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1 Fractions.notebook
September 09, 2014
Hint
List what you remember about fractions.
What do you know about solving fractions using the operations?
Fractions
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Greatest Common Factor
We can use prime factorization to find the greatest common factor (GCF). 1. Factor the given numbers into primes.
2. Circle the factors that are common.
3. Multiply the common factors together to find the greatest common factor.
2
Find the GCF of 72 and 75.
Pull
Find the GCF of 18 and 44.
Pull
1
2
3
1
1 Fractions.notebook
Find the GCF of 52 and 78.
A multiple of a whole number is the product of the number and any nonzero whole number. Pull
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26
A multiple that is shared by two or more numbers is a common multiple.
Multiples of 6: 6, 12, 18, 24, 30, 36, 42, 48, ...
Multiples of 14: 14, 28, 42, 56, 70, 84,...
The least of the common multiples of two or more numbers is the least common multiple (LCM). The LCM of 6 and 14 is 42. There are 2 ways to find the LCM:
EXAMPLE: 6 and 8
1. List the multiples of each number until you find the first one they have in common.
Multiples of 6: 6, 12, 18, 24, 30
Multiples of 8: 8, 16, 24
2. Write the prime factorization of each number. Multiply all factors together. Use common factors only once (in other words, use the highest exponent for a repeated factor).
LCM = 24
Prime Factorization:
8
6
2 3 2 4
2 2 2
Find the least common multiple of 10 and 14.
5
Pull
4
C
Find the least common multiple of 6 and 14.
A
10
20
B
30
C
70
C
42
D
140
D
150
A
2
B
LCM: 23 3 = 8 3 = 24
Pull
2 3 23
C
2
1 Fractions.notebook
Find the LCM of 24 and 60.
Which is easier to solve?
28 + 42
Pull
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7(4 + 6)
Do they both have the same answer?
You can rewrite an expression by removing a common factor. This is called the Distributive Property.
In order to rewrite this expression using the Distributive Property, what GCF will you factor?
1. Rewrite an expression by factoring out the GCF.
56 + 72
Pull
7
The Distributive Property allows you to:
2. Rewrite an expression by multiplying by the GCF.
8
EXAMPLE
Rewrite by factoring out the GCF:
45 + 80
5(9 + 16)
28 + 63
7(4 + 9)
Rewrite by multiplying by the GCF:
8(4 + 13)
3(12 + 7)
32 + 101
36 + 21
48 + 84
Use the distributive property to rewrite this expression:
36 + 84
12
A
3(12 + 28)
B
4(9 + 21)
C
2(18 + 42)
D
12(3 + 7)
Pull
9
In order to rewrite this expression using the Distributive Property, what GCF will you factor?
Pull
8
D
3
1 Fractions.notebook
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September 09, 2014
Use the distributive property to rewrite this expression:
Pull
Adding Fractions...
88 + 32
1. Rewrite the fractions with a common denominator.
2. Add the numerators.
3. Leave the denominator the same.
4. Simplify your answer.
B
A
4(22 + 8)
B
8(11 + 4)
C
2(44 + 16)
D
11(8 + 3)
Adding Mixed Numbers...
1. Add the fractions (see above steps).
2. Add the whole numbers.
3. Simplify your answer. (you may need to rename the fraction)
Link Back
to List
3 10
12
14
Find the sum.
5 3 10
+
7 5 10
Is the equation below true or false?
True
False
Pull
13
+ 1 8
Pull
+ 2 10
5 8
Pull
Pull
11
1 8 12
+
1 5 12
3 1 12
Click
For reminder
Don't forget to regroup to the whole number if you end up with the numerator larger than the denominator.
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Common Denominators
Another way to find a common denominator is to multiply the two denominators together.
A quick way to find LCDs...
List multiples of the larger denominator and stop when you find a common multiple for the smaller denominator.
1 3
Ex: and
Ex: 2 5
2 1 and 3 x 5 = 15
3
5
x 5
x 3
6 2 5 x 3 15
5 3 x 5 15
= = 1 Multiples of 5: 5, 10, 15 3 4
Ex: and
2 9
Multiples of 9: 9, 18, 27, 36 17
5 8
+ 3 5
3 10
Pull
+ 1 3
16
+ 2 5
18
5
3 +
4
2
7 12
=
Pull
2 5
Pull
C
Pull
15
A
7
16
12
C
8 1 3
B
8
4 12
D
7
5 8
5
1 Fractions.notebook
2
3 +
8
5
5 12
=
3
A
1 +
4
2
1 6
=
Pull
20
Pull
A
7
19
24
C
7 8 12
A
5
2 10
C
5 1 2
B
7
8 20
D
8
7 12
B
5
5 12
D
6
5 12
Subtracting Fractions...
