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5.20: Mixed Numbers as Decimals

Difficulty Level: At Grade Created by: CK-12
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Practice Mixed Numbers as Decimals

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Have you ever had to tile a floor? Take a look at this dilemma.

Kara is learning to work with mixed numbers. At the same time, she is working on tiling the entryway with her mother. Together, they have \begin{align*}6 \frac{1}{2}\end{align*} feet left to tile.

How could they write this number as a decimal?

This Concept will teach you all about how to write mixed numbers as decimals. Pay attention and you will be able to complete this problem at the end of the Concept.

Guidance

In the last Concept, you learned how to write fractions as decimals. You can use the two methods that you used in the last Concept to write mixed numbers as decimals.

How can we write a decimal from a mixed number that has a base ten denominator?

When we have a base ten denominator in the fraction part of a mixed number, we can think in terms of place value. Read the fraction to yourself and picture what this would look like as a decimal. You know that tenths have one decimal place, hundredths have two, thousandths have three and so on. This information will guide you in your work writing decimals.

\begin{align*}5\frac{3}{10}\end{align*}

The five is our whole number it goes to the left of the decimal point. Three-tenths can become .3. Our final answer is 5.3.

How do we write a decimal when we don’t have a base ten denominator?

When this happens, we need to use division.

\begin{align*}8\frac{1}{5}\end{align*}

We have the 8 as our whole number. It goes to the left of the decimal point. We divide 1 by 5 to get our decimal part of the number. Once again, we add a decimal point and a zero placeholder to divide completely.

\begin{align*}& \overset{ \quad \ .2}{5 \overline{ ) {1.0 \;}}}\\ & \ \underline{-10}\\ & \quad \ \ 0\end{align*}

Our final answer is \begin{align*}8.2\end{align*}.

Try a few of these on your own. Write each mixed number as a decimal.

Example A

\begin{align*}6\frac{13}{100}\end{align*}

Solution:\begin{align*}6.13\end{align*}

Example B

\begin{align*}15\frac{9}{10}\end{align*}

Solution:\begin{align*}15.9\end{align*}

Example C

\begin{align*}6\frac{1}{4}\end{align*}

Solution:\begin{align*}6.25\end{align*}

Now back to Kara and the floor. Here is the original problem.

Kara is learning to work with mixed numbers. At the same time, she is working on tiling the entryway with her mother. Together, they have \begin{align*}6 \frac{1}{2}\end{align*} feet left to tile.

How could they write this number as a decimal?

To do this, we will need to separate the wholes from the parts.

Then we can divide the numerator of the fraction by the denominator to find the part of the decimal.

\begin{align*}1 \div 2 = .50\end{align*}

Kara and her mom have \begin{align*}6.50\end{align*} feet left to tile.

Vocabulary

Here are the vocabulary words found in this Concept.

Decimal
a part of a whole written using place value and a decimal point.
Fraction
a part of a whole written with a fraction bar dividing the numerator and the denominator.
Mixed Number
a number that has a whole number and a fraction.
Equivalent
means equal

Guided Practice

Here is one for you to try on your own.

Write the following mixed number as a decimal.

\begin{align*}16 \frac{3}{4}\end{align*}

To convert the fraction part into a decimal, we can divide or use a proportion. Here is a proportion.

\begin{align*} \frac{3}{4} = \frac{75}{100}\end{align*}

Our final answer is \begin{align*}6.75\end{align*}.

Video Review

Here are videos for review.

Practice

Directions: Write each mixed number as a decimal.

1. \begin{align*}4\frac{1}{10}\end{align*}

2. \begin{align*}6\frac{8}{10}\end{align*}

3. \begin{align*}14\frac{6}{100}\end{align*}

4. \begin{align*}7\frac{18}{100}\end{align*}

5. \begin{align*}12\frac{9}{10}\end{align*}

6. \begin{align*}24\frac{11}{100}\end{align*}

7. \begin{align*}8\frac{19}{100}\end{align*}

8. \begin{align*}5\frac{10}{20}\end{align*}

9. \begin{align*}4\frac{1}{2}\end{align*}

10. \begin{align*}7\frac{1}{3}\end{align*}

11. \begin{align*}5\frac{2}{10}\end{align*}

12. \begin{align*}9\frac{1}{8}\end{align*}

13. \begin{align*}10\frac{2}{100}\end{align*}

14. \begin{align*}46\frac{1}{4}\end{align*}

15. \begin{align*}65\frac{4}{5}\end{align*}

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Color Highlighted Text Notes

Vocabulary Language: English

TermDefinition
Decimal In common use, a decimal refers to part of a whole number. The numbers to the left of a decimal point represent whole numbers, and each number to the right of a decimal point represents a fractional part of a power of one-tenth. For instance: The decimal value 1.24 indicates 1 whole unit, 2 tenths, and 4 hundredths (commonly described as 24 hundredths).
Equivalent Equivalent means equal in value or meaning.
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 $4\frac{3}{5}$.

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