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# Positive and Negative Fraction and Decimal Comparison

## Use <, > and/or = to compare positive and negative fractions and decimals.

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Positive and Negative Fraction and Decimal Comparison

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

Keisha has written these amounts down.

Blueberry pie 12\begin{align*}\frac{1}{2}\end{align*}

Chocolate cookies 14\begin{align*}\frac{1}{4}\end{align*}

Blueberry muffins 13\begin{align*}\frac{1}{3}\end{align*}

Double Fudge Brownies 34\begin{align*}\frac{3}{4}\end{align*}

Apple pie 56\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 0.5=12\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 14\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 14\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 14\begin{align*}\frac{1}{4}\end{align*} written as a decimal is 0.25.

We compare it as 14=0.25\begin{align*}\frac{1}{4} = 0.25\end{align*}.

Here is another one.

Compare 1220\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 1220\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 1110\begin{align*}1 \frac{1}{10}\end{align*}.

Now we can take 1.30 and make it a mixed number. 1.30 becomes 1310\begin{align*}1 \frac{3}{10}\end{align*}.

Our final answer is that 1220<1.30\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

.5\begin{align*}.5\end{align*} and 14\begin{align*}\frac{1}{4}\end{align*}

Solution: >

#### Example B

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

Solution: >

#### Example C

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

Keisha has written these amounts down.

Blueberry pie 12\begin{align*}\frac{1}{2}\end{align*}

Chocolate cookies 14\begin{align*}\frac{1}{4}\end{align*}

Blueberry muffins 13\begin{align*}\frac{1}{3}\end{align*}

Double Fudge Brownies 34\begin{align*}\frac{3}{4}\end{align*}

Apple pie 56\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

Peach Pie .10

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

Apple pie 56\begin{align*}\frac{5}{6}\end{align*}

Double Fudge Brownies 34\begin{align*}\frac{3}{4}\end{align*}

Blueberry Pie 12\begin{align*}\frac{1}{2}\end{align*}

Chocolate Cookies 14\begin{align*}\frac{1}{4}\end{align*}

Blueberry Muffins 13\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 =.

.45\begin{align*}.45\end{align*} and 610\begin{align*}\frac{6}{10}\end{align*}

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

610=.6\begin{align*}\frac{6}{10} = .6\end{align*}

Now we can easily compare.

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

### Practice

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

1. 13\begin{align*}\frac{1}{3}\end{align*} and .5

2. 610\begin{align*}\frac{6}{10}\end{align*} and .9

3. .25 and 110\begin{align*}\frac{1}{10}\end{align*}

4. .16 and 33100\begin{align*}\frac{33}{100}\end{align*}

5. 35\begin{align*}\frac{3}{5}\end{align*} and .6

6. 315\begin{align*}\frac{3}{15}\end{align*} and .15

7. 67\begin{align*}\frac{6}{7}\end{align*} and .99

8. 34\begin{align*}\frac{3}{4}\end{align*} and .75

9. 19\begin{align*}\frac{1}{9}\end{align*} and .33

10. 710\begin{align*}\frac{7}{10}\end{align*} and .8

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

11. .25,13,.54\begin{align*}.25, \frac{1}{3}, .54\end{align*}

12. .55,34,.613\begin{align*}.55, \frac{3}{4}, .613\end{align*}

13. .252,19,.31\begin{align*}.252, \frac{1}{9}, .31\end{align*}

14. .05,78,.546\begin{align*}.05, \frac{7}{8}, .546\end{align*}

15. .09,110,.88\begin{align*}.09, \frac{1}{10}, .88\end{align*}

### Notes/Highlights Having trouble? Report an issue.

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