6

Addition: Unlike Signs

Unlike Integers

Integers that have different signs (positive or negative) are called unlike integers.

Add ⁺4 and ^–8.

Step 1: Use a number line to help you understand addition of unlike integers. Begin on the number line at the first addend, ⁺4.

Step 2: To add a positive value on a number line, move right. To add a negative value on a number line, move left. Move left 8 units.

Step 3: You end at ^–4.

⁺4 + ^–8 = ^–4

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TEST TIME: Multiple Choice

What is the sum of ^–3 + ⁺2?

The addends in this problem have different signs. You can use mental reasoning to understand that the negative integer is one unit farther from zero than the positive integer. That means the sum or combination will be one negative unit.

Solution: Answer b is correct.

You can check the answer to this problem using a number line. Begin at the first addend, ^–3. To add a positive 2, move right 2 units.

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TEST TIME: Show Your Work

In a beanbag game, a team gains points for tossing a beanbag into a hole. They lose points when a beanbag goes into the other team’s hole. In one round, the red team gained 6 points and lost 4 points. Write an equation and solve it to find the gain or loss for that round.

A positive integer can be used to represent gains. A negative integer can be used to represent losses. Write an equation that adds the total gains and losses.

⁺6 + ^–4 = ___

Unlike integers can be added by finding the difference of their absolute values. Subtract the smaller absolute value from the larger absolute value.

|⁺6| – |^–4| = 6 – 4 = 2

The final answer has the same sign as the integer with the greater absolute value. Since 6 > 4, the answer is positive.

Solution: ⁺6 + ^–4 = ⁺2

The red team had a gain of 2 points for that round.

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Test-Taking Hint

Word problems, or story problems, should be answered in complete sentences.

Rational Numbers

Rational numbers that have different signs are added in the same way as integers.

Add ^–7/₁₀ and ⁺³/₁₀.

Step 1: Unlike rationals are added by first finding the difference between their absolute values.

|^–7/₁₀| – |⁺³/₁₀| = ⁷/₁₀ – ³/₁₀

Step 2: To subtract like fractions, subtract only the numerators and keep the same denominator.

⁷/₁₀ – ³/₁₀ = ⁴/₁₀

Step 3: Reduce to lowest terms.

⁴/₁₀ = ²/₅

Step 4: The sum has the same sign as the addend with the greater absolute value.

⁷/₁₀ > ³/₁₀
^–7/₁₀ + ⁺³/₁₀ = ^–2/₅