Generate Equivalent Fractions
Basics on the topic Generate Equivalent Fractions
Equivalent Fractions – Definition
In this learning text we will be looking at equivalent fractions and how to find equivalent fractions. You may already know from our previous videos what a fraction is. Let’s look at the recap of the definition of what fractions and equivalent fractions are.
Fractions always represent a part of a whole. For example, if a pizza is divided into four equal pieces, one piece is called $\frac{1}{4}$ of a whole pizza.
Equivalent fractions are fractions which have the same value but are represented with a different numerator and denominator.
Equivalent fractions are created by breaking a whole into smaller equal parts. For example, the equivalent fractions visual diagram below is showing a whole as a fraction of $\frac{2}{2}$ and another fraction which is still one whole as a fraction $\frac{8}{8}$. So, the fractions $\frac{2}{2}$ and $\frac{8}{8}$ are equivalent fractions.
To create equivalent fractions, we can increase the number of pieces by multiplying the numerator and the denominator by the same n factor.
In mathematics, we use a multiplication expression to represent an equivalent fraction. The left-hand side of the expression represents our fraction and the right-hand side of the expression represents an equivalent fraction multiplied by n, where n represents any number. The equal sign shows that both sides of the expression are equal to each other. The bigger the number we multiply the fraction by, the more equal parts the whole has.
| original fraction | how to find the equivalent fraction |
|---|---|
| $\frac{a}{b}$ | $\frac{a x n}{b x n}$ |
Now, we can look at some examples for better understanding of equivalent fractions and after that you can practice equivalent fractions worksheet 4th grade or play equivalent fractions bingo.
Equivalent Fractions – Example 1
Let’s look at our first fraction, which is $\frac{1}{2}$. If we multiply the numerator and the denominator by two, we have generated an equivalent fraction which is $\frac{2}{4}$. The size of these parts is different, but the size of the whole remains the same.
| fraction | equivalent fraction |
|---|---|
| $\frac{1}{2}$ | $\frac{2}{4}$ |
Equivalent Fractions – Example 2
In our second example, we are looking at $\frac{3}{4}$. Let’s multiply the numerator and the denominator of the fraction by three, so we will get $\frac{9}{12}$. In this example, the n equals three.
We can also use a different factor; this time let’s multiply the numerator and the denominator of $\frac{3}{4}$by six, so we will get an equivalent fraction which is $\frac{18}{24}$. This time, the n factor equals six.
We can change the n factor for any other number, we just must remember to multiply the numerator and the denominator by the same n factor.
| fraction | equivalent fraction |
|---|---|
| $\frac{1}{2}$ | $\frac{2}{4}$ |
Equivalent Fractions – Summary
How do we generate or create an equivalent fraction? Look at the summary below:
- Equivalent fractions are fractions that have the same value but have different numbers in the numerators and denominators.
- Equivalent fractions are created by breaking a whole into smaller equal parts and having a greater number of pieces.
- We can increase the number of parts in a fraction by multiplying the numerator and the denominator by the same factor.
- Use the multiplication expression.
- Pick a number and then multiplying the numerator and denominator by the chosen factor.
Frequently Asked Questions about Equivalent Fractions
Transcript Generate Equivalent Fractions
“B(....) TWO-THIRDS!” It’s fraction night down at the bingo hall and Axel and Tank are excited to try to win the night’s top prize… which is a trip for two to Submersive Studios! In order to be the first to fill their bingo card, they need to find… Equivalent Fractions. Equivalent fractions are fractions that have the same value but have different numbers in the numerators and denominators. They are created by breaking the whole into smaller parts and having a greater number of pieces. We increase the number of parts in the fraction by multiplying the numerator and denominator by the same factor. Mathematically, we can show how to generate, or create, equivalent fractions through a multiplication expression. In this formula, the over represents our fraction. We use the
Generate Equivalent Fractions exercise
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What is an equivalent fraction?
HintsAll fractions are part of a whole.
Think about the pieces of a fraction. Are all pieces the same size?
A fraction is made up of two numbers. What do we call those numbers?
SolutionEquivalent fractions are fractions that have the same value but have different numbers in the numerators and denominators. An example of a fraction equivalent to $\frac{1}{2}$ is $\bf{\frac{2}{4}}$.
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How are equivalent fractions created?
HintsWhat mathematical equation is being shown here? What operation is being used?
Equivalent fractions represent the same number, but have different size pieces.
Use the image to help you.
The fraction to the left is $\dfrac{1}{2}$ what do you notice about the relationship between that and the fraction represented on the right $\dfrac{4}{8}$?
SolutionBy multiplying the fraction's numerator and denominator by the same factor.
Equivalent fractions are created by using multiplication. You multiply the numerator and denominator of the first fraction by the same number to get an equivalent fraction. You can see this in the model example $\frac{1}{2}$ is equal to $\frac{4}{8}$
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Determine an equivalent fraction.
HintsRemember, you have to multiply both the numerator and the denominator by the same number.
Think about how you create equivalent fractions.
Draw models to help you.
SolutionThe correct answer is $\frac{18}{27}$. You multiply both numerator and denominator by 3.
6 x 3 = 18
9 x 3 = 27
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Identify equivalent fractions.
HintsRemember, in order to make equivalent fractions, you must multiply the numerator and the denominator by the same number.
The fraction $\frac{3}{9}$ could have both the numerator and denominator multiplied by $10$ to find an equivalent fraction.
$\frac{3\ \ \ \ \times 10}{9\ \ \ \ \times 10}=\ \frac{30}{90}$
SolutionThe following fractions are equivalent to $\frac{3}{9}$
- $\frac{12}{36}$- multiply the numerator and denominator by 4
- $\frac{15}{45}$- multiply the numerator and denominator by 5
- $\frac{9}{27}$- multiply the numerator and denominator by 3
- $\frac{18}{54}$- multiply the numerator and denominator by 6
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Can you find the equivalent fractions?
HintsThink about what you would multiply the numerator and denominator by. Remember it has to be the same number.
Look for the same value, just different size piece.
In the image here you notice that $\frac{1}{2}$ and $\frac{4}{8}$ are the same size, but are split up into different sized groups. These fractions are equivalent.
SolutionEquivalent Fraction Solutions:
- $\frac{3}{6}$ = $\frac{9}{18}$
- $\frac{1}{8}$ = $\frac{2}{16}$
- $\frac{2}{8}$ = $\frac{6}{24}$
- $\frac{1}{4}$ = $\frac{4}{16}$
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How can we determine which fractions are equivalent?
HintsRemember equivalent means equal. They will not have the same number or size pieces, but they will take up the same amount of space.
When finding equivalent fractions, you multiply the numerator and denominator by the same number. For example, if I have $\frac{3}{5}$ and I multiply both parts by 3, I get $\frac{9}{15}$. These are equivalent.
There can be multiple equivalent fractions for one given model. You just have to think about what are you multiplying by.
SolutionIn order to find the correct pairs, you have to think about what you would multiply the numerator and denominator by in order to make the fractions equivalent.
Let's look at the first pair as an example: The model shows $\frac{4}{8}$. If you multiply both the numerator and denominator by 4, you get the fraction $\frac{16}{32}$ and these fractions are equivalent.
Here are the remaining pairs and their matches: The model $\frac{2}{3}$ is equivalent to $\frac{4}{6}$ because you multiply by 2.
The model $\frac{3}{4}$ is equivalent to $\frac{15}{20}$ because you multiply by 5.
The model $\frac{5}{7}$ is equivalent to $\frac{10}{14}$ because you multiply by 2.
