Lesson 8.3 · Geometry and Fractions
Halves, thirds and fourths
You already know halves and fourths. Now you will learn thirds, for when 3 friends share one thing fairly.
Equal shares
When you cut a shape into parts that are all the same size, the parts are equal shares.
- 2 equal shares: each is a half.
- 3 equal shares: each is a third.
- 4 equal shares: each is a fourth.
Making a whole
2 halves make a whole. 3 thirds make a whole. 4 fourths make a whole.
Same size, different shape
These squares are the same size. Both are cut in half, but in different ways. One makes 2 rectangles. One makes 2 triangles.
Each rectangle is half of a square. Each triangle is half of the same square. So they are the same size, even with different shapes.
Worked example: Name the share
A pizza is cut into 3 equal slices. What is each slice called?
Each slice is a third of the pizza.
Worked example: What is left?
A pie is cut into thirds. Dad eats 1 third. How many thirds are left?
There are 3 thirds. thirds are left.
Worked example: Which is bigger?
Which is bigger: a third or a fourth of the same cake?
A third means 3 parts. A fourth means 4 parts. Fewer parts are bigger, so a third is bigger.
Common mistake
Parts must be the same size. A shape cut into 3 parts is only cut into thirds if all 3 parts are equal.
Practice
How many thirds make a whole?
Type a number.
A pizza is cut into 3 equal parts. What is each part called?
Which piece of the same cake is the smallest?
Ana cuts a rectangle into 3 parts. One part is much bigger than the others. Is it cut into thirds?
A sandwich is cut into fourths. Leo eats 2 fourths. How many fourths are left?
Type a number.
Two crackers are the same size. One is cut in half into 2 rectangles. The other is cut in half into 2 triangles. Which is true?
Two pies are each cut into thirds. How many thirds are there in all?
Type a number.