Why Is 1/4 Larger Than 1/5? - Math Central

Subject: Why is 1/4 bigger than 1/5

Name: Sherry Who is asking: Student Level: Elementary

Question: I have to do a math project for my teacher education class. The question that I am working on is why is 1/4 bigger than 1/5.

I have replies for you from three people. First from Paul.

Answer1: Dividing by a larger number produces a smaller number.

Answer2: 1/4 is the same as 5/20 (multiply top and bottom by 5) 1/5 is the same as 4/20 (multiply top and bottom by 4) Now the denominators (bottom number of a fraction) are the same so the size of the numerator (top number of a fraction) determines the size of the fraction.

Answer3: Draw a circle and divide it into 4 equal parts by drawing 2 lines through the centre that intersect at 90 degress. Each slice of the circle is 1/4 of the circle. If you divide the same circle into five equal slices then the slices will be smaller. Hence 1/5 of the circle is smaller than 1/4 of the circle.

And then from Claude.

My friend's 4 year old son is starting to understand fractions also. Recently he was asked what he gets when cutting a pizza in two and said "halves". Then he was asked what he gets when cutting halves in two and said "quarters". Then he was asked what he gets when cutting quarters in two and said "eights". Then he was asked what he gets when cutting eights in two and said "I don't know", then he tought about it for a while and said "sixteenths".

Then he was asked what he gets when putting four quarters together and said "one". Then he was asked what he gets when putting eight eights together and said "I don't know", then he tought about it for a while and said "one".

Of course, the ordering of fourths and fifths would have to come a bit later, but my guess is that children can understand elementary facts about fractions early enough if you respect their own pace.

Finally from Penny.