Fractions Vocabulary Fraction Integer Whole Number Natural Number
Fractions - Vocabulary • Fraction • Integer • Whole Number • Natural Number • Quotient • Dividing • Numerator • Denominator • Rational Number • Irrational Number • Proper Fraction • Improper Fraction • Remainder • Common Denominator • Least Common Denominator • Subtracting
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 Ø Change to improper fractions, if necessary Ø Change to common denominator Ø Add numerators, Ø Keep the same denominators (think of them as units, 3 apples plus 7 apples is 10 apples) Ø 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 Ø Change to improper fractions, if necessary Ø Change to common denominator Ø Subtract smallest numerator from largest numerator Ø Keep the sign of the largest numerators Ø Keep denominators Ø Reduce to common fractions, if necessary
Multiplying Fractions • The denominator does not have to be the same to multiply fractions • Remember: “Of” means “multiply” Ø Change to improper fractions, if necessary Ø Multiply numerators Ø Multiply denominators Ø 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 Ø Change numerator and denominator to improper fractions, if necessary Ø Inverse the denominator (turn in upside down) Ø Multiply the two fractions by: Ø Multiply the numerators Ø Multiply the denominators Ø Simplify to a common fraction, if necessary
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