Understanding equivalent Fractions

Equivalent fractions stand for the same component of a whole


The best way to think around equivalent fountain is that they room fractions that have the same all at once value.

You are watching: 3/4 is equal to

For example, if we reduced a pie exactly down the middle, right into two equally sized pieces, one piece is the exact same as one fifty percent of the pie.

And if one more pie (the very same size) is cut into 4 same pieces, then two pieces of that pie stand for the very same amount that pie that 1/2 did.

So we have the right to say that 1/2 is equivalent (or equal) come 2/4.

Don’t let indistinguishable fractions confused you!

Take a look at the 4 circles above.Can you check out that the one “1/2”, the 2 “1/4” and also the four “1/8” take up the exact same amount that area colored in orange for their circle?Well that way that each area colored in orange is an equivalent portion or same amount. Therefore, we have the right to say that 1/2 is same to 2/4, and also 1/2 is likewise equal come 4/8. And also yes grasshopper, 2/4 is an equivalent fraction for 4/8 too.As you currently know, we are nuts about rules. So, let’s look at the Rule to inspect to view if two fractions are equivalent or equal. The rule for equivalent fractions have the right to be a tiny tough come explain, but hang in there, we will certainly clear points up in just a bit.

Here’s the Rule


What this Rule claims is that two fractions are equivalent (equal) just if the product of the molecule (a) the the very first fraction and the denominator (d) that the other portion is equal to the product that the denominator (b) the the an initial fraction and also the molecule (c) that the other fraction.

A product simply way you multiply.

That sounds prefer a mouthful, for this reason let’s shot it with numbers…


Test the Rule

Now let’s plug the numbers right into the Rule for identical fractions come be sure you have it down “cold”. 3/4 is identical (equal) to 9/12 just if the product the the molecule (3) the the first fraction and also the denominator (12) of the other portion is equal to the product of the denominator (4) that the first fraction and the molecule (9) the the various other fraction. So we know that 3/4 is identical to 9/12, because 3×12=36 and also 4×9=36. A simple method to watch at exactly how to inspect for tantamount fractions is to carry out what is dubbed “cross-multiply”, which means multiple the molecule of one fraction by the denominator that the various other fraction. Then do the exact same thing in reverse. Now compare the 2 answers to view if they room equal. If they room equal, then the 2 fractions are indistinguishable fractions.

The graphic below shows you how to cross multiply…


Okay, let’s execute one through numbers whereby the fractions are not equivalent…


As you deserve to see by this example, 1/2 is not an equivalent portion of 2/3.

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If friend remember to usage the cross-multiply method, you have to not have any problems verifying tantamount fractions.

The table below lists some typical fractions and also their equivalents. Just read the table from left-to-right. What it shows you room values multiply by different variations of fractions equal to “1”. You execute remember that any number split by chin is same to “1” right?