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# Decimals as Mixed Numbers

## Whole number and fraction with denominator of 10, 100 or 1000

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Decimals as Mixed Numbers

Henry is working on building a dog house. He needs to get lumber that is 6 inches wide and 1.5 inches thick. He goes to the hardware store and sees that they have 6 by \begin{align*}1\frac{1}{4}\end{align*}, 6 by \begin{align*}1 \frac{1}{2}\end{align*}, and 6 by \begin{align*}\frac{3}{4}\end{align*}. Which one does Henry need?

In this concept, you will learn to convert decimals to mixed numbers.

### Converting Decimals to Mixed Numbers

Some decimal numbers represent both a part and a whole. These decimal numbers can be written as mixed numbers. The decimal number must have both a whole and a part to be written as a mixed number. The mixed number and the decimal are equal because they both have the same value.

Here is a decimal number.

\begin{align*}4.5\end{align*}

Let’s write this decimal in a place value chart.

 Tens Ones Decimal Point Tenths Hundredths Thousandths Ten-Thousandths 4 . 5

This decimal number has 4 ones and 5 tenths. The 4 represents the wholes. The 5 tenths represents the fraction.  The five is the numerator and the tenths is the denominator.

\begin{align*}4.5 = 4 \frac{5}{10}\end{align*}

Next, check and see if the fraction can be simplified. In this case, five-tenths can be simplified to one-half.

\begin{align*}\frac{5}{10} =\frac{1}{2}\end{align*}

\begin{align*}4.5\end{align*} can be written as \begin{align*}4 \frac{1}{2}\end{align*}.

A decimal value can only be expressed one way. However, many fractions can be written to express the same value.

\begin{align*}0.75\end{align*} can be written as \begin{align*}\frac{75}{100}\end{align*}. You can make an equivalent fraction that has the same value.

Simplify \begin{align*}\frac{75}{100}\end{align*}.

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

You can keep on creating equivalent fractions that have the same value as \begin{align*}0.75\end{align*}.

\begin{align*}\frac{75}{100}= \frac{3}{4}=\frac{ 6}{8} = \frac{9}{12}\end{align*}

Finding equivalent fractions for mixed numbers is similar.  The whole number stays the same, but the fraction can vary.

Here is a decimal number.

\begin{align*}4.56\end{align*}

Convert the decimal number to a mixed number and find equivalent fractions.

First, convert the decimal to a mixed number. \begin{align*}4.56\end{align*} is read as four and fifty-six hundredths, the four is the whole number, the fifty-six is the numerator, and the denominator is the hundredths.

\begin{align*}4 \frac{56}{100}\end{align*}

Then, simplify the fraction part of this mixed number to get another mixed number that is equivalent to the one above. The greatest common factor of 56 and 100 is 4.

\begin{align*}4 \frac{56}{100}=4 \frac{14}{25}\end{align*}

### Examples

#### Example 1

Earlier, you were given a problem about Henry building a dog house.

He needs lumber that is 6 inches wide and \begin{align*}1.5\end{align*} inches thick. Convert \begin{align*}1.5\end{align*} inches into a fraction to find the lumber he needs.

First, convert the decimal to a fraction. \begin{align*}1.5\end{align*} is 1 and 5 tenths.

\begin{align*}1.5 = 1 \frac{5}{10}\end{align*}

Then, write the fraction in simplest form. The GCF of 5 and 10 is 5.

\begin{align*}1 \frac{5}{10} = 1\frac{1}{2}\end{align*}

Henry needs to by the 6 by \begin{align*}1 \frac{1}{2}\end{align*} inch pieces of wood.

#### Example 2

Convert the following decimal to a mixed number in simplest form.

\begin{align*}6.55\end{align*}

First, convert the decimal to a mixed number. \begin{align*}6.55\end{align*} is read as six and fifty-five hundredths. 6 is the whole number, 55 is the numerator, and 100 is the denominator.

\begin{align*}6.55 = 6 \frac{55}{100}\end{align*}

Then, write the fraction in simplest form. The GCF of 55 and 100 is 5.

\begin{align*}6\frac{55}{100} = 6 \frac{11}{20}\end{align*}

\begin{align*}6.55\end{align*} is written as \begin{align*} 6 \frac{11}{20}\end{align*} in simplest form.

#### Example 3

Convert the decimal to a mixed number in simplest form.

\begin{align*}7.8\end{align*}

First, convert the decimal to a mixed number. \begin{align*}7.8\end{align*} is 7 and 8 tenths.

\begin{align*}7.8 = 7 \frac{8}{10}\end{align*}

Then, write the fraction in simplest form. The GCF of 8 and 10 is 2.

\begin{align*}7 \frac{8}{10} = 7 \frac{4}{5}\end{align*}

\begin{align*}7.8\end{align*} is written as \begin{align*}7 \frac{4}{5}\end{align*} in simplest form.

#### Example 4

Convert the decimal to a mixed number in simplest form.

\begin{align*}4.45\end{align*}

First, convert the decimal to a mixed number. \begin{align*}4.45\end{align*} is 4 and 45 hundredths.

\begin{align*}4.45 = 4 \frac{45}{100}\end{align*}

Then, write the fraction in simplest form. The GCF of 45 and 100 is 5.

\begin{align*}4 \frac{45}{100} = 4 \frac{9}{20}\end{align*}

\begin{align*}4.45\end{align*} is written as \begin{align*}4 \frac{9}{20}\end{align*} in simplest form.

#### Example 5

Convert the decimal to a mixed number in simplest form.

\begin{align*}2.25\end{align*}

First, convert the decimal to a mixed number. \begin{align*}2.25\end{align*} is 2 and 25 hundredths.

\begin{align*}2.25 = 2 \frac{25}{100}\end{align*}

Then, write the fraction in simplest form. The GCF of 25 and 100 is 25.

\begin{align*}2 \frac{25}{100} = 2 \frac{1}{4}\end{align*}

\begin{align*}2.25\end{align*} is written as \begin{align*}2 \frac{1}{4}\end{align*} in simplest form.

### Review

Convert each decimal to a mixed number in simplest form.

1. 3.5
2. 2.4
3. 13.2
4. 25.6
5. 3.45
6. 7.17
7. 18.18
8. 9.20
9. 7.65
10. 13.11
11.  7.25
12. 9.75
13. 10.10
14. 4.33
15. 8.22

To see the Review answers, open this PDF file and look for section 5.18.

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Color Highlighted Text Notes

### Vocabulary Language: English

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).

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 $4\frac{3}{5}$.