Understanding fractions (age 9+)
Understand a fraction a/b with a > 1 as a sum of fractions 1/b (e.g. 3/5 = 1/5 + 1/5 + 1/5)
What a learner can do afterwards
- Express 5/8 as a sum of five copies of 1/8
- Show on a number line how 4/3 is built by iterating 1/3 four times
- Explain why 7/4 = 1/4 + 1/4 + 1/4 + 1/4 + 1/4 + 1/4 + 1/4
The lesson
You already know that 1/5 means one piece when a whole is cut into 5 equal parts. Today you will see that a fraction like 3/5 is just several of those pieces added up. 3/5 means 1/5 + 1/5 + 1/5.
Look at a number line marked in thirds. Start at 0 and take four hops, each hop the size of 1/3. After four hops you land past one whole, at 4/3.
Any fraction a/b is just a copies of the piece 1/b, added together. The top number tells you how many pieces to add; the bottom number tells you the size of each piece.
A fraction a/b means you add the piece 1/b to itself a times.
Watch it
Where it sits
Where this leads
Jobs that lean on this skill. Follow one to see everything it is built on.
8 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.