๐ Topic Summary
Adding integers involves combining positive and negative whole numbers. When adding integers with the same sign (both positive or both negative), you simply add their absolute values and keep the sign. For example, $3 + 5 = 8$ and $-2 + (-4) = -6$. When adding integers with different signs, you subtract the smaller absolute value from the larger absolute value and keep the sign of the integer with the larger absolute value. For instance, $-7 + 4 = -3$ (because 7 is larger than 4, and 7 is negative) and $6 + (-2) = 4$ (because 6 is larger than 2, and 6 is positive).
Understanding number lines can also be a helpful visual aid. Moving to the right on a number line represents adding a positive integer, while moving to the left represents adding a negative integer.
๐งฎ Part A: Vocabulary
Match the following terms with their definitions:
| Term |
Definition |
| 1. Integer |
A. The distance of a number from zero |
| 2. Absolute Value |
B. Whole numbers and their opposites, including zero |
| 3. Positive Integer |
C. An integer greater than zero |
| 4. Negative Integer |
D. An integer less than zero |
| 5. Additive Inverse |
E. Two numbers that add up to zero |
Match the numbers:
- โ 1. Integer - ๐ฆ B. Whole numbers and their opposites, including zero
- ๐ 2. Absolute Value - ๐ฏ A. The distance of a number from zero
- โ
3. Positive Integer - ๐ C. An integer greater than zero
- โ 4. Negative Integer - ๐ D. An integer less than zero
- ๐ 5. Additive Inverse - 0๏ธโฃ E. Two numbers that add up to zero
โ๏ธ Part B: Fill in the Blanks
Complete the following paragraph with the correct terms.
When adding two negative integers, the result will always be a __________ integer. When adding a positive integer and a negative integer, the sign of the result depends on the __________ values of the integers. If the __________ value of the positive integer is greater, the result will be positive. If the __________ value of the negative integer is greater, the result will be __________.
Possible answers:
- โ 1. negative
- โ๏ธ 2. absolute
- ๐ 3. absolute
- ๐ 4. absolute
- โ 5. negative
๐ค Part C: Critical Thinking
Explain how you can use a number line to add -5 and 3. What is the final result?
Answer:
- ๐งญ Start at 0 on the number line.
- โฌ
๏ธ Move 5 units to the left to represent -5.
- โก๏ธ From -5, move 3 units to the right to represent +3.
- ๐ You will end up at -2. Therefore, -5 + 3 = -2.