Equivalent fractions appear frequently in KS2 math, and some kids, parents, and even primary school teachers may be confused about what are equivalent fractions and how to find them. In this article, we will clarify the definition, properties, examples, and how to find equivalent fractions. Check it out!
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What is a fraction?
Fractions are equal parts of a whole or a collection. A fraction is made up of two parts. The number at the top of the line is referred to as the numerator, and it indicates how many equal parts of the whole or collection are taken. The number below the line is known as the denominator, and it represents the total number of equal parts into which the whole is divided or the total number of equal parts in a collection.
What are equivalent fractions?
Equivalent fractions are fractions that depict the same value but have different appearances (i.e. different numerators or denominators). In other words, 2 or more fractions are described as equivalent if, after simplifying them, they equal the same fraction. For example, 2/4 and 4/8 are equivalent fractions because they both simplify to 1/2.
As seen in the preceding example, all equivalent fractions are simplified to the same fraction in their simplest form. Explore this entire post to gain a better understanding of how to find equivalent fractions and how determine whether the specified fractions are equivalent.
Examples of Equivalent Fractions
While solving math problems, kids will frequently come across some frequently used fractions. The curriculum asks them to be capable of writing equivalent fractions such as 1/2, 1/3, and 1/4. But that’s not all.
Let’s look at a few examples of equivalent fractions below.
- Fractions equivalent to 1/2 include 2/4, 3/6, 4/8, 5/10 and so on …
- Fractions equivalent to 1/3 include 2/6, 3/9, 4/12, 5/15 and so on …
- Fractions equivalent to 2/3 include 4/6, 6/9, 8/12, 10/15 and so on …
- Fractions equivalent to 1/4 include 2/8, 3/12, 4/16, 5/20 and so on …
- Fractions equivalent to 2/4 include 4/8, 6/12, 8/16, 10/20 and so on …
- Fractions equivalent to 1/5 include 2/10, 3/15, 4/20, 5/25 and so on …
- Fractions equivalent to 2/5 include 4/10, 6/15, 8/20, 10/25 and so on …
- Fractions equivalent to 1/6 include 2/12, 3/18, 4/24, 5/30 and so on …
- Fractions equivalent to 1/7 include 2/14, 3/21, 4/28, 5/35 and so on …
Of course, memorizing these would be extremely difficult and pointless. Equivalent fractions calculators are also available, but students will not use them as part of the learning process.
Instead, it is preferable to learn how to find equivalent fractions. Students will be able to identify the equivalent values of any given fractions by doing so. Let us take a look.
How do Find if two Fractions are Equivalent?
How can we determine whether two fractions are equivalent? It is possible to do so using the following methods:
- Make the Denominators Equal
- Determining the decimal form of the given fractions
- Cross Multiplication method
Cross Multiplication method
Cross-multiply two fractions to determine whether they are equivalent. If both products are equal, the fractions are equivalent.
Example: Determine whether 2/3 and 4/6 are equivalent fractions or not.
To make the denominators equal, multiply 2/3 with 6/6 (6 is the denominator of 4/6) and multiply 4/6 with 3/3 (3 is the denominator of 2/3).
2/3 × 6/6 = 12/18
4/6 × 3/3 = 12/18
We can determine whether or not the given fractions are equivalent by matching their denominators. By changing the denominators, we can see that 2/3 and 4/6 are equivalent fractions, i.e., the given fractions are equivalent.
Determining the decimal form of the given fractions
Example: Determine whether 1/2 and 5/10 are equivalent fractions or not.
1/2 = 1 ÷ 2 = 0.5
5/10 = 5 ÷ 10 = 0.5
Because the decimal values of the given fractions are the same (0.5), they are equivalent.
Make the Denominators Equal
Example: Determine whether 2/3 and 4/6 are equivalent fractions or not.
The Least Common Multiple (LCM) of 3 and 6 is 6.
Multiply 2/3 by 2/2 and 4/6 by 1/1 to make their denominators equal to 6.
2/3 × 2/2 = 4/6
4/6 × 1/1 = 4/6
From the above multiplications, we can see that they are equivalent fractions.
Read more >> What Are Mean Mode Median And Range? How To Find Them?
How to Simplify the Equivalent Fractions?
An equivalent fraction is obtained by dividing the numerator and denominator by the same non-zero number. This is known as simplifying or reducing the fraction. An irreducible fraction is one that has a numerator and denominator that are both prime numbers.
For example, to find the equivalent fraction of 15/20, divide both the numerator and denominator by their largest common factor 5, yielding the equivalent fraction of 3/4.
How to determine Equivalent Fractions?
We can find an equivalent fraction for any fraction by multiplying or dividing both the numerator and the denominator by the same number. As a result, when all equivalent fractions are simplified, they all become the same fraction. Let us now look at these two examples.
