1. Brought to you by Tutorial Services – The Math Center
Fractions
Brought to you by
Tutorial Services – The Math Center

2. 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

3. Fractions What is a numerator and a denominator? Numerator - part
Denominator - whole

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.
Example 1. Change to simpler terms
Solution: 25 15 3 = 25  5 = 5
and = 15  4 = 3 5 4 4

5. 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.
Solution: + 4 34 6 = 5 5 x

6. 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
Example 1: Find the LCD of
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
LCD = 4 x 3 = 12

7. 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
Example 3: Find the LCD of 8 12 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
LCD = 3 x 5 x 7 = 105

8. 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 to fractions with a denominator of 20. 1 10 10 1 4 4
Solution: x
and x = = 2 10 20 5 4 20
Example 2: Reduce to lowest terms. 9  9 1
Solution: = 18  9 2

9. 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. 12 1
Example 1: = 12 2 1
Example 2: = 14 7 3 1
Example 3: 3 = 3 9 3 5 1
Example 4: 5 = 5 15 3

10. 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. 15 8 23 3
Example 1: + = = 1 20 20 20 20 10 3 7
Example 2: - = 15 15 15 8 3 11
Example 3: 4 + 6 = 10 12 12 12 2 6 8 2 -
Example 4: 25 11 = 13 = 13 12 12 12 3

11. 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 1 2 3 3 8 6 2
Example 1: x x = 4 9 10 5 1 3 5 1 3 7 9 21 1 10
Example2: x = = 3 2 2 2 1

12. 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. 5 5 25 1
Example 1: x = = 2 6 2 12 12 9 11 9 3 27
Example2: x =  = 4 3 4 11 44

13. Tutorial Services – The Math Center
Brought to you by
Tutorial Services – The Math Center
Questions?

14. Additional Fraction Help
Fractions Handout
Common Denominator Handout
Fractions, Decimals, & Percentages Workshop
Fractions Quiz
Fractions, Decimals, & Percentages Quiz
Understanding Percentages Handout