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Picture this! Dividing by fractions

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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

There’s a 4 in the denominator (fourths),
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 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

goes into 1 ¾ 3½ times

1¾ ÷ ½ = 3 ½

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