1. Picture this! Dividing by fractions
solving 1¾ ÷ ½ with Pattern Blocks

2. Get out the pattern blocks
We’ll use them to build 1 ¾ ÷ ½ and find out the answer

3. 1 ¾ We have to build 1¾ 1¾ is a mixed number with a whole number part1
plus a fraction part

4. There’s a 4 in the denominator (fourths),1¾
so we’ll need to build something that can be covered by 4 equal, smaller things.

5. Since each blue rhombus is exactly covered by 2 triangles

6. 2 blue rhombi will be exactly covered by 4 triangles

7. So let’s put 2 blue rhombi together and call it 1.

8. Since 4 green equilateral triangles cover it exactly, we can call it 4/4 (four fourths)
4/4 = 1 whole

9. A trapezoid covers that
Now we have to build ¾
4/4 is
 so ¾ means 3 triangles
A trapezoid covers that

10. So now we have 1¾ 1 1
Dividing it by ½ is the same thing as saying, “How many ½ blocks cover it?”

11. What’s a ½ block?
1 whole is
so ½ must be

12. How many ½ blocks does it take to cover 1 ¾ ?
so 1¾ ÷ ½ = 3
with a triangle left over

13. What about the leftover?
What part of a ½ block
is that leftover triangle?

14. 2 triangles cover the blue rhombus.
So the leftover triangle is ½ of the rhombus.
= ½ of

15. goes into
1 ¾
3½ times

16. 1¾ ÷ ½ = 3 ½