Frank thinks he will need at about Estimate the amount of sand he will need to the nearest whole number.

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?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*} or \begin{align*}\frac{1}{2}\end{align*}.

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*}, round up to the nearest whole number.

Here is a mixed number.

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

Compare the fraction to

. The equivalent fraction for in terms of sixths is .\begin{align*}\frac{1}{6} < \frac{1}{2}\end{align*}

Round the mixed number down to the nearest whole number.

is less than .rounds down to 5.

### Examples

#### Example 1

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

Frank will need about

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

of a whole divided into 4 parts is .\begin{align*}\frac{1}{4}<\frac{2}{4}\end{align*}

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

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

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

. of a whole divided into 16 parts is .Then, round the mixed number to the nearest whole number.

is greater than . \begin{align*}6\frac{12}{16}\approx 7\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

. 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.

is greater than .rounds up to 8.

#### Example 4

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

First, compare the fraction to

. of a whole divided into 4 parts is .

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

is less than .rounds down to 4.

#### Example 5

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

First, compare the fraction to

. of a whole divided into 10 parts is .

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

is equal torounds up to 7.

### Review

Round each number to the nearest whole number.

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