What is the difference between one eighth and one fourth?

Answer 1

When people think of numbers, we can easily compare them, e.g. 8 is bigger than 4; 10 is smaller than 89; etc. BUT in fractions and percentages, we cannot simply use one part of the fraction to make a "bigger-smaller" comparison. Instead, we must use the entire fraction. So in comparing 1/4th to 1/8th, we use both the upper and lower numbers, as compared to ONE.

The easiest way to think of fraction comparisons is to think of your favorite pie (apple? cherry? pumpkin?). You ask your mom for a piece of the pie, but your mom, dad, and sister also want a piece. So ONE whole pie must be split into 4 pieces, so you get 1/4th, and your mom, dad, and sister also get their 1/4th piece.

However, let's say your mom baked or bought a pie to be shared by your family of 4 people, plus your grandparents on both sides of the family; your mom's parents are 2, and your dad's parents are 2. So ONE pie must be split for 8 people now. If you first cut the pie in half, that equals 1/2 or 50%. If you make another cut all the way across, making another new half, then the whole pie is now cut into 1/4th pieces or each being 25% of one pie. To have enough to feed the grandparents, you'd need to cut each 1/4th piece into half, which would give you 8 pieces in the pie, which equals 1/8th... (which I think is 0.125%?) for each piece.

If your sister decides she doesn't want her 1/8 piece and gives it to you, when you already have your own 1/8th piece, you'd have 1/4th (25%) of the pie to eat by yourself.

So, as you see, 1/4th is larger than 1/8th.