Fractions: Simplification, Multiplication & Division Lesson 1e Next.
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Transcript of Fractions: Simplification, Multiplication & Division Lesson 1e Next.
Fractions: Simplification, Multiplication &
Division
Lesson 1e
Next
Fractions have two parts: A Numerator & A Denominator
Fractions Numerals such as , , and are
called fractionsfractions.5
3
4
12
8
2
b
a Numerator
Denominator
Since you cannot divide by zero, the denominator of a fraction can never equal zero. However, a numerator can equal zero.
Next
Fractions Any fraction with the same
nonzero numerator and denominator equals 1.
1a
a
122
22
1322
322
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Fractions Any fraction with a denominator of
1 names the same number as its numerator.
a1
a
221
22
01
0
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Product Rule for Fractions Multiply the numerators. Multiply the denominators
Next
“•” is a symbol for multiplication (X).
Examples: Multiplying Fractions Multiply the numerators. Multiply the denominators
Next
“•” is a symbol for multiplication (X).
5
1
4
3 .1
5
4
3
2 .2
8
7
5
3 .3
Multiply:
8
3
2
1 .4
3
1
6
5 .5
7
3
10
9 .6
Click here to check your answers!
Examples: Multiplying Fractions Multiply the numerators. Multiply the denominators
Next
“•” is a symbol for multiplication (X).
5
1
4
3 .1
5
4
3
2 .2
8
7
5
3 .3
Multiply:
8
3
2
1 .4
3
1
6
5 .5
7
3
10
9 .6
20
3
15
8
40
21
16
3
18
5
70
27
Writing Fractions in Lowest Terms A fraction is in lowest terms when the
numerator and denominator have no common prime factors.
In each of the fractions below, what common prime factor do each the numerator and denominator share?
6
3 The common factor is 3
4
2 The common factor is 2
10
5 The common factor is 5
12
9 The common factor is 3
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6
1
Writing Fractions in Lowest Terms: Example 1 The first step in writing fractions in
lowest terms is to write the numerator and denominator as a product of prime factors. Write in lowest
terms: 42
7
Solution: Write the prime factorization. 732
7
42
7
Write as a product of two fractions.32
1
7
7
Any number multiplied by one is equal to itself. 6
11
6
1
6
1
Next
5
2
Writing Fractions in Lowest Terms: Example 2
Write in lowest terms: 30
12
Solution: Write the prime factorization. 532
322
30
12
Divide the numerator and the denominator by common
factors.532
322
Write in lowest terms.5
2
5
2
5
2
1
1
1
1
Next
Practice Next
Click here to check your answers!
20
5 .1
15
9 .2
36
16 .3
Write the following in lowest terms:
3322
2222
53
33
Practice
20
5 .1
Next
15
9 .2
36
16 .3
522
5
522
5
1
1
4
1
53
33
1
1
5
3
3322
2222
1
1
9
4
1
1
Write the following in lowest terms:
More on Multiplying Fractions Sometimes after multiplying fractions your
answer needs to be reduced to lowest terms. For example:
Next
1
2
More on Multiplying Fractions To reduce fractions, you can often use a
shortcut when multiplying. If possible reduce by dividing a denominator
and a numerator by the same number(a common factor).
Then multiply. For Example:
Next
1
2
5 and 10 havea common factorof 5.
Examples: Multiplying Fractions
Multiply and then write your answers in lowest terms.
Next
15
14
7
2 1 .
12
5
11
6 2 .
6
5
10
3 3 .
15
14
7
6 4 . 36
8
7 5 .
7
4
20
3
12
5 6 .
Click here to check your answers!
1
36
8
7 5 .
Examples: Multiplying Fractions
Multiply and then write your answers in lowest terms.
Next
15
14
7
2 1 .
12
5
11
6 2 .
6
5
10
3 3 .
15
14
7
6 4 .
7
4
20
3
12
5 6 .
1
2
15
4
1
222
5
1
2
1
24
1
2
51
2
5
4
2
9
2
63
1
4
1
4 28
1
1
12
1 31
Multiplying Mixed Numbers In order to multiply mixed numbers
you must change all mixed numbers to fractions. For Example:
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• 4 = 82
????Multiplythe 2 & 4
Now add the 8 tothe numerator 3.
8 + 3 = 11
11
• 5 = 204
????Multiplythe 4 & 5
Now add the 20 tothe numerator 1.
20 + 1 = 21
21
Multiplying Mixed Numbers Now that we can change mixed numbers into
fractions, we can multiply mixed numbers. First, we change the mixed number to a fraction. Next, we multiply the fractions as we have learned
previously.
Next
Example 1: Example 2:
? ?
Examples: Multiplying Mixed Numbers
Multiply and then write your answers in lowest terms.
Next
7
4
2
19 1 .
8
5
5
21 2 .
4
3
7
13 3 .
43
15 4 .
6
11
5
33 5 .
7
43
5
42 6 .
Click here to check your answers!
Examples: Multiplying Mixed Numbers
Multiply and then write your answers in lowest terms.
Next
7
4
2
19 1 .
8
5
5
21 2 .
4
3
7
13 3 .
43
15 4 .
6
11
5
33 5 .
7
43
5
42 6 .
7
4
2
19
7
35
7
38
1
2
8
5
5
7
1
1
8
7
4
3
7
22
11
2
14
33
1
4
3
16
3
121
3
64
6
7
5
18
3
1
5
14
5
21
7
25
5
14
2
11
5
101
10
Dividing Fractions Now that you can multiply fractions, you
can learn to divide fractions.
Next
Example 1:
?
Lastly, we change the division to multiplication, and multiply the fractions as we have learned previously.
First, we change any mixed numbers to fractions. The second step is to write the reciprocal of the fraction
that follows the division symbol (That fraction is called the divisor).
Example 2:
?
1
2
Examples: Dividing Fractions
Multiply and then write your answers in lowest terms.
Next
3
2
6
5 1 .
8
5
17
10 2 .
10
710 3 .
Click here to check your answers!
Examples: Dividing Fractions
Multiply and then write your answers in lowest terms.
Next
3
2
6
5 1 .
8
5
17
10 2 .
10
710 3 .
2
3
6
5
4
52
1
5
8
17
10
1
2
17
16
7
10
1
10
7
214
7
100
Definition: Reciprocal Two numbers whose product is 1
are reciprocals. The reciprocal of is .
X = 1
The reciprocal of 7 is . 7 X = 1
The reciprocal of 2 is 3/7
2 = X 3/7 = 1
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