Transcript Fractionsws

Fractions
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Fractions
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In this workshop, you will learn to:
Change mixed numbers to improper fractions
and improper fractions to mixed numbers
How to find common denominators
Add and subtract fractions and mixed
numbers
Raise and reduce fractions
Multiply and divide using fractions and mixed
numbers
Fractions
What is a numerator and a denominator?
Numerator - part
Denominator - whole
2
4
Mixed Numbers and Improper Fractions
What are mixed numbers and improper fractions?
How can we convert improper fractions into mixed numbers?
To change an improper fraction into a mixed number:
1.Divide the numerator by denominator to get a whole number
part.
2. Put the remainder over the denominator to get the fractional
part of the mixed number.
25
15
and
Example 1. Change
to simpler terms
5
4
Solution:
25
= 25
5

5=5
and
15
= 15
4

4 = 3
3
4
Mixed Numbers and Improper Fractions
To change a mixed number into improper fraction:
1. Multiply the whole number by the denominator.
2. Add the value to the numerator of the fraction.
3. Write the sum over the original denominator.
Example 2. Change 6
4
to an improper fraction.
5
Solution:
+
6
x
4
5
=
34
5
Common Denominators
To find a common denominator, you look for the lowest number that
each denominator can divide into evenly. What is this number
called? Lowest Common Denominator or the LCD
2
2
and
.
Example 1: Find the LCD of
9
3
LCD = 9
If this was not possible, and the denominators of the fractions are
small, try multiplying their denominators times each other.
Example 2: Find the LCD of
1
2
and
4
3.
LCD = 4 x 3 = 12
Common Denominators Continued
In some occasions, you will have to go through a series of multiples
of each in order to find the lowest number both the denominators
can divide into equally.
4
6
4
6
2
1
8
12
and .
Example 3: Find the LCD of
4
6
12 18
If finding an LCD becomes too time consuming, try multiplying the
set of denominators by each other.
Example 4: Find the LCD of
1 1
1
, , and .
3 5
7
LCD = 3 x 5 x 7 = 105
Raising and Reducing Fractions
In some cases fractions will either be raised to higher terms or be
reduced to lower terms. In either case, you are changing both the
numerator and denominator of the fraction to a fraction that has the
same numerical value, or an equivalent fraction.
Example 1: Raise
Solution:
1
1
and to fractions with a denominator of 20.
2
5
1
10
x
=
2
10
Example 2: Reduce
Solution:
9
18


10
20
and
9
to lowest terms.
18
9
9
=
1
2
1
4
x
5
4
=
4
20
Adding and Subtracting Fractions and
Whole Numbers with Common Denominators
So what is the LCD good for? Lets put it into practice with adding
and subtracting these mixed numbers and fractions.
7 5
 
Example 1:
12 12
Example 2:
12
=
12
9 7
2
 
14
14 14
=
1
1
7
8
5
Example 3: 9  6  3 3 = 3 1
9
3
9
9
1
4
 5 5 = 5 1
Example 4: 1  4
15
3
15
15
Adding and Subtracting Fractions and
Whole Numbers with Unlike Denominators
Now we need to find the common denominators in order to add
these fractions. Lets try a few examples.
3 2
Example 1:  
4 5
15
2 1
Example 2:  
3 5
10
Example 3: 4
+
20
2
1
6  4
3
4
1
6
1
2
Example 4: 25  11 
20
3
-
15
8
15
8
12
25
=
12
= 1
20
3
20
7
=
+ 6
2
23
15
3
12
- 11
= 10
6
12
11
12
= 13
8
12
= 13
2
3
Multiplying Fractions and Mixed
Numbers
When you are multiplying fractions you do not have to find the LCD.
Yet reducing and canceling the fraction can make the process easier.
1
3
3 8 6

Example 1:  
4 9 10
1
3
Example2: 2  4
1

2
2
8
x
4
1
7
3
1
1
3
6
x
9
3
1
x
3
9
2
10
5
=
21
2
2
=
= 10
5
1
2
Dividing Fractions and Whole
Numbers
Now that we understand multiplying fractions, we can divide them
as well. Dividing fractions goes hand in hand with multiplying
fractions, so once we establish the reciprocal then we can multiply
them.
Example 1: 5  2 
6
5
1
2
Example2: 2  3 
4
3
5
x
6
9
4

5
=
2
11
3
25
12
9
=
4
x
= 2
3
11
1
12
=
27
44
Brought to you by
Tutorial Services – The Math Center
Questions?
Additional Fraction Help
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