How To Find If Two Fractions Are Equivalent

Understanding Equivalent Fractions

Equivalent fractions represent the aforementioned part of a whole

The best way to think about equivalent fractions is that they are fractions that have the same overall value.

For example, if we cut a pie exactly down the middle, into ii equally sized pieces, ane piece is the same equally i half of the pie.

And if another pie (the aforementioned size) is cut into iv equal pieces, so two pieces of that pie represent the same amount of pie that one/2 did.

And then nosotros can say that one/2 is equivalent (or equal) to 2/4.

Don't let equivalent fractions confuse you!

Take a look at the 4 circles above.Can you see that the one "1/2", the two "ane/four" and the four "1/eight" take upwardly the same corporeality of area colored in orange for their circle?Well that means that each area colored in orange is an equivalent fraction or equal amount. Therefore, nosotros can say that 1/2 is equal to 2/four, and 1/two is also equal to four/eight. And yes grasshopper, two/4 is an equivalent fraction for 4/eight too.As you already know, we are nuts about rules. So, let's expect at the Rule to cheque to encounter if ii fractions are equivalent or equal. The dominion for equivalent fractions can be a little tough to explain, but hang in at that place, we volition clear things up in just a flake.

Here's the Rule

What this Dominion says is that 2 fractions are equivalent (equal) but if the product of the numerator (a) of the showtime fraction and the denominator (d) of the other fraction is equal to the product of the denominator (b) of the first fraction and the numerator (c) of the other fraction.

A product simply ways you multiply.

That sounds similar a mouthful, so allow's endeavour it with numbers…

$equivalent fractions cross multiply check$

Test the Dominion

At present let's plug the numbers into the Rule for equivalent fractions to be sure you take it downwards "cold". 3/4 is equivalent (equal) to 9/12 simply if the product of the numerator (3) of the first fraction and the denominator (12) of the other fraction is equal to the product of the denominator (4) of the get-go fraction and the numerator (9) of the other fraction. Then we know that 3/4 is equivalent to 9/12, because 3×12=36 and four×ix=36. A simple way to look at how to bank check for equivalent fractions is to practise what is called "cross-multiply", which means multiple the numerator of one fraction by the denominator of the other fraction. Then do the same thing in reverse. At present compare the two answers to see if they are equal. If they are equal, then the two fractions are equivalent fractions.

The graphic below shows you how to cross multiply…

$cross multiplying equivalent fractions$

Okay, permit'due south exercise one with numbers where the fractions are not equivalent…

Every bit you lot can see by this example, one/2 is not an equivalent fraction of 2/3.

If you remember to employ the cross-multiply method, you should not have whatever problems verifying equivalent fractions.

The tabular array below lists some mutual fractions and their equivalents. Just read the tabular array from left-to-right. What it shows you are values multiplied by dissimilar variations of fractions equal to "1". You exercise remember that whatsoever number divided by itself is equal to "1" correct?

Equivalent Fractions Table