Joey is cooking and needs

teaspoon of pepper. He only has a teaspoon measuring spoon. How many teaspoons of cinnamon does Joey need to make his dish?In this concept, you will learn how to round a fraction to the nearest half.

### Rounding Fractions to the Nearest Half

A **fraction** is a part of a whole. Instead of finding the exact value of a fraction, you can use an estimate to get a general idea. An **estimate** is an approximate value that makes sense or is reasonable given the problem.

Here is a representation of a fraction.

There are 12 out of 20 shaded boxes. This fraction is exactly \begin{align*}\frac{12}{20}\end{align*}. You could also say that about half of the boxes are shaded. This is called rounding to the nearest half.

Think of fractions in terms of halves. There are three main values to round to when rounding a fraction to the nearest half.

The first is zero. Zero is also \begin{align*}\frac{0}{2}\end{align*}, or zero halves. The second value is \begin{align*}\frac{1}{2}\end{align*}, or one half. The third value is 1, which can be thought of as \begin{align*}\frac{2}{2}\end{align*}, or two halves. When rounding to the nearest half, round the fraction to whichever half the fraction is closest to on the number line. If a fraction is equally close to two different halves, round the fraction up.

Here is a fraction.

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

To figure out which value five-sixths is closest to, first think in terms of sixths. Since the denominator is six, that means that the whole is divided into six parts. The fraction \begin{align*}\frac{0}{6}\end{align*} would be the value of zero, \begin{align*}\frac{3}{6}\end{align*} would be the value of \begin{align*}\frac{1}{2}\end{align*}, and \begin{align*}\frac{6}{6}\end{align*} is the same as 1.

The fraction \begin{align*}\frac{5}{6}\end{align*} is closest to \begin{align*}\frac{6}{6}\end{align*}, so rounding to the nearest half would be rounding to 1.

### Examples

#### Example 1

Earlier, you were given a problem about Joey and his measuring spoon.

Joey needs \begin{align*}\frac{5}{8}\end{align*} teaspoon of cinnamon but only has a one-half teaspoon measuring spoon. Round \begin{align*}\frac{5}{8}\end{align*} to the nearest \begin{align*}\frac{1}{2}\end{align*} to find out how many one-half teaspoon Joey needs.

Use a number line of 1 whole divided into 8 parts to round

to the nearest .

is close to

#### Example 2

Round the following fraction to the nearest half: \begin{align*}\frac{1}{5}\end{align*}.

Use a number line of 1 whole divided into 5 equal parts.

\begin{align*}\frac{1}{5}\end{align*} rounds to 0.

#### Example 3

Round the following fraction to the nearest half: \begin{align*}\frac{3}{8}\end{align*}.

Use a number line of 1 whole divided into 8 equal part.

\begin{align*}\frac{3}{8}\end{align*} rounds to .

#### Example 4

Round the following fraction to the nearest half: \begin{align*}\frac{7}{9}\end{align*}.

Use a number line of 1 whole divided into 9 equal parts. \begin{align*}\frac{7}{9}\end{align*} is closer to 1.

rounds to 1.

#### Example 5

Jessica discovered that \begin{align*}\frac{4}{9}\end{align*} of a pan of brownies had been eaten. Is the amount of brownies left closer to one-half or one whole?

First, find the amount of brownies left. If \begin{align*}\frac{4}{9}\end{align*} of the pan had been eaten, then that means that \begin{align*}\frac{5}{9}\end{align*} of the pan had not been eaten.

Then, use a number line to round

whole is divided into 9 parts. The fraction is zero, one half is between and , and 1 would be .

\begin{align*}\frac{5}{9}\end{align*} is closer to . There was about one-half of the pan of brownies left.

### Review

Round each fraction to the nearest half.

- \begin{align*}\frac{2}{15}\end{align*}
- \begin{align*}\frac{1}{7}\end{align*}
- \begin{align*}\frac{8}{9}\end{align*}
- \begin{align*}\frac{7}{15}\end{align*}
- \begin{align*}\frac{6}{13}\end{align*}
- \begin{align*}\frac{10}{11}\end{align*}
- \begin{align*}\frac{7}{8}\end{align*}
- \begin{align*}\frac{4}{7}\end{align*}
- \begin{align*}\frac{3}{7}\end{align*}
- \begin{align*}\frac{1}{19}\end{align*}
- \begin{align*}\frac{2}{10}\end{align*}
- \begin{align*}\frac{4}{5}\end{align*}
- \begin{align*}\frac{2}{3}\end{align*}
- \begin{align*}\frac{2}{11}\end{align*}
- \begin{align*}\frac{1}{9}\end{align*}

### Review (Answers)

To see the Review answers, open this PDF file and look for section 6.1.