Are you a high school student and have always wondered what equivalent fractions are? Then you should be glad to know that it is not difficult. If you have a basic idea about fractions, you will find equivalent fractions as a piece of cake.
The Equivalent fraction topic is simply comparative. You can compare two fractions together and see if they will lead to the same answer. That is the idea of this topic, and it is straightforward. That being said, this article will consider everything that you need to know about Equivalent fractions.
What is A fraction?
Of course, you should know that a fraction is simply a simple mathematical division with a numerator and a denominator. It is important you know this if you want to deal with equivalent fractions comprehensively.
¾, for example, is a fraction, and so is the fraction 7/6.
The two examples considered above are actually different fractions. The first is a proper fraction because the numerator 3 is lesser than the denominator 4. The second is an improper fraction because the numerator 7 is larger than the denominator 6.
Apart from the two fractions considered above, the fraction is still known as a mixed fraction. A mixed fraction is a fraction with a mix of whole numbers and fractional expressions.
The fraction below
Is actually a mixed fraction
The mixed fraction can be turned into a pure fraction like the first two types of fractions considered above. All you need to do is multiply the denominator with the whole number and add it to the numerator. This will give us a new numerator while the denominator remains the same. We will use the above mixed fraction as an example.
The denominator 6 multiplied by the whole number 1 will be 6 x 1 = 6. Then we will add this 6 to the numerator 5, giving us 6 + 5 = 11. 11 will therefore be the new numerator.
As such;
Knowing everything about fractions is very important to understand what an equivalent fraction is
What are Equivalent Fractions?
Equivalent fractions are fractions with different numerators and denominators yet have the same answer or solutions.
Equivalent fractions are very straightforward and must be comparable. As such, you cannot carry out an equivalent fraction problem with just one fraction. There need to be at least two fractions, and there could be as many as 5 fractions to be compared to see if they are equivalent.
How to Calculate Equivalent Fractions
Step 1: Compute the fractions separately and get the solutions for each one.
Step 2: Compare the solutions; if all are equal, they are equivalent fractions. If they are not, then they are not equivalent.
Examples of Equivalent Fractions
Example 1
Now consider the fraction 1/2. Its equivalent fraction will be
2/4.
This is because ½ = 0.5 and;
2/4 = 0.5 as well.
Because the two fractions, despite having different numerators and denominators, still lead to the same answer of 0.5, then they are indeed equivalent fractions.
Now it is quite obvious that ½ and 2/4 are actually equivalent fractions. If you notice, you will see that 2/4 is actually ½, only that its numerator and denominator are further multiplied by 2 hence the difference in fractions.
The peculiarities of ½ and 2/4 are extremely common for all Equivalent fractions, so you should know how to spot them.
½, 3/6, 7/14, 8/16, and 32/64 are all equivalent fractions as they will give the same value of 0.5
Example 2
Consider the three fractions and determine whether they ae equivalent fractions.
7/76, 5/125 and 15/375
Solution
If we consider all three fractions, we will be able to tell whether they are equivalent or not.
Clearly, 7/76 cannot be simplified anymore than they are. The value for the fraction is actually 0.0921
We will consider the next fraction 5/125
Clearly, 5/125 can be simplified to 1/25 when divided all through by 5. This is the final simplification and will give the answer 0.04.
Finally, we will consider 15/375
15/375 can be simplified to 3/75 when divided by 5 all through.
3/75 can be further simplified by 3 all through, which will lead to 1/25. Clearly;
1/25 = 0.04
Based on the three fractions, it is clear that 5/125 is an equivalent fraction to 15/375. However, 7/76 is not equivalent to the duo.
Therefore, it is apparent that 7/76, 5/125, and 15/375 are not equivalent fractions.
Example 3
Are the three fractions below equivalent?
Solutions
Now we can see that all the fractions above are mixed fractions, and the first thing to do is turn them into normal fractions.
Now following the steps highlighted already in this lecture;
Now we will have to consider their respective values to see if they are all the same so we can tell whether they are equivalent or not.
68/7 = 9.714
23/5 = 4.6
19/3 = 6.333
Clearly, all the values are totally different, and we can clearly confirm that they are not equivalent fractions.
Conclusion
Equivalent fractions are not difficult to determine. They are actually quite straightforward as the main goal is to determine whether independent fractions will lead to the same answer. If the fractions end up being the same, then good. If it does not, then it only means they are not equivalent.
You may, however, need to improve your ability to do your fractions. You have to learn more about the different fractions, including mixed, proper, and improper fractions. You can also continue to work on different examples until you achieve reasonable perfection.
