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Mixed Number Rounding to the Nearest Whole

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Mixed Number Rounding to the Nearest Whole
License: CC BY-NC 3.0

Frank thinks he will need at about \begin{align*}12\frac{1}{4}\end{align*}1214 pounds of sand for a sandbox he is building. The sand he wants is $3 per pound. About how much will Frank spend on sand? Estimate the amount of sand he will need to the nearest whole number. 

In this concept, you will learn how to round mixed numbers to the nearest whole number.

Round Mixed Numbers to the Nearest Whole

You can also estimate by rounding mixed numbers. A mixed number is a number that has a whole number and a fraction. It refers to a value that is between two whole numbers.

When rounding decimal numbers to the the nearest whole number, you look at the number in the tenths place. If the number less than 5, round down. If the number is greater than or equal to 5, round up. Five tenths can be written into a fraction as \begin{align*}\frac{5}{10}\end{align*}510 or  \begin{align*}\frac{1}{2}\end{align*}12.

To round mixed numbers to the nearest whole number, look at the fraction part of the mixed number. If the fraction is less than , round down to the nearest whole number. If the fraction is greater than or equal to \begin{align*}\frac{1}{2}\end{align*}12, round up to the nearest whole number. 

Here is a mixed number.

\begin{align*}5 \frac{1}{6}\end{align*}516

Compare the fraction to \begin{align*}\frac{1}{2}\end{align*}12. The equivalent fraction for \begin{align*}\frac{1}{2}\end{align*}12 in terms of sixths is \begin{align*}\frac{3}{6}\end{align*}36.

\begin{align*}\frac{1}{6} < \frac{1}{2}\end{align*}16<12

Round the mixed number down to the nearest whole number. \begin{align*}\frac{1}{6}\end{align*}16 is less than \begin{align*}\frac{1}{2}\end{align*}12

\begin{align*}5\frac{1}{6} \approx 5\end{align*}5165

\begin{align*}5\frac{1}{6}\end{align*}516 rounds down to 5. 

Examples

Example 1

Earlier, you were given a problem about Frank's sandbox project.

Frank will need about \begin{align*}12\frac{1}{4}\end{align*}1214 pounds of sand that costs $3 per pound. Round the mixed number to a whole number and multiply to find the estimate price of the sand. 

First, compare the fraction to \begin{align*}\frac{1}{2}\end{align*}12\begin{align*}\frac{1}{2}\end{align*}12 of a whole divided into 4 parts is \begin{align*}\frac{2}{4}\end{align*}24.

 \begin{align*}\frac{1}{4}<\frac{2}{4}\end{align*}14<24

Then, round the mixed number to the nearest whole number.

 \begin{align*}12\frac{1}{4}\approx 12\end{align*}121412

Next, multiply the number of pounds by the price per pound, $3.

 \begin{align*}$3 \times 12 = $36\end{align*}

Frank will spend about $36 on the sand.

Example 2

Sarah is helping to measure a hem on a dress. She measures that the dress needs to be shortened \begin{align*}6 \frac{12}{16}\end{align*} inches. Given this measurement, does it make sense for Sarah to round down to 6 or up to 7 inches?

First, compare the fraction to \begin{align*}\frac{1}{2}\end{align*}. \begin{align*}\frac{1}{2}\end{align*} of a whole divided into 16 parts is \begin{align*}\frac{8}{16}\end{align*}

Then, round the mixed number to the nearest whole number. \begin{align*}\frac{12}{16}\end{align*} is greater than \begin{align*}\frac{1}{2}\end{align*}.  

 \begin{align*}6\frac{12}{16}\approx 7\end{align*} 

\begin{align*}6\frac{12}{16}\end{align*} rounds up to 7.

Sarah should round up and shorten the dress by about 7 inches.

Example 3

Round this mixed number: \begin{align*}7 \frac{6}{9}\end{align*}.

First, compare the fraction to \begin{align*}\frac{1}{2}\end{align*}. \begin{align*}\frac{1}{2}\end{align*} of a whole divided into 9 parts is between 4 and 5 ninths.

\begin{align*}\frac{6}{9} > \frac{5}{9}\end{align*}

Then, round the mixed number to the nearest whole number. \begin{align*}\frac{6}{9}\end{align*} is greater than \begin{align*}\frac{1}{2}\end{align*}.

\begin{align*}7\frac{6}{9}\end{align*} rounds up to 8.

Example 4

Round this mixed number: \begin{align*}4 \frac{1}{4}\end{align*}.

First, compare the fraction to \begin{align*}\frac{1}{2}\end{align*}. \begin{align*}\frac{1}{2}\end{align*} of a whole divided into 4 parts is \begin{align*}\frac{2}{4}\end{align*}.

\begin{align*}\frac{1}{4} < \frac{2}{4}\end{align*}

Then, round the mixed number to the nearest whole number. \begin{align*}\frac{1}{4}\end{align*} is less than \begin{align*}\frac{1}{2}\end{align*}.

\begin{align*}4\frac{1}{4}\end{align*} rounds down to 4. 

Example 5

Round this mixed number: \begin{align*}6 \frac{5}{10}\end{align*}.

First, compare the fraction to \begin{align*}\frac{1}{2}\end{align*}. \begin{align*}\frac{1}{2}\end{align*} of a whole divided into 10 parts is \begin{align*}\frac{5}{10}\end{align*}.

\begin{align*}\frac{5}{10}=\frac{5}{10}\end{align*}

Then, round the mixed number up to the nearest whole number. \begin{align*}\frac{5}{10}\end{align*} is equal to \begin{align*}\frac{1}{2}\end{align*}.

\begin{align*}6\frac{5}{10}\end{align*} rounds up to 7.

Review

Round each number to the nearest whole number.

  1. \begin{align*}3 \frac{8}{10}\end{align*}
  2. \begin{align*}1 \frac{2}{3}\end{align*}
  3. \begin{align*}5 \frac{5}{6}\end{align*}
  4. \begin{align*}6 \frac{4}{13}\end{align*}
  5. \begin{align*}11 \frac{5}{7}\end{align*}
  6. \begin{align*}26 \frac{5}{9}\end{align*}
  7. \begin{align*}14 \frac{2}{11}\end{align*}
  8. \begin{align*}13 \frac{1}{10}\end{align*}
  9. \begin{align*}17 \frac{6}{13}\end{align*}
  10. \begin{align*}19 \frac{4}{7}\end{align*}
  11. \begin{align*}21 \frac{11}{12}\end{align*}
  12. \begin{align*}34 \frac{12}{25}\end{align*}
  13. \begin{align*}46 \frac{16}{24}\end{align*}
  14. \begin{align*}21 \frac{18}{20}\end{align*}
  15. \begin{align*}9 \frac{19}{30}\end{align*}

Review (Answers)

To see the Review answers, open this PDF file and look for section 6.2. 

Resources

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Vocabulary

Difference

The result of a subtraction operation is called a difference.

Estimate

To estimate is to find an approximate answer that is reasonable or makes sense given the problem.

fraction

A fraction is a part of a whole. A fraction is written mathematically as one value on top of another, separated by a fraction bar. It is also called a rational number.

Mixed Number

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

Sum

The sum is the result after two or more amounts have been added together.

Image Attributions

  1. [1]^ License: CC BY-NC 3.0

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