Take a look at this dilemma.

At the bake sale, the seventh grade has set up two tables full of baked goods. There was so much baked that they also have extras on reserve. The students have decided to run the bake sale for three days so that they can try to sell their good throughout all three lunch periods at school. They hope to raise a lot of money.

Derek and Keisha have been assigned the task of keeping track of sales. They need to keep track of how much of each item is sold. For example, if there are twelve cupcakes and six of them sell, then they could write one-half as the statistic for cupcakes. The students think that if they keep track of each item sold, that they will have a good idea of which items are the big sellers.

The first day goes smoothly. Derek and Keisha each keep track of one table and they split the third table in half. At the end of the sale day, they sit down to compare notes.

Derek has written these amounts down.

Peach pie .10

Cupcakes .75

Brownies .50

Bread .25

Keisha has written these amounts down.

Blueberry pie \begin{align*}\frac{1}{2}\end{align*}

Chocolate cookies \begin{align*}\frac{1}{4}\end{align*}

Blueberry muffins \begin{align*}\frac{1}{3}\end{align*}

Double Fudge Brownies \begin{align*}\frac{3}{4}\end{align*}

Apple pie \begin{align*}\frac{5}{6}\end{align*}

They are surprised to see that one of them has written all of the data in decimals while the other has written all of the data in fraction form. To figure out which items were the biggest sellers they will have to order their data.

Derek needs to write his decimals in order from greatest to least and Keisha needs to write her fractions in order from greatest to least.

**This Concept will teach you all you need to know about comparing and ordering fractions and decimals.**

### Guidance

Eventually, you will be able to convert common fractions to decimals and common decimals to fractions in your head. You already know some of the classics like \begin{align*}0.5 = \frac{1}{2}\end{align*}.

Knowing this off the top of your head will make it easy for you to compare and order between fractions and decimals. For now, we will use our expertise at converting to compare and order. It’s always helpful to check.

Compare \begin{align*}\frac{1}{4}\end{align*} and 0.25 using <, > or =

**To compare a fraction to a decimal or a decimal to a fraction, we will need to convert one of them, so that we can compare a fraction to a fraction or a decimal to a decimal.** For this one, I will convert \begin{align*}\frac{1}{4}\end{align*} to a decimal. I divide 1.0 by 4. 4 goes into 1.0 .2 times. There is also a remainder of 0.20 and 4 goes into 0.20 0.05 times. Now we know that \begin{align*}\frac{1}{4}\end{align*} written as a decimal is 0.25.

**We compare it as \begin{align*}\frac{1}{4} = 0.25\end{align*}.**

Here is another one.

Compare \begin{align*}1 \frac{2}{20}\end{align*} and 1.30

**Our work in estimating the value of fractions and rounding decimals can be helpful when comparing fractions and decimals because you can look at a fraction or a decimal and quickly have a sense of what the approximate value is.** Take a look at the mixed number \begin{align*}1 \frac{2}{20}\end{align*}. Don’t be intimidated by the large denominator, it looks like we can simplify it. If we simplify it to \begin{align*}1 \frac{1}{10}\end{align*}.

Now we can take 1.30 and make it a mixed number. 1.30 becomes \begin{align*}1 \frac{3}{10}\end{align*}.

**Our final answer is that \begin{align*}1 \frac{2}{20} < 1.30\end{align*}.**

We can use all of these strategies when ordering fractions and decimals too. Be sure that they are in the same form and then order them from least to greatest or from greatest to least.

Now it's time for you to try a few on your own. Compare using <,> or =.

#### Example A

\begin{align*}.5\end{align*} and \begin{align*}\frac{1}{4}\end{align*}

**Solution: >**

#### Example B

\begin{align*}3 \frac{3}{5}\end{align*} and \begin{align*}3.56\end{align*}

**Solution: >**

#### Example C

\begin{align*}\frac{2}{8}\end{align*} and \begin{align*}.25\end{align*}

**Solution: =**

Let’s go back to our original problem now and apply what we have learned.

Here is the original problem once again.

At the bake sale, the seventh grade has set up two tables full of baked goods. There was so much baked that they also have extras on reserve. The students have decided to run the bake sale for three days so that they can try to sell their good throughout all three lunch periods at school. They hope to raise a lot of money.

