Solving Equations with Rational Numbers

Warmup

Activity #1

Match Numbers with their Inverses.

• Match the numbers in the applet below with their additive inverses.

• Match the numbers in the applet below with their multiplicative inverses.

What do you notice about the numbers and their inverses?

Activity #2

Determine the Sign of a Rational Number Relative to a Position.

A number line is shown here below.

The numbers 0 and 1 are marked on the line, as are two other rational numbers  and  .

• Answer the following questions about the number line above.

(1.) Decide if is positive or negative.

(2.) Decide if is positive or negative.

(3.) Decide if is positive or negative.

(4.) Decide if is positive or negative.

(5.) Decide if is positive or negative.

(6.) Decide if is positive or negative.

Activity #3

Add rational Numbers.

This exercise is very useful to practice adding fractions. Keep in mind that a common multiple does not have to be the least common multiple in other to add or subtract fractions. It works as long as the number is a multiple of the denominator of the fractions. The answer of course, will not be in the simplest form if you did not use the least common multiple.

• Start by enter the L.C.M. of the denominators in each fraction. When you enter the correct value, it appears numbers green. If it is not, it will appear red.
• Fill in the remaining boxes. You will not receive a formal feedback of your answer. The green color is the approval.
• As usual, click to do more.

Challenge #1

Match each equation to a value that makes it true by dragging the answer to the corresponding equation.

Challenge #2

Match each equation to a step that will help to solve the equation.

Challenge #3

Evaluate each the expression if is , is -4, and isis -0.2. Enter your answer as a decimal if you have a fraction.