ASVAB Study GuideRules for adding and subtracting integers
Addition $$(+)$$
$$(+) + (+) = (+)$$
$$(-) + (-) = (-)$$
Subtraction $$(-)$$
$$a - b = a + (-b)$$
$$a - (-b) = a + b$$ (subtracting a negative becomes addition)
Addition $$(+)$$
Same Signs: Add the absolute values and keep the original sign.
Different Signs: Subtract the smaller absolute value from the larger one, then use the sign of the larger number.
Subtraction $$(-)$$
Conversion Rule: To subtract a number, add its opposite.
(Subtracting a negative becomes addition)
Example
Calculate:
1) $$(-12) + (-8)$$
2) $$15 - (-10)$$
Show solution
Step 1: For $$(-12) + (-8)$$, same signs: add $$12 + 8 = 20$$, keep negative sign -> -20.
Step 2: For $$15 - (-10)$$, double negative turns to positive: $$15 + 10 = 25$$
Practice problems
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Problem 1
Calculate the value of: $$25 - (-10)$$
Show solution
Answer: 35
Step 1: Identify double negative: $$-(-10)$$ becomes $$+10$$.
Step 2: Rewrite equation: $$25 + 10$$
Step 3: Calculate result = 35.
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Problem 2
Calculate the value of: $$-50 + 75 - 15$$
Show solution
Answer: 10
Step 1: Work from left to right: $$(-50 + 75) = 25$$ (different signs, $$75 - 50 = 25$$, sign of +75).
Step 2: Subtract 15: $$25 - 15$$
Step 3: Calculate result = 10.
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Problem 3
Calculate the value of $$x - y + z$$
given $$x = -45$$, $$y = -15$$, $$z = -30$$
Show solution
Answer: -60
Step 1: Substitute values: $$(-45) - (-15) + (-30)$$
Step 2: Convert double negative: $$-45 + 15 - 30$$
Step 3: Combine: $$(-45 + 15) = -30$$
Step 4: Add final term: $$-30 + (-30) = -60$$
Pay close attention to double negatives! Subtracting a negative number always turns into adding a positive number: $$a - (-b) = a + b$$