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How Do You Add and Subtract a Bunch of Numbers with Different Signs?

Compute 30 + (-25) - 15 + 10 - (-15) + (-7)

Summary

  1. As you rewrite the expression change the subtracted numbers into added numbers
  2. Subtracting a positive 15 is the same as adding a negative 15
  3. Subtracting a negative 15 is the same as adding a positive 15
  4. Group the positive numbers, 30, 10, and 15
  5. Group the negative numbers, -25, -15, and -7
  6. 30+10+15=55
  7. (-25)+(-15)+(-7)=-47

Notes

    1. To rewrite subtraction as addition:
    2. Change the subtraction sign to an addition sign
    3. Flip the sign on the subtracted term, from positive to negative or from negative to positive
    1. Subtracting a positive 15 is the same as adding a negative 15
    1. Subtracting a negative 15 is the same as adding a positive 15
    1. What are the positive numbers?
    2. They are 30, 10, and 15
    1. The associative property says that we can rearrange the numbers we're adding without changing our answer
    2. Group the positive numbers using the associative property of addition
    3. The positive numbers are 30, 10, and 15
    1. What are our negative numbers?
    2. They are -25, -15, and -7
    1. The associative property says that we can rearrange the numbers we're adding without changing our answer
    2. Group the negative numbers using the associative property of addition
    3. The negative numbers are -25, -15, and -7
    1. Add each number in each grouping together
    1. Add the positive numbers together
    2. 30 + 10 + 15 = 55
    1. Add the negative numbers together
    2. -25 + -15 + -7 = -47
    1. Add the two sums together
    2. 55 + (-47) = ?
    1. Add the two sums together
    2. 55 + (-47) = 8
    3. So the long equation:
    4. 30+(-25)-15+10-(-15)+(-7)
    5. is equal to 8