Picture this! Dividing by fractions

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Picture this!Dividing by fractions

• solving 1¾ ½ with Pattern Blocks

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Get out the pattern blocks
Well use them to build 1 ¾ ½and find out the
answer
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We have to build 1¾
1¾ is a mixed number
with a whole number part
 
1
plus a fraction part
¾
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Theres a 4 in the denominator (fourths),
1¾
 
so well need to build something that can be
covered by 4 equal, smaller things.
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Since each blue rhombus is exactly covered by 2
triangles
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2 blue rhombi will be exactly covered by 4
triangles
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So lets put 2 blue rhombi together and call it 1.
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Since 4 green equilateral triangles cover it
exactly, we can call it 4/4 (four fourths)
4/4 1 whole
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Now we have to build ¾
4/4 is
 so ¾ means 3 triangles
A trapezoid covers that
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So now we have 1¾
1
¾
Dividing it by ½ is the same thing as saying,
How many ½ blocks cover it?
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Whats a ½ block?
1 whole is
so ½ must be
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How many ½ blocks does it take to cover 1 ¾ ?
so 1¾ ½ 3
with a triangle left over
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What about the leftover?
What part of a ½ block
is that leftover triangle?
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2 triangles cover the blue rhombus.
So the leftover triangle is ½ of the rhombus.
½ of
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½
goes into
3½ times
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1¾ ½ 3 ½