# Equivalent Decimal Fractions Rating

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## Equivalent Decimal Fractions

A fraction is a portion or part of any quantity out of a whole. There are different types of fractions including: improper fractions, mixed fractions, proper fractions, and decimal fractions.

In this video we will learn about decimal fractions and how to identify equivalent decimal fractions as well as how to write decimal fractions. We will show a couple of examples after which you can practice a set of decimal fractions problems with ease.

## Revision – Decimal Fractions

Let’s recap what decimal fractions are first:

Decimal fractions are fractions where the denominator is a power of ten. A power of ten means multiplying ten by itself a certain number of times. For example, 10x10 = 100, and 10x10x10 =1000.

## Equivalent Decimal Fractions – Definition

Equivalent decimal fractions are fractions that are equal in value and the denominator is a power of ten. For example, fractions with denominators of 10, 100, 1000 and so on.

## Comparing Decimal Fractions – Examples

A great visual method to compare decimal fractions is to use the base 10 blocks. Below are some examples.

### Comparing Decimal Fractions – Example 1

In this first base 10 block the whole is divided into ten equal parts, so the denominator is ten. Four out of ten parts are shaded in blue; so we label the shaded parts in the numerator as four, making the decimal fraction $\frac{4}{10}$.

On the other base 10 block, the whole is divided into one hundred equal parts, so the denominator is one hundred. Forty sections out of one hundred parts are shaded in red which we can represent as the decimal fraction $\frac{40}{100}$. The base 10 blocks below help us when comparing fractions with denominators of 10 and 100. We can convert fractions with denominators of 10 and 100 to decimals. Our $\frac{4}{10}$ and $\frac{40}{100}$ can be written as 0.4 = 0.40.

Denominator 10 Denominator 100
fraction $\frac{4}{10}$ $\frac{40}{100}$
decimal 0.4 0.40

### Comparing Decimal Fractions – Example 2

Let’s look at different examples to clarify our understanding of equivalent fractions with denominators of 10 and 100. Equivalent fractions and decimals with denominators of 10 and 100 are more comprehensible if we visualize them.

In this base 10 block the whole is divided into one hundred equal parts, and ninety out of one hundred parts are shaded in red which we can write as a decimal fraction $\frac{90}{100}$.

In the second base 10 block the whole is divided into ten equal parts, and nine out of ten parts are shaded in blue, so we can represent the shaded parts as a decimal fraction $\frac{9}{10}$.

The base 10 blocks represent two equivalent fractions with denominators of 10 and 100. Denominator 10 Denominator 100
fraction $\frac{9}{10}$ $\frac{90}{100}$
decimal 0.9 0.90

## Equivalent Decimal Fractions – Summary

How do we compare decimal fractions? Look at the summary below:

• Look at each of the base 10 blocks
• Set up each fraction and label the denominators based on how many parts each base 10 block is broken into
• Look at the shaded parts of each base 10 block* Label the numerator with the number of shaded parts in each base 10 block.
• Use the less than, greater than, or equal to symbol to record your answer

You can also look at our worksheets and videos on equivalent decimal fractions with denominators of 10 and 100 for more practice. We also provide worksheets on adding fractions with denominators of 10 and 100 as well as place value and decimal fractions worksheets. Soon you’ll be able to answer questions like “what is a fraction with a denominator of 10 ?” and “what is a fraction that has a denominator of 100?”easily!

##Frequently Asked Questions on Equivalent Decimal Fractions

What are decimal fractions?
What are equivalent decimal fractions?

Decimal fractions are fractions where the denominator is a power of ten: 10, 10, 100, etc. What are equivalent decimal fractions? Equivalent decimal fractions are fractions that are an equal in value but still the denominator is a power of ten.

## Equivalent Decimal Fractions exercise

Would you like to apply the knowledge you’ve learned? You can review and practice it with the tasks for the video Equivalent Decimal Fractions.
• ### What does equivalent mean when we are talking about fractions?

Hints

Remember to look at the shading in the picture. Are they the same? Does one have more than the other?

The fractions we see in the previous hint are equivalent to each other: $\dfrac{4}{10}$ is equivalent to $\dfrac{40}{100}$.

Solution

Equivalent means equal to or the same as. When two fractions are different, but have the same value they are equivalent.

• ### Can you identify the correct base ten block?

Hints

Remember, you are finding the fraction represented in tens or hundreds blocks.

The number in the denominator determines how many boxes are in the picture. The numerator is represented by the amount of blocks shaded in.

Solution
• There are 2 out of 10 bars filled in, which represent the fraction $\dfrac{2}{10}$.
• There are 70 out of 100 boxes filled in, which represent the fraction $\dfrac{70}{100}$.
• There are 5 out of 10 bars filled in, which represents the fraction $\dfrac{5}{10}$.
• There are 10 out of 100 boxes filled in, which represents the fraction $\dfrac{10}{100}$.
• ### What is the fraction represented on the base ten block?

Hints

Remember that the numerator represents the number of boxes shaded.

The base ten block below illustrates $\frac{4}{10}$. How can this help you complete the above fractions?

Solution

1.The first image represents $\frac{8}{10}$. 8 of the 10 boxes are shaded in.

2.The second image represents $\frac{50}{100}$. 50 of the 100 boxes are shaded in.

3.The third image represent $\frac{80}{100}$. 80 of the 100 boxes are shaded in.

4.The fourth image represents $\frac{5}{10}$. 5 of the 10 boxes are shaded in.

• ### Match the equivalent fractions.

Hints

These images will help you find one of the pairs above. They are equivalent fractions. Remember that the shaded part represents the numerator and the total number of boxes the denominator.

Remember that we can also think of these numbers as being multiplied by 10.

For example, $\frac{4}{10}$ = $\frac{40}{100}$ When we multiply 4 by 10 we get 40 and when we multiply 10 by 10 we get 100. These are equivalent fractions.

Solution

$\frac{9}{10}$ = $\frac{90}{100}$ We can see on the shaded blocks that 9 of the 10 blocks are shaded, which looks the same as 90 of the 100 blocks that are also shaded. If we were to lay one on top of the other the same amount would be shaded in, making them equivalent.

$\frac{6}{10}$ = $\frac{60}{100}$

$\frac{2}{10}$ = $\frac{20}{100}$

$\frac{1}{10}$ = $\frac{10}{100}$

• ### What is the missing fraction?

Hints

We can tell from looking at the base ten block images if this is an equivalent fraction or not.

Remember the total number of boxes the square is divided into represents the denominator, or the number that goes in the bottom half of the fraction.

The numerator is represented by the number of blocks shaded in.

Solution

The second fraction represents our original fraction changed into a hundredth denominator. 30 out of 100 blocks are filled in, so $\frac{3}{10}$ becomes $\frac{30}{100}$. The two fractions are equivalent.

• ### How much pizza have Axel and Tank eaten after their adventure?

Hints

Remember that the pizza is similar to the base 10 block. Look at the pizza represented in a base 10 block.

Remember the numerator is the number of pieces eaten and the denominator is the total number of pieces of pizza.

Solution

Count all of the pieces of the pizza. There are 10 in total. Of those 10, how many are missing? There are 4 pieces of pizza missing. That means that Axel and Tank ate 4 pieces out of 10 or, they ate $\frac{4}{10}$ of the pizza.

$\dfrac{4}{10}$ = $\dfrac{40}{100}$ =. $\dfrac{400}{1000}$