Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a/b as a parts of size 1/b
You already know how to split a shape into equal parts and how to write a fraction like 3/4. Now look at what those two numbers do. Cut a whole into 5 equal parts, and one single part is called 1/5. Cut it into 8 equal parts instead, and one part is called 1/8. The parts must be the same size, or the name does not work.
Alex cuts a pizza into 6 equal slices. Each slice is 1/6 of the pizza. Alex takes 4 slices, so that's 4 parts of size 1/6, or 4/6 of the pizza.
The bottom number tells you how many equal parts the whole is cut into. The top number tells you how many of those parts you have. Change the top number, and you have more or fewer parts. Change the bottom number, and the parts change size.
A fraction like 3/8 means the whole is cut into 8 equal parts, and you have 3 of them.
Practice items adapted from WeBWorK Open Problem Library problems by Carl Yao (PCC) (CC BY-NC-SA 3.0).
Back at Meadow Lane. Last spring you drew the plots on paper and cut the long bed into equal strips so nobody got a bigger share. Today the plan is out on the soil: 5 strips, all the same size, and Mia has planted basil in one of them.
What fraction of that bed is planted?
Jobs that lean on this skill. Follow one to see everything it is built on.
18 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.