The document discusses raising and reducing fractions. It explains that to raise a fraction, you multiply the numerator and denominator by the same number. This is equivalent to multiplying by 1. To reduce a fraction, you divide the numerator and denominator by the same number. The document also discusses the differences between proper, improper, and mixed numbers and how to convert between them using division or multiplication. Examples are provided to demonstrate these fraction concepts.

1. Equivalent Fractions
Raising and Reducing
Mathematics
D206

2. Pizza

3. Pizza
3/4
6/8 9/12

4. Multiply by 1
5 x 1 =
235 x 1 =
2/3 x 1 =
a x 1 =
5
235
2/3
a

5. What is 1?
1
2
2
= 1
5
5
=
1
453
453
= 1=
α
α

6. Raising Fractions
1
4
3
x
3 2 6
4 2 8
x =
3 3 9
4 3 12
x =

7. Raising Fractions
A man walks into the pizza store
and orders a medium pizza.
The clerk asks “ Would you like that
cut in 8 pieces or 6?”
The man replied “ Make it 6. I
don’t think I can eat 8.”

8. Raising Fractions
To raise fractions make the
denominator larger.
Multiply numerator and
denominator (top and bottom) of the
fraction by the same number.
This is the same thing as
multiplying by 1.

9. Raising Fractions
Multiply numerator and denominator
(top and bottom) of the fraction by the
same number.
This is the same thing as multiplying
by 1.
15
6
3
3
5
2
=
×
×

10. Raising Fractions
Raise 3/8 to 56ths.
Multiply numerator and denominator
(top and bottom) of the fraction by the
same number.
568
3
=×

11. Raising Fractions
Raise 3/8 to 56ths.
Multiply numerator and denominator
(top and bottom) of the fraction by the
same number.
3 7 21
8 7 56
× =

12. Reducing Fractions
Opposite of raising.
Make the denominator smaller.
Divide numerator and denominator
by the same number.
21 7 3
56 7 8
÷
=
÷

13. Reducing Fractions
Might take more than one step.
More than one way.
Divide numerator and denominator
by the same number.
40 2 20 2 10 2 5
56 2 28 2 14 2 7
÷ ÷ ÷
= = =
÷ ÷ ÷

14. Reducing Fractions
Divide numerator and denominator
by the same number.
44
77
÷
=
÷

15. Reducing Fractions
Divide numerator and denominator
by the same number.
44 11 4
77 11 7
÷
=
÷

16. Proper and Improper
An improper
fraction has a
numerator
larger than the
denominator.
A proper
fraction has a
numerator
smaller than the
denominator.
5
12
,
5
5
,
1
2
,
5
8
8 2 5 12
, , ,
9 35 10 51

17. Mixed vs. Improper
A mixed number has a whole and
fraction part.
A mixed number can be written as
an improper and visa versa.
5
17
5
2
3 =

18. Work this on paper.
We have 5 full crates of apples
and one crate with only7 apples.
The full crates contain 30
apples.
How many apples altogether?

19. Work this on paper.
We have 5 full crates of apples
and one crate with only7 apples.
The full crates contain 30
apples.
How many apples altogether?
157 apples.
How did you get the answer?

20. Mixed to Improper.
You multiplied the 5 times 30 and
added the 7
To change a mixed number to
improper, multiply the denominator by
the whole part and add the numerator.
Keep the denominator the same.
30
157
30
7
5 =
N DxW N
W
D D
+
=

21. Mixed to improper
Try some.
8
3
7
2
1
5
7
2
3
=
=

22. Mixed to improper
Try some. 2 23
3
7 7
1 11
5
2 2
3 59
7
8 8
=
=
=

23. Try this on paper.
We have 135 pencils and
boxes that hold 12 each.
How many full boxes? How
many loose pencils?
How did you get your answer?

24. Try this on paper.
We have 135 pencils and
boxes that hold 12 each.
How many full boxes? 11 How
many loose pencils? 3
How did you get your answer?
Divided 135 by 12. The
remainder was the left over.
135/12 = 11 3/12

25. Improper to Mixed
Divide.
D
R
W
RW
ND
D
N
R
5
2
3
23
125
5
12

26. Try these.
3
51
2
15
3
41

27. Answers
2
3
1
2
41
13
3
15 7
2
51
17
3
=
=
=