Equivalent Fractions

Many of my students come to me needing to learn, or at least review, on how to handle operations involving fractions. I have found that the mere appearance of a fraction in a problem can invoke anxiety in some students. My goal for this post, and any that follow relating to this topic, is to not only teach you how to work with fractions, but to also help you gain confidence.
First, we will start by looking at the parts of the fraction. The number before the slash is the numerator, and the number after the slash is the denominator. In this case, the numerator is 1, and the denominator is 2.


To work with fractions it is also necessary to understand equivalent fractions, which are different fractions that represent the same number. You might be wondering how this can be true, so I will do my best to explain it.

Since one half is the most easily understood and recognized of the fractions, I will use it in my example. Say you want to divide a pie into two pieces, so you would make one cut down the middle. Each piece would be the same size, which is equal to 1/2.

What if that pie were cut into 4 equal pieces instead of 2? How many pieces of the pie would equal 1/2? Our goal is to get the denominator to equal 4 (the total pieces of the pie), and we know that we want 1/2 of that amount. We start by multiplying the denominator of 1/2 by 2. What we do to the denominator we must do to the numerator, so we find that 1/2 equals 2/4.

1/2 = (1 times 2) / (2 times 2) = 2/4

If we needed to find 1/2 of a pie cut into six pieces, the process is the same, but you multiply by 3.

1/2 = (1 times 3) / (2 times 3) = 3/6

Below you will find more fractions that are equivalent to 1/2. Can you figure out how they were calculated?

1/2 = 2/4 = 3/6 = 4/8 = 5/10 = 6/12

I hope that this post has helped you to understand equivalent fractions. If you need more instruction, please contact me to find out about my online tutoring services.
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