1. Fractions - Vocabulary
Irrational Number
Integer
Proper Fraction
Whole Number
Improper Fraction
Natural Number
Remainder
Quotient
Common Denominator
Dividing
Least Common Denominator
Numerator
Denominator
Subtracting
Rational Number

2. What are Fractions? Fractions are the ratio of two integers
POP QUIZ!!!
What is an integer?
How is that different from a whole number?
How is that different from a Natural number?
What is a Rational number
How is that different from an Irrational number?

3. Adding Fractions You can ONLY ADD LIKE things.
This is true for fractions as well as everything else.
Must have common denominator to add fractions.

4. Common Denominator
Get common denominator by multiplying each fraction by “ONE”
The easiest “ONE” consists of the product of the other’s denominator(s)
If the number gets too large, we can find the least common denominator

5. Adding Fractions Change to improper fractions, if necessary
Change to common denominator
Add numerators,
Keep the same denominators (think of them as units, 3 apples plus 7 apples is 10 apples)
Reduce to common fractions, if necessary

6. Subtracting Fractions
Remember: Subtracting can be thought of adding the negative.
You can ONLY ADD (SUBTRACT) LIKE things.
Must have common denominator to subtract fractions (same as above).

7. Subtracting Fractions
Change to improper fractions, if necessary
Change to common denominator
Subtract smallest numerator from largest numerator
Keep the sign of the largest numerators
Keep denominators
Reduce to common fractions, if necessary

8. Multiplying Fractions
The denominator does not have to be the same to multiply fractions
Remember: “Of” means “multiply”
Change to improper fractions, if necessary
Multiply numerators
Multiply denominators
Simplify to common fraction, if necessary
NOTE: One-half-OF a number is the same as dividing by two.

9. Dividing Fractions
The denominator does not have to be the same to divide fractions
Remember: Dividing means you are taking a large group of items and “dividing” them into equal piles.
Go over dividing an integer by an integer
Dividing by a fraction means the piles are fractions – i.e., parts of the whole. If the denominator is 0 < denominator < 1, the number of piles will be larger than the number you started with.

10. Dividing Fractions There are several “cases” of dividing fractions:
Numerator in an integer, denominator is a fraction
Numerator is a fraction, the denominator in an integer
Both numerator and denominator are fractions.
Best thing to do is write BOTH, the numerator and denominator into fractions
The fractions may be proper or improper

11. Dividing Fractions
Change numerator and denominator to improper fractions, if necessary
Inverse the denominator (turn in upside down)
Multiply the two fractions by:
Multiply the numerators
Multiply the denominators
Simplify to a common fraction, if necessary