Adding and Subtracting Integers

Front

When can you simply add the absolute values of two numbers and keep the same sign as the original numbers?

Back

When the numbers have the same sign

Answer explanation

When adding two numbers with the same sign (either both positive or both negative), you can simply add their absolute values and keep the same sign as the original numbers. For example, you have 6 and 2. Adding their absolute values (|6| + |2|) equals 6 + 2 = 8. Since both numbers are positive, the sum stays positive: 8. Now, add the numbers -7 and -2. Adding their absolute values (|-7| + |-2|) gives you 7 + 2 = 9. Since both numbers are negative, the sum will also be negative: -9.

Front

When can you subtract the smaller absolute value from the larger absolute value and keep the sign of the number with the larger absolute value?

Back

When the numbers have opposite signs

Answer explanation

When adding two numbers with opposite signs (one positive and one negative), you can subtract the smaller absolute value from the larger absolute value and keep the sign of the number with the larger absolute value. For instance, add -4 and 9. Subtracting the smaller absolute value from the larger absolute value (|9| - |-4|) results in 9 - 4 = 5. Since the number with the larger absolute value is positive (9), the result is positive: 5. Now, add -12 and 7. Subtracting the smaller absolute value from the larger absolute value (|-12| - |7|) gives 12 - 7 = 5. Since the number with the larger absolute value is negative (-12), the result is negative: -5.

Front

What is the result of adding -8 and -5?

Back

-13

Answer explanation

To add two negative integers, add their absolute values and keep the negative sign. You can write the problem as -8 + (-5). First, ignore the signs and add the absolute values: |(-8)| + |(-5)| = 8 + 5 = 13. Now, since both numbers are negative, the sum will also be negative. Therefore, the result is -13. Visually, you can think of it as starting at -8 on the number line and moving 5 units to the left (in the negative direction), which brings you to -13. Adding negative numbers moves you further to the left on the number line.

Front

-6 + 9

Back

3

Answer explanation

To add positive and negative integers, first subtract the smaller absolute value from the larger absolute value: |9| − |-6| = 9 − 6 = 3. Next, consider the signs of the numbers. Since the positive number (9) has a greater absolute value, the result will be positive. Therefore, the result is 3. You can visualize this on the number line by starting at -6 and moving 9 units to the right (in the positive direction), which brings you to 3. This shows that when you add a positive number, its value can be stronger than that of a negative number, resulting in an answer that is positive.

Front

7 + (-11)

Back

-4

Answer explanation

When adding positive and negative integers, first subtract the smaller absolute value from the larger absolute value: |-11| − |7| = 11 − 7 = 4. Next, consider the signs of the numbers. Since the negative number (-11) has a greater absolute value, the result will be negative. Therefore, the result is -4. You can visualize this on the number line by starting at 7 and moving 11 units to the left (in the negative direction), which brings you to -4. This shows that when you add a negative number, its value can be stronger than that of a positive number, resulting in an answer that is negative.

Front

True or False: Subtracting integers can be made simple by thinking of it as adding the opposite.

Back

True

Answer explanation

When you subtract integers, you can think of it as adding the opposite of the number you're subtracting. This works because subtracting a positive number is the same as adding a negative number. For example, you can think of 10 - 5 as adding the opposite of 5, which is -5. So, 10 - 5 can be thought of as 10 + (-5), which equals 5.

Front

4 - 19

Back

-15

Answer explanation

Subtraction can be made simpler by thinking of it as adding the opposite. When subtracting 19 from 4, you can think of it as adding the opposite of 19, which is -19. So, 4 - 19 can be simplified as 4 + (-19), which equals -15. This works because subtracting a positive number is equivalent to adding its negative. On the number line, starting at 4 and moving 19 units to the left (in the negative direction) brings you to -15.

Front

-7 - 6

Back

-13

Answer explanation

Subtraction can be made simpler by thinking of it as adding the opposite. When subtracting 6 from -7, you can think of it as adding the opposite of 6, which is -6. So, -7 - 6 can be simplified as -7 + (-6), which equals -13. This works because subtracting a positive number is equivalent to adding its negative. On the number line, starting at -7 and moving 6 units to the left (in the negative direction) brings you to -13.

Front

13 - (-11)

Back

24

Answer explanation

Subtraction can be made simpler by thinking of it as adding the opposite. When subtracting a negative number, like -11, it is equivalent to adding the positive version of that number. So, 13 - (-11) can be simplified as 13 + 11, which equals 24. This works because subtracting a negative number is the same as adding its positive counterpart. On the number line, starting at 13 and moving 11 units to the right (in the positive direction) brings you to 24.

Front

-18 - (-6)

Back

-12

Answer explanation

Subtraction can be made simpler by thinking of it as adding the opposite. When subtracting a negative number, like -6, it is equivalent to adding the positive version of that number. So, -18 - (-6) can be simplified as -18 + 6, which equals -12. This works because subtracting a negative number is the same as adding its positive counterpart. On the number line, starting at -18 and moving 6 units to the right (in the positive direction) brings you to -12.