Derek and Keisha have been assigned the task of keeping track of sales. They need to keep track of how much of each item is sold. For example, if there are twelve cupcakes and six of them sell, then they could write one-half as the statistic for cupcakes. The students think that if they keep track of each item sold, that they will have a good idea of which items are the big sellers.

The first day goes smoothly. Derek and Keisha each keep track of one table and they split the third table in half. At the end of the sale day, they sit down to compare notes.

Derek has written these amounts down.

Peach pie .10

Cupcakes .75

Brownies .50

Bread .25

Keisha has written these amounts down.

Blueberry pie \begin{align*}\frac{1}{2}\end{align*}

Chocolate cookies \begin{align*}\frac{1}{4}\end{align*}

Blueberry muffins \begin{align*}\frac{1}{3}\end{align*}

Double Fudge Brownies \begin{align*}\frac{3}{4}\end{align*}

Apple pie \begin{align*}\frac{5}{6}\end{align*}

They are surprised to see that one of them has written all of the data in decimals while the other has written all of the data in fraction form. To figure out which items were the biggest sellers they will have to order their data.

Derek needs to write his decimals in order from greatest to least and Keisha needs to write her fractions in order from greatest to least.

**First, Derek needs to write his data in order from greatest to least.**

**Cupcakes .75**

**Brownies .50**

**Bread .25**

**Peach Pie .10**

**Next, Keisha needs to write her data in order from greatest to least.**

**Apple pie \begin{align*}\frac{5}{6}\end{align*}**

**Double Fudge Brownies \begin{align*}\frac{3}{4}\end{align*}**

**Blueberry Pie \begin{align*}\frac{1}{2}\end{align*}**

**Chocolate Cookies \begin{align*}\frac{1}{4}\end{align*}**

**Blueberry Muffins \begin{align*}\frac{1}{3}\end{align*}**

**Given this information, the top seller were the apple pies, the double fudge brownies, the cupcakes and the brownies. Derek and Keisha report their sales to their teacher and they decide to put out more of those items for day two of the bake sale.**

### Vocabulary

- Fraction
- a part of a whole written using a numerator and a denominator and a fraction bar

- Decimal
- a part of a whole written using a decimal point and place value

- Mixed Number
- a number written with a whole number and a fraction.

### Guided Practice

Here is one for you to try on your own.

Compare the following values using <, > or =.

\begin{align*}.45\end{align*} and \begin{align*}\frac{6}{10}\end{align*}

**Answer**

To compare these two values, let's convert the fraction into a decimal.

\begin{align*}\frac{6}{10} = .6\end{align*}

Now we can easily compare.

\begin{align*}.45 < .6\end{align*}

**This is our answer.**

### Video Review

- This is a James Sousa video on ordering decimals and fractions from least to greatest.

### Practice

Directions: Compare the following decimals and fractions using <, > or =

1. \begin{align*}\frac{1}{3}\end{align*} *and* .5

2. \begin{align*}\frac{6}{10}\end{align*} *and* .9

3. .25 *and* \begin{align*}\frac{1}{10}\end{align*}

4. .16 *and* \begin{align*}\frac{33}{100}\end{align*}

5. \begin{align*}\frac{3}{5}\end{align*} *and* .6

6. \begin{align*}\frac{3}{15}\end{align*} *and* .15

7. \begin{align*}\frac{6}{7}\end{align*} *and* .99

8. \begin{align*}\frac{3}{4}\end{align*} *and* .75

9. \begin{align*}\frac{1}{9}\end{align*} *and* .33

10. \begin{align*}\frac{7}{10}\end{align*} *and* .8

Directions: Write the following values in order from least to greatest.

11. \begin{align*}.25, \frac{1}{3}, .54\end{align*}

12. \begin{align*}.55, \frac{3}{4}, .613\end{align*}

13. \begin{align*}.252, \frac{1}{9}, .31\end{align*}

14. \begin{align*}.05, \frac{7}{8}, .546\end{align*}

15. \begin{align*}.09, \frac{1}{10}, .88\end{align*}