Fractions. Review R.7. Dr. Doug Ensley. January 7, Dr. Doug Ensley Review R.7
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1 Review R.7 Dr. Doug Ensley January 7, 2015
2 Equivalence of fractions As long as c 0, a b = a c b c
3 Equivalence of fractions As long as c 0, a b = a c b c Examples True or False? = = = 10 x 2 + 2x 4x = 1 8 = x (x + 2) 4 x = x + 2 4
4 Equivalence of fractions As long as c 0, a b = a c b c Examples True or False? = = = 10 x 2 + 2x 4x = 1 8 = x (x + 2) 4 x = x The Bottom Line: You can only cancel common multiplicative factors from numerator and denominator.
5 Adding/subtracting fractions Fractions with the same denominator can be easily added (or subtracted): a d + b d = a + b d
6 Adding/subtracting fractions Fractions with the same denominator can be easily added (or subtracted): a d + b d = a + b d Examples Evaluate and simplify:
7 Adding/subtracting fractions Fractions with the same denominator can be easily added (or subtracted): a d + b d = a + b d Examples Evaluate and simplify: The Bottom Line: You can only add or subtract fractions when they have the same denominator.
8 Fraction Multiplication Multiply numerators and multiply denominators: a b c d = a c b d
9 Fraction Multiplication Multiply numerators and multiply denominators: a b c d = a c b d Examples Evaluate and simplify: x
10 Fraction Multiplication Multiply numerators and multiply denominators: a b c d = a c b d Examples Evaluate and simplify: x The Bottom Line: You can simplify as you go when you notice common multiplicative factor in numerator and denominator.
11 Fraction Arithmetic Examples Add
12 Fraction Arithmetic Examples Add Subtract
13 Fraction Arithmetic Examples Add Subtract Multiply
14 Fraction Arithmetic Examples Add Subtract Multiply Divide
15 Fraction Algebra Examples Subtract x 4 2x + 1 3
16 Fraction Algebra Examples Subtract x 4 2x Add x x
17 Fraction Algebra Examples Subtract x 4 2x Add x x Multiply x x 2
18 Fraction Algebra Examples Subtract x 4 2x Add x x Multiply x Divide 2x 1 3 x 2 x 6
19 To solve an equation of the form 3 x = 5, we multiply both sides by the reciprocal of 3: x = which is the same equation as x = 5 3.
20 To solve an equation of the form 3 x = 5, we multiply both sides by the reciprocal of 3: x = which is the same equation as x = 5 3. Thus, if we can write an equation in the form a x = b, we can easily solve the equation by multiplying both sides by the reciprocal of a.
21 Fraction Equations Examples Solve x 2 + x 4 = 3
22 Fraction Equations Examples Solve x 2 + x 4 = 3 Solve x = x
23 Fraction Equations Examples Solve x 2 + x 4 = 3 Solve x = x Solve x = x 6 1 3
24 No matter what numbers a and b are, if a b = 0, then either a = 0 or b = 0. This is the reason that in solving equations, we often manipulate the equation first to get 0 on one side. Examples Solve (2x + 1)(x 3) = 0. Solve x = x + 1. Solve x 2 x = 6.
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