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

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?

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.

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

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

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).

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

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.

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.

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

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