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Equivalent FractionsEquivalent FractionsRaising and ReducingRaising and Reducing
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PizzaPizza
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3/4
6/8 9/12
Multiply by 1Multiply by 1
5 x 1 =5 x 1 =
235 x 1 =235 x 1 =
2/3 x 1 =2/3 x 1 =
a x 1 =a x 1 =
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5
235
2/3
a
What is 1?What is 1?
12
2 1
5
5
1453
453 1
a
a
Raising FractionsRaising Fractions
14
3x
3 2 64 2 8
x
3 3 94 3 12
x
Raising FractionsRaising Fractions A man walks into the pizza A man walks into the pizza
store and orders a medium pizza.store and orders a medium pizza.
The clerk asks “ Would you like The clerk asks “ Would you like that cut in 8 pieces or 6?”that cut in 8 pieces or 6?”
The man replied “ Make it 6. I The man replied “ Make it 6. I don’t think I can eat 8.”don’t think I can eat 8.”
Raising FractionsRaising FractionsTo raise fractions make the To raise fractions make the
denominator larger.denominator larger.
Multiply numerator and Multiply numerator and denominator (top and bottom) of denominator (top and bottom) of the fraction by the same number.the fraction by the same number.
This is the same thing as This is the same thing as multiplying by 1.multiplying by 1.
Raising FractionsRaising FractionsMultiply numerator and Multiply numerator and
denominator (top and bottom) of denominator (top and bottom) of the fraction by the same number.the fraction by the same number.
This is the same thing as This is the same thing as multiplying by 1.multiplying by 1.
15
6
3
3
5
2
Raising FractionsRaising FractionsRaise 3/8 to 56ths. Raise 3/8 to 56ths.
Multiply numerator and Multiply numerator and denominator (top and bottom) of denominator (top and bottom) of the fraction by the same number.the fraction by the same number.
568
3
Raising FractionsRaising FractionsRaise 3/8 to 56ths. Raise 3/8 to 56ths.
Multiply numerator and Multiply numerator and denominator (top and bottom) of denominator (top and bottom) of the fraction by the same number.the fraction by the same number.
3 7 218 7 56
Reducing FractionsReducing FractionsOpposite of raising.Opposite of raising.
Make the denominator smaller.Make the denominator smaller.
Divide numerator and Divide numerator and denominator by the same denominator by the same number.number.
21 7 356 7 8
Reducing FractionsReducing FractionsMight take more than one step.Might take more than one step.
More than one way.More than one way.
Divide numerator and Divide numerator and denominator by the same denominator by the same number.number.40 2 20 2 10 2 5
56 2 28 2 14 2 7
Reducing FractionsReducing FractionsDivide numerator and Divide numerator and
denominator by the same denominator by the same number.number.
4477
Reducing FractionsReducing FractionsDivide numerator and Divide numerator and
denominator by the same denominator by the same number.number.
44 11 477 11 7
Proper and Proper and ImproperImproper
An improper An improper fraction has a fraction has a numerator numerator larger than the larger than the denominator.denominator.
A proper fration A proper fration has a numerator has a numerator smaller than the smaller than the denominator.denominator.
5
12,5
5,1
2,5
8
8 2 5 12, , ,
9 35 10 51
Mixed vs. ImproperMixed vs. Improper A mixed number has a whole A mixed number has a whole
and fraction part.and fraction part.
A mixed number can be written A mixed number can be written as an improper and visa versa.as an improper and visa versa.
5
17
5
23
Work this on paper.Work this on paper.
We have 5 full crates of apples and one crate We have 5 full crates of apples and one crate with only7 apples. The full crates contain 30 with only7 apples. The full crates contain 30 apples.apples.
How many apples altogether? How many apples altogether?
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Work this on paper.Work this on paper.
We have 5 full crates of apples and one crate We have 5 full crates of apples and one crate with only7 apples. The full crates contain 30 with only7 apples. The full crates contain 30 apples.apples.
How many apples altogether? How many apples altogether?
157 apples. 157 apples.
How did you get the answer?How did you get the answer?
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Mixed to Improper.Mixed to Improper.
You multiplied the 5 times 30 and added the 7You multiplied the 5 times 30 and added the 7
To change a mixed number to improper, To change a mixed number to improper, multiply the denominator by the whole part multiply the denominator by the whole part and add the numerator. Keep the and add the numerator. Keep the denominator the same.denominator the same.
30
157
30
75
N DxW NW
D D
Mixed to improperMixed to improperTry some.Try some.
8
37
2
15
7
23
Mixed to improperMixed to improperTry some.Try some. 2 23
37 7
1 115
2 2
3 597
8 8
Try this on paper.Try this on paper.
We have 135 pencils and boxes that hold 12 We have 135 pencils and boxes that hold 12 each.each.
How many full boxes? How many loose How many full boxes? How many loose pencils?pencils?
How did you get your answer?How did you get your answer?
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Try this on paper.Try this on paper.
We have 135 pencils and boxes that hold 12 We have 135 pencils and boxes that hold 12 each.each.
How many full boxes? How many full boxes? 1111 How many loose How many loose pencils? pencils? 33
How did you get your answer?How did you get your answer?
Divided 135 by 12. The remainder was the Divided 135 by 12. The remainder was the left over.left over.
135/12 = 11 3/12135/12 = 11 3/12
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Improper to MixedImproper to MixedDivide.Divide.
D
RW
RWND
D
N
R
5
23
23125
5
12
Try these.Try these.
3
51
215
3
41
AnswersAnswers
23
12
4113
3
15 72
5117
3
