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FRACTIONS!
A slight review of all 4 operations
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OBJECTIVE
Today we will review the basic operations, add, subtract, multiply and divide, of fractions!
NOOOOoooo!! Not fractions!!!
YES!!! FRACTIONS!!!!
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Let’s start easy on ya;-)
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Multiply Fractions
To multiply fractions, multiply the numerators and multiply the denominators.
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Multiply. Write in simplest form.
12
13
X
12
X 13
1 x 12 x 3
=
Multiply the numerators
Multiply the denominators
=16
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example
2 x 34
34
x2 = 21
34
x
Write 2 as
Multiply the numerators
21
Multiply the denominators
2 x 31 x 4
=
64
=
= 32
SIMPLIFY
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YOUR TURN
35
12
x
3 x 15 x 2
= 310
1)
2) 23
x 4
2 x 43 x 1
23
41
x=
= = 83
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Simplify Before Multiplying
If the numerator and denominator of either fraction have common factors, you can simplify before multiplying.
THIS WILL MAKE YOUR LIFE EASIER IN THE END!!
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Multiply Mixed Numbers
Find x 4 12
25
Rewrite the mixed number as an improper fraction
= 225
254
12 X
225 = 1 x 22
2 x 5
= 115
//1
11
= 1 x 111 x 5
SIMPLIFY BEFORE MULTIPLYING TO MAKE LIFE EASIER!!
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example
56
116
35
31 x
x 185
Write mixed #’s as improper fractions
11 x 18
6 x 5=
= 335
3
1
//
= 11 x 31 x 5
(take out common factor)
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Dividing Fractions
To divide by a fraction, multiply by its reciprocal. Two numbers whose product is 1 are reciprocals.
23
32
The reciprocal of is
15
51
155 = xx = 1
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8 ÷ 2 = 4 8 x = 412
reciprocals_____ _____
same results __________
Dividing 8 by 2 gives the same result as multiplying 8
by the reciprocal of 2, or 12
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Dividing fractions is simple as pie; flip the
second number and multiply!
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Divide by a Fraction
Find 34
12
÷
34
12
34
21
= x÷ Multiply by the reciprocal of ,which is 2.
12
= 34
21
x
=
3 x 24 x 1
32
=
Multiply
SIMPLIFY!!!
=
64
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YOUR TURN!!
23
56
_..
56
32
x
= 5 x 36 x 2
= 1512
= 54
Multiply by the reciprocal
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Divide by Mixed Numbers
15 12
1÷
15 ÷ 32
Rename 1 as an improper fraction12
15 23
x=
= x
Multiply by the reciprocal
151
23
= 15 x 21 x 3
= 303
= 10
Rewrite whole #’s over 1
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YOUR TURN!!
6 12
57
3
x
÷
÷132
267
Rename the mixed #’s as improper fractions
132
726
Multiply by the reciprocal
726
132
x/
/1
2
Simplify before multiplying
1 x 72 x 2
74
=
=
=
=
=
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AANNDDD NOOWWW…
The semi (but not really) harder part!
OH NOOOOOOO!!
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ADDING AND SUBTRACTING FRACTIONS!!
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Fractions that have the same denominators are called like fractions
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Add and Subtract like fractions
1) add/subtract numerators
2) write the result over the denominator
3) SIMPLIFY!!!
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EXAMPLE
59
29
+ = 5 + 29
= 79
9-110
110
910
810
- = = 45
=
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YOUR TURN!!
89
29
8-29
69
=- = 23
=
58
78
5+78
128
32
+ = = =
1)
2)
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Add and Subtract unlike fractions
1) Find the LCD
2) Rewrite your fractions using the LCD. (you will now have like fractions)
3) Add/subtract the like fractions
4) SIMPLIFY
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12
1)
+ 16
2 = 1 x 26 = 2 x 3LCD= 2 x 3 = 6
12
2) ?6
=
=16
16
Find the LCD
Rewrite using the LCD= 3
6
3) 36
+ 16
= 3+16
46
23
4) SIMPLIFY
Add/Subtract=
EVALUATE
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YOUR TURN!!
56
+ 78
4124
=
LCD = 24
56
= 2024
2124
78
=
2024
2124
+ = 20+2124
= 4124