SOLUTION: Why is 4 over 5 greater than 2 over 3?

Question 1085450: Why is 4 over 5 greater than 2 over 3?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
to compare fractions, put them both under the same denominator.

your fractions are 4/5 and 2/3

5 and 3 have a common multiple of 15, so make both fractions have a denominator of 15.

you do this by:

multiplying 4/5 by 3/3 to get 12/15

multiplying 2/3 by 5/5 to get 10/15

12/15 is greater than 10/15.

why can you multiply by 3/3 or 5/5 and not change the fraction?

because 3/3 is equal to 1 and 5/5 is equal to 1 and multiplying any number by 1 gives you the same number.

another way to do it physically is to cut strips of paper the same length and then divide one strip into 3 equal parts and the divide the other strip into 5 equal parts.

then put 2 of the 3 strips together and compare them to 4 of the 5 strips together.

you will see that the 4/5 strip is larger than the 2/3 strip.

most of the time when you compare fractions, you put them under the same denominator.

you do this to add them together and to subtract them from each other as well.

not sure what grade you're in, but there are other methods, such as setting up an inequality and then solving that inequality to see if it's true.

for example:

4/5 > 2/3 means 4/5 is greater than 2/3.

multiply both sides of this inequality by 15 and you get 12 > 10 which is true, therefore confirming that 4/5 truly is greater than 2/3.

if you haven't learned that yet, don't worry about it; you will eventually.

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