Review R.7 Dr. Doug Ensley January 7, 2015
Equivalence of fractions As long as c 0, a b = a c b c
Equivalence of fractions As long as c 0, a b = a c b c Examples True or False? 10 18 = 2 5 2 9 = 5 9 10 18 = 10 x 2 + 2x 4x 10 + 8 = 1 8 = x (x + 2) 4 x = x + 2 4
Equivalence of fractions As long as c 0, a b = a c b c Examples True or False? 10 18 = 2 5 2 9 = 5 9 10 18 = 10 x 2 + 2x 4x 10 + 8 = 1 8 = x (x + 2) 4 x = x + 2 4 The Bottom Line: You can only cancel common multiplicative factors from numerator and denominator.
Adding/subtracting fractions Fractions with the same denominator can be easily added (or subtracted): a d + b d = a + b d
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: 5 6 1 6 3 4 + 1 2 11 5 2 3 5 4 + 1 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: 5 6 1 6 3 4 + 1 2 11 5 2 3 5 4 + 1 6 The Bottom Line: You can only add or subtract fractions when they have the same denominator.
Fraction Multiplication Multiply numerators and multiply denominators: a b c d = a c b d
Fraction Multiplication Multiply numerators and multiply denominators: a b c d = a c b d Examples Evaluate and simplify: 5 2 3 4 3 4 2 5 2 3 3x 5 1 4 8 3
Fraction Multiplication Multiply numerators and multiply denominators: a b c d = a c b d Examples Evaluate and simplify: 5 2 3 4 3 4 2 5 2 3 3x 5 1 4 8 3 The Bottom Line: You can simplify as you go when you notice common multiplicative factor in numerator and denominator.
Fraction Arithmetic Examples Add 1 2 + 2 5
Fraction Arithmetic Examples Add 1 2 + 2 5 Subtract 3 4 2 6
Fraction Arithmetic Examples Add 1 2 + 2 5 Subtract 3 4 2 6 Multiply 4 3 3 10
Fraction Arithmetic Examples Add 1 2 + 2 5 Subtract 3 4 2 6 Multiply 4 3 3 10 Divide 8 3 3 2
Fraction Algebra Examples Subtract x 4 2x + 1 3
Fraction Algebra Examples Subtract x 4 2x + 1 3 Add x 2 + 1 x
Fraction Algebra Examples Subtract x 4 2x + 1 3 Add x 2 + 1 x Multiply x + 1 3 x 2
Fraction Algebra Examples Subtract x 4 2x + 1 3 Add x 2 + 1 x Multiply x + 1 3 Divide 2x 1 3 x 2 x 6
To solve an equation of the form 3 x = 5, we multiply both sides by the reciprocal of 3: 1 3 3 x = 1 3 5 which is the same equation as x = 5 3.
To solve an equation of the form 3 x = 5, we multiply both sides by the reciprocal of 3: 1 3 3 x = 1 3 5 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.
Fraction Equations Examples Solve x 2 + x 4 = 3
Fraction Equations Examples Solve x 2 + x 4 = 3 Solve x 3 1 2 = x
Fraction Equations Examples Solve x 2 + x 4 = 3 Solve x 3 1 2 = x Solve x 4 2 5 = x 6 1 3
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 2 + 1 = x + 1. Solve x 2 x = 6.