21
1. Rewrite the fractions with a common denominator.
2. Subtract the numerators.
3. Leave the denominator the same.
4. Simplify your answer.
7 8
Pull
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4 8
Subtracting Mixed Numbers...
1. Subtract the fractions (see above steps..).
(you may need to borrow from the whole number)
2. Subtract the whole numbers.
3. Simplify your answer. (you may need to simplify the fraction)
6 7
4 5
23
2 3
1 5
Pull
22
Pull
Link Back
to List
6
1 Fractions.notebook
25
True
False
Is the equation below true or false?
Pull
Is the equation below true or false?
Pull
24
September 09, 2014
True
False
False
2 7 9
3 9
1 1 9
3 2 9
1 2 3
4 7 8
6 7
3 5
2 3 8
A Regrouping Review
When you regroup for subtracting, you take one of your whole numbers and change it into a fraction with the same denominator as the fraction in the mixed number.
3 3 5
=
3 2 5 5 5
=
2 8 5
Pull
27
Find the difference.
Pull
26
4 5 9
5 1 4
5 3 12
3 4 12
12
4 15
3 7 12
3 7 12
3 7 12
3 7 12
12
12
1 8 12
1 2 3
Don't forget to add the fraction you regrouped from your whole number to the fraction already given in the problem.
7
Do you need to regroup in order to complete this problem?
Yes
or No
Pull
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3 What does 17 become when regrouping?
10
31
Pull
1 Fractions.notebook
3 1 2
8
33
6
2 7
3
2 3
=
Pull
32
D
1 4
4
1 6
A
2
1 12
C
1 11
12
B
1
22
24
D
1 1 12
2
15
8
10
12
=
Pull
5 What does 21 become when regrouping?
=
Pull
30
Pull
1 4
A
3
8 21
C
2 2 3
A
7
5 6
C
7 1 6
B
3
13
21
D
2 13
21
B
6
1 6
D
6 2 12
B
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Multiplying Fractions...
34
Pull
1 x 2 =
3
5
1. Multiply the numerators.
2. Multiply the denominators.
3. Simplify your answer.
Multiplying Mixed Numbers...
1. Rewrite the Mixed Number(s) as an improper fraction.
(write whole numbers / 1)
2. Multiply the fractions.
3. Simplify your answer. 37
5
x 1 = 5 x 1 2
1
2
True
False
Pull
2 x 3 =
7
3
38
4 9
( 3 8) =
3
x 4 7
A
12
Pull
36
Pull
35
Pull
Link Back
to List
B
12
7
1 5 7
C
D
21
3 5 7
9
2
1 x
4
True
3
1 =
8
6
3 8
40
(5 5 8 ) (3 2 5)
False
Pull
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Pull
1 Fractions.notebook
A
15
1 4
C
20
3 8
B
18
1 8
D
19
1 8
To divide fractions, multiply the first fraction by the reciprocal of the second fraction. Make sure you simplify your answer!
Dividing Fractions...
1. Leave the first fraction the same.
2. Multiply the first fraction by the reciprocal of the second fraction.
3. Simplify your answer.
Some people use the saying "Keep Change Flip" to help them remember the process.
1. Rewrite the Mixed Number(s) as an improper fraction(s).
(write whole numbers / 1)
2. Divide the fractions.
3. Simplify your answer. 42
4 5
True
False
8 = 5 x 8 10
10
4
Pull
41
3 5
7 = 3 x 8 = 3 x 8 = 24
8
7
5
35
5 x 7
1 5
1 = 1 x 2 = 1 x 2 = 2 2
1
5
5
5 x 1
3 4
True
False
2 =
7
2 7 8
Pull
Dividing Mixed Numbers...
10
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8 =
10
Pull
4 5
Pull
43
1
A
B
C
40
42
39
40
45
1 1 2
2 2 3
=
Pull
To divide fractions with whole or mixed numbers, write the numbers as an improper fractions. Then divide the two fractions by using the rule (multiply the first fraction by the reciprocal of the second).
Make sure you write your answer in simplest form.
1 2 3 1 =
3
2
6 1 1 =
2
3 = 6 x 2 = 12 =
2
3
3
1
6 1
2 1 2
7 = 5 x 2 = 10
2
21
7
3
4
Pull
46
5 3
5
=
11