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Fractions How to Tame Them. 6/25/2013 Fractions 2 5/25/2013 Fractions 2 Numerator and Denominator For real numbers A and B with B 0 we can write a fraction.

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Presentation on theme: "Fractions How to Tame Them. 6/25/2013 Fractions 2 5/25/2013 Fractions 2 Numerator and Denominator For real numbers A and B with B 0 we can write a fraction."— Presentation transcript:

1 Fractions How to Tame Them

2 6/25/2013 Fractions 2 5/25/2013 Fractions 2 Numerator and Denominator For real numbers A and B with B 0 we can write a fraction as Denominator shows the denomination to be counted Halves, thirds, fourths, fifths, tenths, etc. Basic Parts A B Numerator Denominator A B 1 =

3 6/25/2013 Fractions 3 5/25/2013 Fractions 3 Numerator and Denominator Numerator enumerates, or counts, how many items of a given denomination Three halves, two thirds, four thirds, six tenths, etc. Basic Parts A B Numerator Denominator A B 1 =

4 6/25/2013 Fractions 4 5/25/2013 Fractions 4 Numerator and Denominator Fraction written as a ratio Three halves is ratio three-to-two or A fraction is a rational number Basic Parts A B Numerator Denominator 3 2 A B 1 = =

5 6/25/2013 Fractions 5 5/25/2013 Fractions 5 Simplest of All Fraction Operations General Rule: Multiplying Fractions = –3 8 = 3 –8 = – 3 8 Multiply numerators together and multiply denominators together Form: A B C D = A B C D Example: = –

6 6/25/2013 Fractions 6 5/25/2013 Fractions 6 Same Denominator Adding fractions requires a single denomination or denominator Example: 3 pints + 4 pints = 7 pints Example: 4 gallons + 5 gallons = 9 gallons Adding Fractions

7 6/25/2013 Fractions 7 5/25/2013 Fractions 7 Same Denominator Adding fractions requires a single denomination or denominator Adding Fractions = NOTE: Example: = 6 3 = 2 The sum is reduced to lowest terms

8 6/25/2013 Fractions 8 5/25/2013 Fractions 8 Common Denominator Adding fractions requires conversion to a single denomination, i.e. a common denominator Since the sum can have only one denomination Example: Add 3 pints to 4 gallons Adding Fractions

9 6/25/2013 Fractions 9 5/25/2013 Fractions 9 Common Denominator Example: Add 3 pints to 4 gallons Adding Fractions 3 pints + 4 gallons = 3 pints + 32 pints 4 gallons = 8 pints 1 gallon 4 gallons = 32 pints Thus = 35 pints Question: What if we converted all to gallons ?

10 6/25/2013 Fractions 10 Common Denominator Example: 3 pints 1 gallon 8 pints = 5/25/2013 Fractions 10 Adding Fractions 3 pints Thus + 4 gallons gallons = ( ) = Add 3 pints to 4 gallons gallons = ( ) gallons 35 8 =

11 6/25/2013 Fractions 11 5/25/2013 Fractions 11 Common Denominator Example: Technique: Multiply each fraction by 1 in clever disguise (i.e., b/b) to produce the same denominator (15 in this case) Adding Fractions = = = ( ) ( )

12 6/25/2013 Fractions 12 5/25/2013 Fractions 12 Find Common Denominator Example: Adding Fractions = = = = = = Question: Is = 180 also a common denominator ? Changes form but not value

13 6/25/2013 Fractions 13 5/25/2013 Fractions 13 Find Common Denominator Example: Subtracting Fractions = – = 7 – = –7 = – = – Question: Is 60 the least common denominator? Changes form NOT value

14 6/25/2013 Fractions 14 5/25/2013 Fractions 14 Simplifying A Complex Fraction Multiply numerator and denominator by a fraction that reduces the denominator to 1 Dividing Fractions A B C D = 1 A B D C = A B D C = A B C D D C D C = A B C D D C ( ) D C ( ) = A B D C General Rule: Invert denominator, multiply by the numerator I In general, for non-zero C Change form, NOT value

15 6/25/2013 Fractions 15 5/25/2013 Fractions 15 Example: Simplify Dividing Fractions = = = OR = = … using the General Rule

16 6/25/2013 Fractions 16 5/25/2013 Fractions 16 Exercise 1: Simplify Exercises x 5 = = 9x 4 = (3x)(3)(5) (5)(4) = (5)(3)(3x) (5)(4) = x (( ) )

17 6/25/2013 Fractions 17 5/25/2013 Fractions 17 Exercise 2 Simplify : Exercises 1 7 x – 1 x + 1 = 1 7 – 7x 7 1 x + x x = x + 1 x 7 – 7x 1 = x x + 1 – 7x 7 1 = 7(x + 1) – x(7x 1)

18 6/25/2013 Fractions 18 5/25/2013 Fractions 18 Think about it


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