Case 1: Multiplying the same number to the numerator and denominator
We can find an equivalent fraction for any fraction by multiplying both the numerator and the denominator by a specific number. To find the equivalent fraction of 1/3, we multiply both the numerator and denominator by the same number, i.e., 3. Thus, 3/9 is the equivalent fraction of 1/3. Similarly, by repeating the procedure with other numbers, we can find several other equivalent fractions.
Equivalent fractions of 1/3
- Multiplying the numerator and denominator with 4, we get 1/3 × 4/4 = 4/12
- Multiplying the numerator and denominator with 5, we get 1/3 × 5/5 = 5/15
- Multiplying both the numerator and denominator with 4, we get 1/3 × 6/6 = 6/18
Hence, we can say that, 1/3 = 4/12 = 5/15 = 6/18.
Case 2: Dividing the numerator and the denominator by the same number.
We can find an equivalent fraction for any fraction by dividing both the numerator and the denominator by the same number. To identify the equivalent fraction of 50/100, for example, we must first find their common factors. In this case, 5 is a common factor of 50 and 100. So, dividing the numerator and denominator of 50/100 by 5 yields the equivalent fraction. The equivalent fraction of 50/100 is thus 10/20.
Let us simplify the fraction even more.
2 is a common factor of 10 and 20. So, 10/20 = (10÷2)/(20÷2) = 5/10
Therefore, the equivalent fractions of 50/100 are 10/20 and 5/10.
Properties of equivalent fractions
- If the values of two fractions are equal or if their decimal values are exactly the same, these fractions are said to be equivalent.
- To get equivalent fractions, multiply or divide both the numerator and denominator of that faction by the same number.
- Equivalent fractions depict the same amount of distance or a number of line points.
- In their simplest form, all equivalent fractions simplify to the same fraction.
- To get equivalent fractions, you could only multiply or divide, not add or subtract.
- The cross-multiplication method is the most basic method for determining equivalent fractions.
- To find equivalent fractions, make all the denominators the same. If you want to find equivalent fractions of more than just 1 fractional value, utilize this method.
In primary school, when do learners acquire equivalent fractions?
The idea of equivalent fractions is not introduced until Year 3, when children recognize and demonstrate equivalent fractions with small denominators using diagrams.
In Year 4, they will recognize and demonstrate families of common equivalent fractions using diagrams. Non-statutory National Curriculum guidance also suggests that students use factors and multiples to recognize equivalent fractions and reduce where appropriate (for example, 6/8 = 3/4).
In Year 5, students learn to identify, name, and write equivalent fractions of a given fraction, such as tenths and hundredths.
They will start adding and subtracting fractions with various denominators and mixed numbers in Year 6 using the idea of equivalent fractions. Non-statutory Year 6 guidance recommends that finding equivalent fractions could be related to common factors and that kids practice calculations with simple fractions… such as listing equivalent fractions to recognize fractions with common denominators.
What is the significance of understanding equivalent fractions?
When performing different math calculations, knowledge of equivalent fractions is applied. Above are just a few examples of how children will be able to put their equivalent fractions knowledge to use.
As previously stated, students must grasp the concept of equivalence in order to add and subtract fractions with unlike denominators. This is significant because they will be tested at school on their ability to complete these calculations.
Another explanation for why understanding equivalent fractions are important is that students will frequently need to simplify fractions before writing the final answer to questions. Kids will find it difficult to understand how and why fractions are simplified if they do not fully grasp the concept of equivalence.
When comparing and ordering fractions, it is also necessary to understand how to find equivalent fractions. This is due to the fact that they will frequently be asked to compare fractions with various denominators. To solve the issue, they must make sure that the denominators are exactly the same, which requires an understanding of equivalent fractions.
Equivalent Fractions Frequently Asked Questions
What Fraction is 2/3 Equivalent to?
4/6, 6/9, 8/12, 10/15 … are equivalent to 2/3. All those fractions obtained by multiplying both the numerator and denominator of 2/3 by the same number are equivalent to 2/3.
What fraction is equivalent to 1/3?
2/6, 3/9, 4/12, 5/15 … are equivalent to 1/3. All those fractions obtained by multiplying both the numerator and denominator of 1/3 by the same number are equivalent to 1/3.
What fraction is equivalent to 1/2?
2/4, 3/6, 4/8, 5/10 … are equivalent to 1/3. All those fractions obtained by multiplying both the numerator and denominator of 1/2 by the same number are equivalent to 1/2.
What fraction is equivalent to 1/4?
2/8, 3/12, 4/16, 5/20 … are equivalent to 1/4. All those fractions obtained by multiplying both the numerator and denominator of 1/4 by the same number are equivalent to 1/4.
What is equivalent to 1/5?
2/10, 3/15, 4/20, 5/25 … are equivalent to 1/5. All those fractions obtained by multiplying both the numerator and denominator of 1/5 by the same number are equivalent to 1/5.
Hope that the above article helps you grasp the perfect answer to the question “What are equivalent fractions?”. If you are planning to teach your kids about this essential topic, you can make your own collections of equivalent fraction worksheets using our worksheet maker.
