Have you ever had an argument with a brother or sister? Well here is one that Casey and her brother Alex had.

Casey and Alex were both working on their homework. Alex bet Casey that he could finish his homework before she did. Even though she knew it wasn't a good idea, Casey agreed to the contest. After about fifteen minutes, Alex looked over at Casey.

"I have completed \begin{align*}52%\end{align*} of my homework," he said.

"Well, I have completed a ratio of 3 out of 5 of my possible assignments," Casey said smirking.

Casey had meant to be a "smart alec" to Alex.

"I have more done," he returned.

"No you don't."

Who is right?

To answer this questions, you will need to know how to compare fractions, decimals and percents.

**This Concept will teach you all that you need to know.**

### Guidance

We have already established that fractions, decimals and percents are all related to one another. Because they are related and we can establish ** equivalents** of each, we can also

**each using greater than, less than or equal to. We can also write them in order.**

*compare*
**To compare fractions, decimals and percents, we should have them in the same form. If we are comparing a fraction and a percent, we have to write both of them either as fractions or percents so we can figure out which is greater.**

Compare \begin{align*}45%\end{align*} and \begin{align*}\frac{4}{5}\end{align*}

**To compare these two quantities, first write them in the same form. Let’s change four-fifths to a percent.** We do that by writing it as a fraction out of 100, which we can then change to a percent.

\begin{align*}\frac{4}{5}=\frac{80}{100}=80\%\end{align*}

**\begin{align*}45%\end{align*} is less than \begin{align*}80%\end{align*}.**

**Our answer is \begin{align*}45\% < \frac{4}{5}\end{align*}.**

**We can do the same thing when working with decimals and percents.**

Compare \begin{align*}18%\end{align*} and \begin{align*}.9\end{align*}

**To complete this, we have to convert both of these to either percents or decimals. Let’s change .9 to a percent. To do this, we move the decimal point two places to the right.**

**.9 = 90%**

**18% is less than 90%.**

**Our answer is 18% < .9.**

**What about ordering fractions, decimals and percents?**

When we ** order** a set of numbers or quantities, we write them from least to greatest or from greatest to least.

**Fractions, decimals and percents are no exception, but it is to order them if they are in the same form.**

Write .56, 34%, \begin{align*}\frac{9}{10}\end{align*} and \begin{align*}\frac{1}{2}\end{align*} in order from least to greatest

**To do this, we need to write them all in the same form. Let’s convert all of them to percents.**

\begin{align*}.56 = 56\%\end{align*}

**\begin{align*}34%\end{align*} stays the same**

\begin{align*}\frac{9}{10} &= \frac{90}{100}=90\%\\ \frac{1}{2} &= \frac{50}{100}=50\%\end{align*}

**So we have 56%, 34%, 90% and 50%, now it becomes easy to write them in order.**

**34%, 50%, 56%, and 90%**

**Our answer is 34%, \begin{align*}\frac{1}{2}\end{align*}, .56, \begin{align*}\frac{9}{10}\end{align*}.**

**Try a few of these on your own. Use greater than >, less than < or = .**

#### Example A

**.19 and 19%**

**Solution: Equal =**

#### Example B

\begin{align*}\frac{2}{5}\end{align*} **and 45%**

**Solution: < Less than**

#### Example C

**56% and 21%**

**Solution: > Greater than**

Remember Casey and Alex? Here is the original problem once again.

Casey and Alex were both working on their homework. Alex bet Casey that he could finish his homework before she did. Even though she knew it wasn't a good idea, Casey agreed to the contest. After about fifteen minutes, Alex looked over at Casey.

"I have completed 52% of my homework," he said.

"Well, I have completed a ratio of 3 out of 5 of my possible assignments," Casey said smirking.

Casey had meant to be a "smart alec" to Alex.

"I have more done," he returned.

"No you don't."

Who is right?

To compare these two values, we need to write them both as the same thing.

Let's convert Casey's fraction to a percent. We can use an equivalent fraction out of 100.

\begin{align*} \frac{3}{5} = \frac{60}{100}\end{align*}

Now we convert that to 60%.

Finally, we can compare the two percents.

60% and 52%

60% is greater.

**Casey has completed more of her homework than Alex has.**

### Vocabulary

Here are the vocabulary words in this Concept.

- Percent
- is "per-cent" or "per-hundred", it is a quantity written with a % sign, a part of a whole (100)

- Fraction
- a part of a whole, related to decimals and percents.

- Decimal
- a part of a whole shown by a decimal point, hundredths means two decimal places.

- Equivalent
- means equal

- Compare
- to determine whether a quantity is greater than, less than, or equal to another quantity.

- Order
- to write in order from least to greatest or from greatest to least.

### Guided Practice

Here is one for you to try on your own.

Write these values in order from least to greatest.

\begin{align*} \frac{83}{100}, .16, 33%, \frac{4}{5}\end{align*}

**Answer**

First, we have to think in terms of parts and which values are closest to a whole.

\begin{align*}.16\end{align*} is a very small value. It comes first.

\begin{align*}33%\end{align*} is also small. It comes second.

The next two are the trickiest. We know that four -fifths is close to one whole and so is 83 out of 100. We can convert four - fifths to a fraction with a denominator of 100 so that we can easily compare these two.

\begin{align*} \frac{4}{5} = \frac{80}{100}\end{align*}

Now we can see that four -fifths is smaller than 83 hundredths.

Here is our final answer.

\begin{align*}.16, 33%, \frac{4}{5}, \frac{83}{100}\end{align*}

### Video Review

Here is a video for review.

James Sousa: Ex: Compare Fractions and Decimals using Inequality Symbols

### Practice

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

1. \begin{align*} \frac{16}{100}, .27, 53%, \frac{1}{5}\end{align*}

2. \begin{align*} \frac{99}{100}, .30, 68%, \frac{9}{10}\end{align*}

3. \begin{align*} \frac{18}{100}, .99, 87%, \frac{10}{20}\end{align*}

4. \begin{align*} \frac{88}{100}, .18, 23%, \frac{1}{5}\end{align*}

5. \begin{align*} \frac{93}{100}, .98, 6%, \frac{1}{2}\end{align*}

6. \begin{align*} \frac{77}{100}, .37, 93%, \frac{2}{5}\end{align*}

7. \begin{align*} \frac{12}{100}, .76, 13%, \frac{1}{3}\end{align*}

8. \begin{align*} \frac{9}{100}, .2, 67%, \frac{4}{5}\end{align*}

9. \begin{align*} \frac{88}{100}, .29, 35%, \frac{2}{10}\end{align*}

Directions: Compare the following pairs of fractions using <,> or =.

10. \begin{align*}\frac{6}{7}\end{align*} **and 35%**

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

12. \begin{align*}\frac{1}{2}\end{align*} **and 55%**

13. \begin{align*}\frac{9}{10}\end{align*} **and 25%**

14. \begin{align*}\frac{1}{4}\end{align*} **and 25%**

15. \begin{align*}\frac{1}{5}\end{align*} **and 15%**