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.

The problem.

Use inverse property.

Simplify.

Check

?

?

?

?

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?

1

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.

The value or values of the variable that make the

statement true is the solution to the equation.

Write an equation for the following

There is only part of a variable. To get a whole

variable use repeated addition which is known as

multiplication.

1

The value or values of the variable that make the

statement true is the solution to the equation.

Multiplication and division are inverse

operations. You can use multiplication to undo

division, and division to undo multiplication.

Write the problem.

1

Use inverse property.

1

Simplify.

Check

Check

The 4 must be in the numerator position or

midway. It should not be written in the

denominator position!

?

?

?

Solve.

Example 1

Example 2

Example 3

1

1

2

1

Do your arithmetic calculations off to the side

(margins).

The 7 must be in the numerator position or

midway. It should not be written in the

denominator position!

Leave the fraction improper in lowest terms.

Use good form - place the negative sign out front

in your answer.

Write an equation and then solve.

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

8.

Do NOT switch the variable to the other side of

the equal sign unless you have reason to move it!

1

CHANGING DECIMALS TO INTEGERS

You can multiply an equation with decimal

coefficients by a power of ten to get an

equivalent equation with integer coefficients.

Multiply each side of the equation by a power of

10 to rewrite the equation without decimals.

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

Solve.

Write the problem.

Multiply by LCM.

Distribute.

Use inverse operations.

Solve.

Write the problem.

Multiply by LCM.

Distribute.

Use inverse operations.

Show division work neatly beside the equation.

Remember In algebra work downward. Line up the

equal signs. Skip one line after the answer.

Example 5 Solve. Round to the nearest tenth.

Example 6 Solve. Round to the nearest hundredth.

Example 7 Solve. Round to the nearest tenth if

necessary.

You need to divide to what decimal position in

order to round to hundredths?

You need to divide to what decimal position in

order to round to tenths?

Example 5 Solve. Round to the nearest tenth.

Example 6 Solve. Round to the nearest hundredth.

Example 7 Solve. Round to the nearest tenth if

necessary.

Homework

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

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.

The problem.

Use inverse property.

Simplify.

Check

?

?

?

?

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?

1

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.

The value or values of the variable that make the

statement true is the solution to the equation.

Write an equation for the following

There is only part of a variable. To get a whole

variable use repeated addition which is known as

multiplication.

1

The value or values of the variable that make the

statement true is the solution to the equation.

Multiplication and division are inverse

operations. You can use multiplication to undo

division, and division to undo multiplication.

Write the problem.

1

Use inverse property.

1

Simplify.

Check

Check

The 4 must be in the numerator position or

midway. It should not be written in the

denominator position!

?

?

?

Solve.

Example 1

Example 2

Example 3

1

1

2

1

Do your arithmetic calculations off to the side

(margins).

The 7 must be in the numerator position or

midway. It should not be written in the

denominator position!

Leave the fraction improper in lowest terms.

Use good form - place the negative sign out front

in your answer.

Write an equation and then solve.

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

8.

Do NOT switch the variable to the other side of

the equal sign unless you have reason to move it!

1

CHANGING DECIMALS TO INTEGERS

You can multiply an equation with decimal

coefficients by a power of ten to get an

equivalent equation with integer coefficients.

Multiply each side of the equation by a power of

10 to rewrite the equation without decimals.

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

Solve.

Write the problem.

Multiply by LCM.

Distribute.

Use inverse operations.

Solve.

Write the problem.

Multiply by LCM.

Distribute.

Use inverse operations.

Show division work neatly beside the equation.

Remember In algebra work downward. Line up the

equal signs. Skip one line after the answer.

Example 5 Solve. Round to the nearest tenth.

Example 6 Solve. Round to the nearest hundredth.

Example 7 Solve. Round to the nearest tenth if

necessary.

You need to divide to what decimal position in

order to round to hundredths?

You need to divide to what decimal position in

order to round to tenths?

Example 5 Solve. Round to the nearest tenth.

Example 6 Solve. Round to the nearest hundredth.

Example 7 Solve. Round to the nearest tenth if

necessary.

Homework

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