Podcast
Questions and Answers
Which of the following expressions will result in a positive outcome?
Which of the following expressions will result in a positive outcome?
Calculate the result of (-12) + 6 - 4?
Calculate the result of (-12) + 6 - 4?
If you subtract a smaller negative integer from a larger negative integer, what will the outcome be?
If you subtract a smaller negative integer from a larger negative integer, what will the outcome be?
Calculate the result of -15 - (-9)?
Calculate the result of -15 - (-9)?
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What is the difference between -10 and -3?
What is the difference between -10 and -3?
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Which of the following will result in the same value as -5 + 2?
Which of the following will result in the same value as -5 + 2?
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Study Notes
Integers
- Integers are whole numbers that can be positive, negative, or zero.
- They are represented on a number line.
- Positive integers are to the right of zero.
- Negative integers are to the left of zero.
Adding Integers
- To add integers with the same sign, add the absolute values and keep the common sign.
- Example: 3 + 5 = 8
- Example: -3 + (-5) = -8
- To add integers with different signs, find the difference between their absolute values and use the sign of the integer with the greater absolute value.
- Example: 3 + (-5) = -2
- Example: -3 + 5 = 2
Subtracting Integers
- To subtract an integer, add its opposite.
- Example: 5 - 3 = 5 + (-3) = 2
- Example: -5 - 3 = -5 + (-3) = -8
- Example: 5 - (-3) = 5 + 3 = 8
- Example: -5 - (-3) = -5 + 3 = -2
Multiplying Integers
- The product of two integers with the same sign is positive.
- Example: 3 * 5 = 15
- Example: -3 * (-5) = 15
- The product of two integers with different signs is negative.
- Example: 3 * (-5) = -15
- Example: -3 * 5 = -15
Dividing Integers
- The quotient of two integers with the same sign is positive.
- Example: 15 / 3 = 5
- Example: -15 / (-3) = 5
- The quotient of two integers with different signs is negative.
- Example: 15 / (-3) = -5
- Example: -15 / 3 = -5
Rules Summary
- Same signs: Positive result
- Different signs: Negative result
Important Concepts
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Absolute value: The distance of a number from zero, always positive.
- Example: |-3| = 3
- Example: |3| = 3
- Example: |0| = 0
Order of Operations
- When evaluating expressions involving integers, follow the order of operations (PEMDAS/BODMAS):
- Parentheses/Brackets
- Exponents/Orders
- Multiplication and Division (from left to right)
- Addition and Subtraction (from left to right)
Examples of Applying Rules
- Calculate 5 + (-3) - 2 * (-1)
- 5 + (-3) - 2 * (-1) = 2 - (-2) = 4
- Calculate -10 ÷ 2 + 8
- -10 ÷ 2 + 8 = -5 + 8 = 3
Practice Problems
- Calculate 12 + (-7) = 5
- Calculate -8 - 5 = -13
- Calculate (-4) * 6 = -24
- Calculate 20 / (-4) = -5
- Evaluate -3 + 5 - (-2) * 4 = -3 + 5 - (-8) = 2 + 8 = 10
Understanding Integer Operations
- Visualizing integers on a number line can help with understanding addition and subtraction.
- Multiplication and division can be understood as repeated additions/subtractions.
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Description
Test your understanding of integers and their operations including addition, subtraction, and multiplication. This quiz covers the rules for working with positive and negative whole numbers. Get ready to apply your knowledge and solve various integer problems!
