Algebra: Solving Algebra: Solving EquationsEquations

6-5 6-5 (pages 258-261)(pages 258-261) P4 P4 Create visual Create visual representations of representations of equation-equation-solving processes that solving processes that model model the use of inverse the use of inverse operations.operations.

Addition and multiplication of fractions have the same properties as addition and multiplication of whole numbers. Two numbers whose product is 1 are multiplicative inverses, or reciprocals.

Multiplicative Inverse Multiplicative Inverse PropertyProperty

For all fractions , where For all fractions , where a, b a, b ≠≠

00,, Multiplicative Property Multiplicative Property

of Equalityof EqualityIf If a = ba = b, then , then ac = bcac = bc

1ab

ba

Example 1Example 1

32

32

(reciprocal)

32

23

123

32

32

23

Find the multiplicative Find the multiplicative inverse ofinverse of

The multiplicative The multiplicative inverse of inverse of is ?? .is ?? .

Multiply by to get the product 1Multiply by to get the product 1

Example 1bExample 1b

If there is a mixed number, rename as an improper fraction, then…

524 5

24

522

225

225

5221

225

522

Rename the mixed Rename the mixed number, number, as an improper fraction.as an improper fraction.Find the multiplicative Find the multiplicative inverse of inverse of

Multiply by to get the Multiply by to get the product 1.product 1.

Example 2Example 2 Solve

Write the problem.

You can undo dividing by 7 by multiplying each side of the equation by 7.

Simplify.

The solution is q = 42.

Example 3Example 3 Solve

Write the problem.

Multiply each side of the equation by the reciprocal of , .

Multiply.

The solution is x = -8.

643

x

643

x

346

43

34

x4334

34)

16( x

Simplify.8324 x

You try…You try… Find the multiplicative inverse of each Find the multiplicative inverse of each

number.number. A. A. B. B.

Solve . Check your solution. Solve . Check your solution.

416

116

p

Homework Homework Periods 1,7,8Periods 1,7,8

Page 260-261 #1, 3-14, 38-51Page 260-261 #1, 3-14, 38-51

Period 5Period 5 Page 260-261 #30-36, 38-51Page 260-261 #30-36, 38-51