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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

Have you ever run track at school?

Henry enjoys running track. He ran a mile in 5.23 last month and hopes to beat his own record this month.

Henry's time was recorded using a decimal.

What would his time have been if it was written as a mixed number?

Writing decimals as mixed numbers is the content of this Concept. At the end of the Concept, you will know how Henry can write his time as a mixed number.

Guidance

Some decimals represent both a part and a whole. We can take these decimals and write them as mixed numbers . The mixed number and the decimal, which contains a part and a whole, are equivalent because they are both referring to the same amount.

How do we write a decimal as a mixed number?

To write a decimal as a mixed number, we need to have a decimal that has both wholes and parts in it.

$4.5$

This decimal has four wholes and five tenths. Let’s write this decimal in a place value chart so that we can convert it to a mixed number.

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

We can read this decimal as four and five tenths. The four represents the wholes. The and represents the decimal point. The five is the numerator of the fraction and the tenths represents the denominator.

The answer is $4\frac{5}{10}$ .

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

Our final answer is $4\frac{1}{2}$ .

When we convert a decimal to a fraction, we are writing two parts that are equivalent or equal. Because of this, we can write more than one equivalent fraction for any single decimal.

You will need to think back to our Concept on creating equivalent fractions for this to make sense.

$.75$

This decimal can be read as “Seventy-five hundredths.” We know that we can write the fraction by using these words as we read the decimal. The seventy-five is our numerator and the hundredths is our denominator.

$\frac{75}{100}$

When we simplify this fraction, we have another equivalent fraction to $.75$ .

$\frac{75}{100}=\frac{3}{4}$

Now we can keep on creating equivalent fractions for three-fourths by simply multiplying the same number with the numerator and the denominator. Let’s create another equivalent fraction by multiplying by two.

$\frac{75}{100}=\frac{3}{4}=\frac{6}{8}$

We could go on and on. The important thing to notice is that each of these fractions is equivalent to .75, since they are just different forms of the same thing.

How do we write equivalent fractions for decimals that have wholes and parts?

We are going to work with these decimals in the same way, except we will be converting them to mixed numbers and then writing equivalent mixed numbers from there.

$4.56$

We can write this as a mixed number by reading the decimal. With four and fifty-six hundredths, the four is the whole number, the fifty-six is the numerator and the denominator is the hundredths.

$4\frac{56}{100}$

If we simplify the fraction part of this mixed number, we will have another mixed number that is equivalent to the one that we just wrote. The greatest common factor of 56 and 100 is four. Now we can simplify the fraction part.

$4\frac{56}{100}=4\frac{14}{25}$

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

Example A

$7.8$

Solution: $7 \frac{4}{5}$

Example B

$4.45$

Solution: $4 \frac{9}{20}$

Example C

$2.25$

Solution: $2 \frac{1}{4}$

Now back to Henry and his running.

Henry enjoys running track. He ran a mile in 5.23 last month and hopes to beat his own record this month.

Henry's time was recorded using a decimal.

What would his time have been if it was written as a mixed number?

To write Henry's time as a mixed number, we have to separate the parts and the wholes.

$5 \frac{23}{100}$

Vocabulary

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.

Guided Practice

Here is one for you to try on your own.

Write the following decimal as a mixed number in simplest form.

$6.55$

First, we separate the wholes and the parts.

$6 \frac{55}{100}$

But our work isn't done yet because this fraction can be simplified.

Our final answer is $6 \frac{11}{20}$ .

Practice

Directions: Write each decimal as a mixed number. Simplify the fraction part if possible.

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

Vocabulary Language: English

Decimal

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

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

Mixed Number

A mixed number is a number made up of a whole number and a fraction, such as $4\frac{3}{5}$.