Meanings for fractions

WRITING FRACTIONS The most prominent way of representing a fraction is to say: or…. 6-2

Part Whole meaning of fractions Three things to keep in mind: – 1. The unit or whole. What = 1? What am I referring to? – 2. The denominator. How many pieces is my whole cut into? (remember all pieces are the same size!) This is the number on the bottom. – 3. The numerator. How many pieces of the whole am I talking about?

Part Whole meaning of fractions Example:. My mom buys a 2-pack of pies. She cuts each one into 8 pieces. My brother eats 3 pieces. – My brother ate of one pie. This is my whole It is cut into 8 pieces This is what my brother ate. It is 3 of the 8 pieces.

Part Whole meaning of fractions Example:. My mom buys a 2-pack of pies. She cuts each one into 8 pieces. My brother eats 3 pieces. – My brother ate of the 2-pack my mom bought. This is my whole. It is cut into 16 pieces This is what my brother ate. It is 3 of the 16 pieces.

Part Whole meaning of fractions Example:. My mom buys a 2-pack of pies. She cuts each one into 8 pieces. My brother eats 3 pieces. – My brother ate of half a pie. This is my whole It is cut into 4 pieces This is what my brother ate. It is 3 of the 4 pieces.

Part Whole meaning of fractions Understanding what you are referring to is very important! When we say 2/5 we need to know, 2/5 of what? In the same problem, changing what we are referring to can change how what our answer means.

Think about it! Using the part-whole way of thinking about fractions, how could each of the following show 2/3?

Fractions as Division We can interpret a fraction to mean a÷b. If I divide “a” into “b” Pieces/groups/shares, how big is each part? We want to share whatever “a” is among “b” groups.

Fractions as Division Ex. Can you see how these give the same answer? Part-whole view of 3/4: As division I split 3 squares into 4 equal parts

As copies of a unit fraction This is similar to part whole. When thinking about a/b, first look at how big 1/b is (1 out of b). Then I copy it until I have “a” of them This is a great way to think about improper fractions.

Copies view of fraction Example 7/4 1 (This is my whole) ¼ (this is 1 out of four equal pieces) 7/4 (I copied my ¼ 7 times) 1 ¾ (I can split my 7/4 into 1 whole and 3 more copies of 1/4