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6.1: Fraction Rounding to the Nearest Half

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Have you ever measured something? Was the measurement perfect or was it too small?

Well, if you were working on a construction site, you would be doing a lot of measuring so rounding up or down if things weren't perfect would be very important. These part measurements are also fractions, just like you have learned about in other Concepts.

Think about how you would round: three - fourths, one - sixth or five - tenths as you work through this Concept.

In this Concept, you will learn how to round a fraction to the nearest half.

Guidance

We use fractions in everyday life all the time. Remember that when we talk about a fraction, we are talking about a part of a whole. Often times, we need to use an exact fraction, but sometimes, we can use an estimate . If you think back to our earlier work on estimation, you will remember that an estimate is an approximate value that makes sense or is reasonable given the problem.

What fraction does this picture represent?

If we wanted to be exact about this fraction, we could say that there are \frac{12}{20} shaded boxes. However, it might be simpler to say that about half of the boxes are shaded.

We call this rounding to the nearest half.

How do we round to the nearest half?

To round a fraction to the nearest half, we need to think in terms of halves. We often think in terms of wholes, so this is definitely a change in our thinking. There are three main values to round to when we round a fraction to the nearest half.

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

\frac{5}{6}

To figure out which value five-sixths is closest to, we must first think in terms of sixths. Since the denominator is six, that means that the whole is divided into six parts. The fraction \frac{0}{6} would be the value of zero, \frac{3}{6} would be the value of \frac{1}{2} , and \frac{6}{6} is the same as 1. The fraction \frac{5}{6} is closest to \frac{6}{6} , so rounding to the nearest half would be rounding to 1.

Our answer is 1.

Try a few of these on your own. Round each fraction to the nearest half.

Example A

\frac{1}{5}

Solution: 0

Example B

\frac{3}{8}

Solution: \frac{1}{2}

Example C

\frac{7}{9}

Solution: 1

Now let's go back and think about those measurements from the very beginning of the Concept.

Think about how you would round: three - fourths, one - sixth or five - tenths as you work through this Concept. We can round three - fourths to 1. We can round one - sixth down to 0. We can round five - tenths to one - half.

Vocabulary

Here are the vocabulary words in this Concept.

Fraction
a part of a whole written with a fraction bar, a numerator and a denominator.
Estimate
to find an approximate answer that is reasonable and makes sense given the problem.

Guided Practice

Here is one for you to try on your own.

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

Answer

If \frac{4}{9} of the pan had been eaten, then that means that \frac{5}{9} of the pan had not been eaten. This is closer to one - half of the pan of brownies.

Video Review

Here are videos for review.

Estimating with fractions - This video is a secondary skill to rounding fractions. It involves estimating with fractions.

Practice

Directions : Round each fraction to the nearest half.

1. \frac{2}{15}

2. \frac{1}{7}

3. \frac{8}{9}

4. \frac{7}{15}

5. \frac{6}{13}

6. \frac{10}{11}

7. \frac{7}{8}

8. \frac{4}{7}

9. \frac{3}{7}

10. \frac{1}{19}

11. \frac{2}{10}

12. \frac{4}{5}

13. \frac{2}{3}

14. \frac{2}{11}

15. \frac{1}{9}

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Date Created:

Oct 29, 2012

Last Modified:

Nov 26, 2014
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