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. Use inverse property. Simplify. ? ? Formally check even numbered homework problems.

2-3 Solving Equations Using Multiplication and Division Algebra 1 Glencoe McGraw-HillLinda Stamper

What equation is shown on the scale? 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. solution The value or values of the variable that make the statement true is the solution to the equation. 1

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. solution The value or values of the variable that make the statement true is the solution to the equation. 1

Multiplication and division are inverse operations. You can use multiplication to undo division, and division to undo multiplication. Check  1  Write the problem. Use inverse property. Simplify. ? The 4 must be in the numerator position or midway. It should not be written in the denominator position! 1

The 7 must be in the numerator position or midway. It should not be written in the denominator position! Example 1 1 Do your arithmetic calculations off to the side (margins). Solve. Example 2 1 Leave the fraction improper – in lowest terms. Use good form - place the negative sign out front in your answer. Example 3 1 2

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 =

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. 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 = = = 250 Multiply each side of the equation by a power of 10 to rewrite the equation without decimals.

Solve. Write the problem. Multiply by LCM. Use inverse operations. Distribute.

Write the problem. Multiply by LCM. Use inverse operations. Show division work neatly beside the equation. Solve. Distribute. Remember: In algebra work downward. Line up the equal signs. Skip one line after the answer.

Example 5 Solve. Round to the nearest tenth. You need to divide to what decimal position in order to round to tenths? Example 6 Solve. Round to the nearest hundredth. You need to divide to what decimal position in order to round to hundredths? Example 7 Solve. Round to the nearest tenth if necessary.

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.

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