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

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

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

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.

Since each blue rhombus is exactly covered by 2 triangles

2 blue rhombi will be exactly covered by 4 triangles

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

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

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

So now we have 1¾ 1 1 ¾ Dividing it by ½ is the same thing as saying, “How many ½ blocks cover it?”

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

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

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

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

½ goes into 1 ¾ 3½ times

1¾ ÷ ½ = 3 ½