Problem 111 - Introductory Algebra for College Students

Question

Explain how to subtract real numbers.

Step-by-Step Solution

Answer

Subtracting real numbers involves writing the subtraction as addition of the opposite, then applying rules for adding real numbers to perform the operation.

Step 1: Arrange the numbers for subtraction

Consider two real numbers, let’s say A and B. To subtract B from A, write it as A - B.

Step 2: Treat subtraction as addition of the opposite

Subtraction can be thought of as adding an opposite. So A - B is the same as A + (-B). This means we are adding the opposite (or additive inverse) of B to A.

Step 3: Apply rules for adding real numbers

Now, use the rules for adding real numbers: If the numbers have the same sign, add them and keep the sign. If the numbers have different signs, subtract them and give the result the sign of the number with the larger absolute value.

Step 4: Perform the operation

Based on the sign of B, apply the rules from step 3. Carry out the numerical Operations and apply the correct sign to your result.