2}{6}\end{align*}

Then, subtract the whole numbers.

 \begin{align*}6-1 &=5\\ \\ 6\frac{4}{6}-1\frac{2}{6} &= 5 \frac{2}{6}\end{align*}

Next, simplify the fraction part of the mixed number.

 \begin{align*}5\frac{2}{6} = 5 \frac{1}{3}\end{align*}

The difference is \begin{align*}5 \frac{1}{3}\end{align*}.

Example 5

Subtract the fractions: \begin{align*}7\frac{8}{9}-4\frac{4}{6}=\underline{\;\;\;\;\;\;\;\;\;}\end{align*}. Answer in simplest form.

First, rewrite the fractions with a common denominator of 18. 

 \begin{align*}& \frac{8}{9}=\frac{16}{18} \quad \quad \frac{4}{6} = \frac{12}{18}\\ \\ & 7\frac{16}{18}-4\frac{12}{18}=\underline {\;\;\;\;\;\;}\end{align*}

Then, subtract the fractions.

 \begin{align*}\frac{16}{18}-\frac{12}{18}=\frac{4}{18}\end{align*}

Next, subtract the whole numbers.

 \begin{align*}7-4 &=3\\ \\ 7\frac{16}{18}- 4 \frac{12}{18} &= 3\frac{4}{18}\end{align*}
Finally, simplify the fraction.
 \begin{align*}3\frac{4}{18}=3\frac{2}{9}\end{align*}

The difference is \begin{align*}3 \frac{2}{9}\end{align*}.

Review

Subtract the following mixed numbers. Answer in simplest form.

  1. \begin{align*}6\frac{2}{9}-4\frac{1}{9}=\underline{\;\;\;\;\;\;\;\;\;}\end{align*}
  2. \begin{align*}5\frac{6}{10}-2\frac{1}{10}=\underline{\;\;\;\;\;\;\;\;\;}\end{align*}
  3. \begin{align*}8\frac{2}{8}-4\frac{1}{8}=\underline{\;\;\;\;\;\;\;\;\;}\end{align*}
  4. \begin{align*}12\frac{4}{8}-4\frac{2}{8}=\underline{\;\;\;\;\;\;\;\;\;}\end{align*}
  5. \begin{align*}6\frac{9}{10}-4\frac{2}{10}=\underline{\;\;\;\;\;\;\;\;\;}\end{align*}
  6. \begin{align*}15\frac{6}{15}-5\frac{3}{15}=\underline{\;\;\;\;\;\;\;\;\;}\end{align*}
  7. \begin{align*}18\frac{4}{12}-7\frac{2}{12}=\underline{\;\;\;\;\;\;\;\;\;}\end{align*}
  8. \begin{align*}20\frac{5}{20}-19\frac{1}{20}=\underline{\;\;\;\;\;\;\;\;\;}\end{align*}
  9. \begin{align*}5\frac{2}{5}-1\frac{1}{3}=\underline{\;\;\;\;\;\;\;\;\;}\end{align*}
  10. \begin{align*}8\frac{1}{2}-4\frac{1}{4}=\underline{\;\;\;\;\;\;\;\;\;}\end{align*}
  11. \begin{align*}6\frac{1}{3}-2\frac{1}{6}=\underline{\;\;\;\;\;\;\;\;\;}\end{align*}
  12. \begin{align*}5\frac{1}{4}-3\frac{2}{10}=\underline{\;\;\;\;\;\;\;\;\;}\end{align*}
  13. \begin{align*}8\frac{1}{3}-2\frac{1}{4}=\underline{\;\;\;\;\;\;\;\;\;}\end{align*}
  14. \begin{align*}12\frac{3}{4}-2\frac{1}{3}=\underline{\;\;\;\;\;\;\;\;\;}\end{align*}
  15. \begin{align*}18\frac{6}{9}-12\frac{1}{4}=\underline{\;\;\;\;\;\;\;\;\;}\end{align*}

Review (Answers)

To see the Review answers, open this PDF file and look for section 6.11. 

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Vocabulary

TermDefinition
Mixed Number A mixed number is a number made up of a whole number and a fraction, such as 4\frac{3}{5}.

Image Attributions

  1. [1]^ Credit: regan76; Source: https://www.flickr.com/photos/j_regan/7612628332/; License: CC BY-NC 3.0

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