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Adding, subtracting, multiplying, and dividing integers
Learn step-by-step with practice exercises built right in.
Integers are whole numbers and their opposites:
Positive integers: Neither positive nor negative
Calculate:
Different signs: subtract and use sign of larger absolute value.
Avoid these 3 frequent errors
See how this math is used in the real world
Solve .
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Same signs: Add the absolute values, keep the sign
Different signs: Subtract the absolute values, use the sign of the larger
Key rule: Subtracting is the same as adding the opposite
Examples:
Sign rules:
Examples:
Same sign rules as multiplication:
Examples:
Since 8 > 5:
Use negative sign (from -8):
Answer:
Calculate:
Different signs: subtract and use sign of larger absolute value.
Since 8 > 5:
Use negative sign (from -8):
Answer:
Calculate:
Change subtraction to adding the opposite:
Different signs: subtract and use sign of larger.
Use positive sign (from 9):
Answer:
Calculate:
Change subtraction to adding the opposite:
Different signs: subtract and use sign of larger.
Use positive sign (from 9):
Answer:
Calculate:
Work left to right:
Step 1: (different signs โ negative)
Step 2: (same signs โ positive)
Answer:
Calculate:
Work left to right:
Step 1: (different signs โ negative)
Step 2: (same signs โ positive)
Answer:
Calculate: (-48) รท 6
Step 1: Identify the signs. Negative รท Positive = Negative
Step 2: Divide the absolute values. 48 รท 6 = 8
Step 3: Apply the negative sign. (-48) รท 6 = -8
Answer: -8
A scuba diver starts at the surface (0 feet), descends 40 feet, rises 15 feet, descends another 25 feet, then rises 30 feet. What is the diver's final depth?
Step 1: Set up with integers. Surface = 0 Descend = negative (down) Rise = positive (up)
Step 2: Write the expression. 0 + (-40) + 15 + (-25) + 30
Step 3: Calculate step by step. 0 - 40 = -40 -40 + 15 = -25 -25 - 25 = -50 -50 + 30 = -20
Step 4: Interpret the result. -20 feet means 20 feet below surface
Answer: 20 feet below the surface (or -20 feet)