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# Mixed Number Rounding to the Nearest Whole

## Make the denominator 1

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Mixed Number Rounding to the Nearest Whole

Frank thinks he will need at about 1214\begin{align*}12\frac{1}{4}\end{align*} 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 510\begin{align*}\frac{5}{10}\end{align*} or 12\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 12\begin{align*}\frac{1}{2}\end{align*}, round up to the nearest whole number. Here is a mixed number. 516\begin{align*}5 \frac{1}{6}\end{align*} Compare the fraction to 12\begin{align*}\frac{1}{2}\end{align*}. The equivalent fraction for 12\begin{align*}\frac{1}{2}\end{align*} in terms of sixths is 36\begin{align*}\frac{3}{6}\end{align*}. 16<12\begin{align*}\frac{1}{6} < \frac{1}{2}\end{align*} Round the mixed number down to the nearest whole number. 16\begin{align*}\frac{1}{6}\end{align*} is less than 12\begin{align*}\frac{1}{2}\end{align*} 5165\begin{align*}5\frac{1}{6} \approx 5\end{align*} 516\begin{align*}5\frac{1}{6}\end{align*} rounds down to 5. ### Examples #### Example 1 Earlier, you were given a problem about Frank's sandbox project. Frank will need about 1214\begin{align*}12\frac{1}{4}\end{align*} pounds of sand that costs3 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 12\begin{align*}\frac{1}{2}\end{align*}12\begin{align*}\frac{1}{2}\end{align*} of a whole divided into 4 parts is 24\begin{align*}\frac{2}{4}\end{align*}.

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

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

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

Next, multiply the number of pounds by the price per pound, $3.$3×12=36\begin{align*}3 \times 12 = 36\end{align*} Frank will spend about36 on the sand.

#### Example 2

Sarah is helping to measure a hem on a dress. She measures that the dress needs to be shortened 61216\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 12\begin{align*}\frac{1}{2}\end{align*}. 12\begin{align*}\frac{1}{2}\end{align*} of a whole divided into 16 parts is 816\begin{align*}\frac{8}{16}\end{align*}

Then, round the mixed number to the nearest whole number. 1216\begin{align*}\frac{12}{16}\end{align*} is greater than 12\begin{align*}\frac{1}{2}\end{align*}.

612167\begin{align*}6\frac{12}{16}\approx 7\end{align*}

61216\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: 769\begin{align*}7 \frac{6}{9}\end{align*}.

First, compare the fraction to 12\begin{align*}\frac{1}{2}\end{align*}. 12\begin{align*}\frac{1}{2}\end{align*} of a whole divided into 9 parts is between 4 and 5 ninths.

69>59\begin{align*}\frac{6}{9} > \frac{5}{9}\end{align*}

Then, round the mixed number to the nearest whole number. 69\begin{align*}\frac{6}{9}\end{align*} is greater than 12\begin{align*}\frac{1}{2}\end{align*}.

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

#### Example 4

Round this mixed number: 414\begin{align*}4 \frac{1}{4}\end{align*}.

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

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

Then, round the mixed number to the nearest whole number. 14\begin{align*}\frac{1}{4}\end{align*} is less than 12\begin{align*}\frac{1}{2}\end{align*}.

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

#### Example 5

Round this mixed number: 6510\begin{align*}6 \frac{5}{10}\end{align*}.

First, compare the fraction to 12\begin{align*}\frac{1}{2}\end{align*}. 12\begin{align*}\frac{1}{2}\end{align*} of a whole divided into 10 parts is 510\begin{align*}\frac{5}{10}\end{align*}.

510=510\begin{align*}\frac{5}{10}=\frac{5}{10}\end{align*}

Then, round the mixed number up to the nearest whole number. 510\begin{align*}\frac{5}{10}\end{align*} is equal to 12\begin{align*}\frac{1}{2}\end{align*}.

6510\begin{align*}6\frac{5}{10}\end{align*} rounds up to 7.

### Review

Round each number to the nearest whole number.

1. 3810\begin{align*}3 \frac{8}{10}\end{align*}
2. 123\begin{align*}1 \frac{2}{3}\end{align*}
3. 556\begin{align*}5 \frac{5}{6}\end{align*}
4. 6413\begin{align*}6 \frac{4}{13}\end{align*}
5. 1157\begin{align*}11 \frac{5}{7}\end{align*}
6. 2659\begin{align*}26 \frac{5}{9}\end{align*}
7. 14211\begin{align*}14 \frac{2}{11}\end{align*}
8. 13110\begin{align*}13 \frac{1}{10}\end{align*}
9. 17613\begin{align*}17 \frac{6}{13}\end{align*}
10. 1947\begin{align*}19 \frac{4}{7}\end{align*}
11. 211112\begin{align*}21 \frac{11}{12}\end{align*}
12. 341225\begin{align*}34 \frac{12}{25}\end{align*}
13. 461624\begin{align*}46 \frac{16}{24}\end{align*}
14. 211820\begin{align*}21 \frac{18}{20}\end{align*}
15. 91930\begin{align*}9 \frac{19}{30}\end{align*}

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

### Vocabulary Language: English

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.