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*}

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*}

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*}

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

### Examples

#### Example 1

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

Joey needs \begin{align*}\frac{5}{8}\end{align*}

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*}

#### 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*}

#### 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.