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You are here: HomeLessons → Comparing fractions, decimals, and percentages

Does your child struggle with fractions, decimals, and percentages? That is not uncommon. Sometimes parents are not clear on these concepts either, which adds to the confusion and pressure on getting math right. Let's find ways you can explain this better to your child.

Let's first take a quick look at what fractions, decimals, and percentages actually are.

### Fractions

In elementary mathematics, children first encounter fractions as representing a part of a whole. For example, suppose you have a cake cut to four equal parts. Then the fraction ¾ means three pieces out of those four.

From that, children need to advance to understand that fractions can also be viewed as NUMBERS — for example, we can place them on a number line.

### Decimals

Decimals (used in everyday life) actually are FRACTIONS – but they are fractions with a denominator that is a power of ten (10, 100, 1000, etc.).

It is important to be able to write decimals as fractions. For example, the decimal 0.8 is the same as the fraction 8/10, and 0.49 is the same as 49/100. Or, 0.002 is 2/1000 and 5.06 is 506/100. The number of decimal digits actually tells us how many zeros are in the power of ten that is used as a denominator — see this video and this for more details about decimal place value.

Decimals are easy to use in calculators, and a calculator also allows you to convert any fraction to a decimal easily. How to use a calculator? You can check the manual of your calculator, or search the internet.

### Percentages

Percentages are fractions (yes, it's that simple!) with a denominator of 100. To put it in other words, they're decimals with two decimal digits (hundredth parts). Or, we can say percentages are ratios where we compare a number to 100. For example, 54 percent means 54/100 (fifty-four hundredths, or 0.54), and 6% means 6/100.

The easiest way to demonstrate percentages to your child might be discounts, using \$100 as the original price of the item. Explain to your child that 20% off means that \$20 of the price goes "off" and you only have to pay \$80.

Another popular use of percentage is VAT or taxes. Both are calculated in terms of percentages. If there is a 10% VAT on clothing, that means you will pay an additional 10 dollars per \$100 of purchase of clothing items (or a tenth part).

Here is a Quiz that helps you check whether you already know the basics of percentages.

## Comparing the three

Comparing fractions, decimals, and percentages is easy once you first learn what decimals and percentages are (the FOUNDATION).

Like I already mentioned, decimals we use in everyday life are simply fractions with a denominator that is a power of ten (10, 100, 1000, etc.). And percentages are fractions with a denominator of 100.

So, to compare the three, you simply convert for example the fraction and the percentage to decimals. Or, you could convert the fraction and the decimal to percentages. After that, comparing them is simply a matter of comparing decimals.

This means that to learn to compare fractions, percentages, and decimals, you really need to first learn to convert fractions to decimals and percentages to decimals. Check out for example this video: Fractions to decimals, and comparing decimals. You can also get lots of help from my worktext (workbook) Math Mammoth Percent.

Example 1. Write in order: 1/4, 20%, 0.34.
We can write 1/4 as the equivalent fraction 25/100, which equals 0.25. And, 20% is 20/100, which equals 0.2.

So, the three numbers, as decimals, are: 0.25, 0.2, and 0.34. And in ascending order, they are: 0.2, 0.25, 0.34.

Example 2. Write in order: 6%, 0.056, 1/14.
Here, it's easiest to use a calculator to convert the fraction 1/14 to the decimal 0.0714285714... . Then, 6% is 6/100 or 0.06. Now we can simply compare the three as decimals, and write them in order as 0.056, 0.06, 0.0714285714... .

## A table of equivalent percentages, fractions and decimals

Here is a comparison table of percentages, fractions, and decimals. You can post this or a similar chart on your wall to help children to learn these things better.

Percent Fraction Decimal
1%1/1000.01
5%1/200.05
10%1/100.1
12.5%1/80.125
20%1/50.2
25% 3/40.75
33.3%1/30.333...
50%1/20.5
66.7% 2/30.666...
75% 3/40.75
80%4/50.8
99%99/1000.99
100%11
150%3/21.5
200%22

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