Expert: Josh - 12/13/2004

Question
5/6,5/8,3/5,1/10,2/7,3/12 is equivalent to what fractions, I am a 4th grader?

Answer
Hi Lonnie,

Let's consider an example.
50/50 is equivalent to 10/10.

If you take a quiz and answered 50 questions correctly, out of a total of 50 questions, you would have scored 100%.

Let's say that you have a spelling test tomorrow, in which you have to spell ten words. If you get ten right, you would have also scored 100%.

The two fractions 50/50 and 10/10 are equivalent, because, they are not distinguishable. They represent the same amount.

As you can tell, you can come up with an unlimited number of fractions which are equivalent to 10/10.
20/20, 30/30 etc. are all equivalent. They all give 100%.

Your teacher will not be expecting one and only one answer,
because there are many possible answers.

Consider the fraction 5/6, to find an equivalent fraction, just multiply it by an identity such as 2/2.
(5/6)x(2/2)=(5x2)/(6x2)=10/12.
In doing so, you do not change the ratio. You are simply expressing the fraction in a different manner.

You can multiply 5/6 by 3/3 to get another equivalent fraction. This time, (5/6)x(3/3)=(5x3)/(6x3)=15/18.

You can repeat this for 4/4, 5/5 etc. if you like.

The last number that you gave me "3/12" is quite easy to do. In this case, you can simplify the fraction, dividing the top (numerator) and bottom (denominator) both by 3.
3/12=(3/3)/(12/3)=1/4.
Three twelves is equivalent to one quarter. Both are 25%.

Let me know how you are finding this.

Cheers.