Fractions

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Fractions 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 - whole4

2

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.

Example 1. Change to simpler terms4

15 and

5

25

Solution: 25

5= 5 and

15

4= 3 3

4 25 5 = 15 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 to an improper fraction.5

46

Solution:

64

5x

+=

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?

.3

2 and

9

2

Lowest Common Denominator or the LCD

Example 1: Find the LCD of

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 3.

2 and

4

1

LCD = 9

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.

Example 3: Find the LCD of .6

1 and

4

2

.7

1and ,

5

1,

3

1

If finding an LCD becomes too time consuming, try multiplying the set of denominators by each other.

Example 4: Find the LCD of

448

12

66

1218

LCD = 3 x 5 x 7 = 105

Raising and Reducing Fractions

18

9

5

1and

2

1Example 1: Raise to fractions with a denominator of 20.

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 2: Reduce to lowest terms.

Solution:1

2x 10

10=

10

20

1

5x 4

4= 4

20and

Solution: 9

18

9

9= 1

2

Adding and Subtracting Fractions and Whole Numbers with Common Denominators

Example 4:

12

5

12

7

14

7

14

9

15

44

15

11

9

56

9

89

Example 1:

Example 2:

Example 3:

So what is the LCD good for? Lets put it into practice with adding and subtracting these mixed numbers and fractions.

12

12= 1

2

14=

1

7

3 39

= 3 13

5 515

= 5 13

Adding and Subtracting Fractions and Whole Numbers with Unlike Denominators

5

2

4

3

5

1

3

2

4

16

3

24

2

111

6

125Example 4:

Example 1:

Example 2:

Example 3:

Now we need to find the common denominators in order to add these fractions. Lets try a few examples.

20 20+

15 8=

23

20= 1

3

20

15 15

310- =

15

7

4 612 12

8 3+ =

1210

11

25 1112 12

2 - 6= 13

12

8= 13

2

3

Multiplying Fractions and Mixed Numbers

2

14

3

12Example2:

When you are multiplying fractions you do not have to find the LCD. Yet reducing and canceling the fraction can make the process easier.

10

6

9

8

4

3Example 1:

4

3x x

8

9

6

10 =2

53

1

1

2 3

5

1

1

3

7x

2

93

1

=21

2= 10 1

2

Dividing Fractions and Whole Numbers

5

2

6

5

3

23

4

12Example2:

Example 1:

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.

5

6x

5

2=

25

12= 2

1

12

4

9x

3

11= 4

9 3

11=

27

44

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