Two operations that undo each other, such as addition and subtraction, are called inverse operations. Inverse operations help you to isolate the variable on one side of the equal sign.

Check

The problem.

4012x Use inverse property.

12 1228x Simplify.

4012x 4012

4040

3215x 15 15

47x

3215x 3215

3232

28 47

? ?

Formally check even numbered homework problems.

2-3 Solving Equations Using Multiplication

and Division

Algebra 1 Glencoe McGraw-Hill Linda Stamper

What equation is shown on the scale? 6 x2 To isolate the variable, divide by 2, but to keep the equation in balance whatever you do to one side you must do to the other side.

2 2x 3

The value or values of the variable that make the statement true is the solutionsolution to the equation.

1

6 x2

Write an equation for the following:

2 4x

There is only part of a variable. To get a whole variable use repeated addition which is known as multiplication.

4 4

x 8

The value or values of the variable that make the statement true is the solutionsolution to the equation.

x41

1

2 4x

15x3

94y

4 3 15x3

Multiplication and division are inverse operations. You can use multiplication to undo division, and division to undo multiplication.

Check

1

Check

3 5x

15x3

3

15

4

36y

94y

9

4

99

Write the problem.Use inverse property.Simplify.

?

5 36

The 4 must be in the numerator

position or midway. It

should not be written in the denominator

position!

94y

1

15

The 7 must be in the numerator

position or midway. It

should not be written in the denominator

position!

Example 1

1

187m 7 7

Do your arithmetic

calculations off to the

side (margins).

7 18

126m

187m

Solve.

Example 2

122 x4

4 4

422

x

Leave the fraction improper – in lowest terms.

211

x

Use good form - place the negative sign out front in your answer.

22 x4 Example 3

1

21

x49

94

94

184

x

92

x

21

x41

2

2

1 1

126m

Write an equation and then solve.

Do NOT switch the variable to the

other side of the equal sign unless

you have reason to move it!

Ex.4 15 is the quotient of a number and negative 8.

1

8n

15 8 8

n120

=8

n15

CHANGING DECIMALS TO INTEGERSYou can multiply an equation with decimal coefficients

by a power of ten to get an equivalent equation with integer coefficients.

Use the LCM (least common multiple) to determine the power of ten needed to clear the decimal/s.

Recall that multiplying a number by 10, 100, or 1000 is equivalent to “moving” the decimal point to the right one, two, or three place respectively.

0.25 • 10 = 2.5 0.25 • 100 = 25

0.25 • 1000 = 250

Multiply each side of the equation by a power of 10 to rewrite the equation without decimals.

Solve.

Write the problem.

21.0m07.0

Multiply by LCM. 21.0m07.0 21m7

7 7 Use inverse operations. 3m

100

Distribute.

100

Write the problem.

75.1295.9m035.0

Multiply by LCM. 75.1295.9m035.0

12750 9950m35

Use inverse operations. 9950 99502800m35

53 53 80m

Show division work neatly beside the equation.

280035

Solve.

Distribute.

1000 1000

Remember: In algebra work

downward. Line up the equal

signs. Skip one line after the

answer.

Example 5 Solve. Round to the nearest tenth. 8.06.40x6.4

You need to divide to what

decimal position in order to round

to tenths?

Example 6 Solve. Round to the nearest hundredth. 61.829.2x35.3

You need to divide to what

decimal position in order to round to hundredths?

Example 7 Solve. Round to the nearest tenth if necessary.

21.0x7.0007.0

Example 5 Solve. Round to the nearest tenth. 8.06.40x6.4

8.06.40x6.4 8406x46

406 406414x46

46 46 9x

10 10

Example 6 Solve. Round to the nearest hundredth. 61.829.2x35.3

10061.829.2x35.3100 861229x335

229 229632x335

335 335 ...886.1x

89.1x

Example 7 Solve. Round to the nearest tenth if necessary.

21.0x7.0007.0

100021.0x7.0007.01000 210x7007

210 210x700217

007 007 x31.0 x3.0

2-A5 Pages 88-89 #14-25,28,46,55,57.