Adding and subtracting integers
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The document defines integers and provides rules for adding and subtracting integers: - Integers include all positive whole numbers and their opposites, including zero. - For addition, if signs are the same, add the numbers and keep the sign; if different, subtract the smaller number from the larger and keep the sign of the number with the larger absolute value. - For subtraction, change a negative number to its positive equivalent by changing the sign, then add. This allows subtraction to follow the same rules as addition.
Adding and subtracting integers
- 2. Some definitions related to integers. Rules for adding and subtracting integers. Different methods that will work for you. Are you ready?? Add with negative integers Subtract positive integers from negative integers
- 3. Positive number – a number greater than zero. 0 1 2 3 4 5 6
- 4. Negative number – a number less than zero. 0 1 2 3 4 5 6-1-2-3-4-5-6
- 5. Opposite Numbers – numbers that are the same distance from zero in the opposite direction 0 1 2 3 4 5 6-1-2-3-4-5-6
- 6. Integers – Integers are all the positive whole numbers and all of their opposites, including zero. 7 opposite -7
- 7. Absolute Value – It is the distance a number is from zero on the number line. The absolute value of +9 or of –9 is 9.
- 10. If you don’t see a negative or positive sign in front of a number it is positive. 9+
- 11. Rule #1 – If the signs are the same, pretend the signs aren’t there. Add the numbers and then put the sign of the addends in front of your answer. 9 + 5 = 14 -9 + -5 = -14
- 12. Rule #2 – If the signs are different pretend the signs aren’t there. Subtract the smaller from the larger one and put the sign of the one with the larger absolute value in front of your answer. -9 + +5 = 9 - 5 = 4 Larger abs. value Answer = - 4
- 13. Integer Subtraction Rule Subtracting a negative number is the same as adding a positive. Change the signs and add. 2 – (-7) is the same as 2 + (+7) 2 + 7 = 9
- 14. -2 – (+7) is the same as -2 + (-7) -2 + -7 = -9 Let’s try another
- 15. 2 – (+7) is the same as 2 + (-7) 2 + -7 = -5 One more…
- 16. 0 1 2 3 4 5 6-1-2-3-4-5-6 I like to call this, “Stand – Turn – Walk” Or STW +-
- 17. 0 1 2 3 4 5 6-1-2-3-4-5-6 Stand at the first integer. If the problem is - +- -2 + (3) Stand at -2
- 19. Since the (3) is positive, you will walk forward from the -2 three spaces. The number you stop on is your answer. The answer is positive 1. -2 + (3) = 1
- 20. You have learned lots of things About adding and subtracting Integers. Let’s review!
- 21. Rule #1 – If the signs are the same, pretend the signs aren’t there. Add the numbers and then put the sign of the addends in front of your answer. 9 + 5 = 14 -9 + -5 = -14
- 22. Rule #2 – If the signs are different pretend the signs aren’t there. Subtract the smaller from the larger one and put the sign of the one with the larger absolute value in front of your answer. -9 + +5 = 9 - 5 = 4 Larger abs. value Answer = - 4
- 23. Let’s try some problems: -6 + (3) = -3 2 + (-4) = -2
- 24. Another? 4 + (-2) = -2 -4 + (-2) = -6
- 25. Same signs add and keep Different signs subtract
- 26. Keep the sign of the higher number Then you’ll be exact
- 27. Same signs add and keep Different signs subtract Keep the sign of the higher number Then you’ll be exact
- 28. Integer Subtraction Rule Subtracting a negative number is the same as adding a positive. Change the signs and add. 2 – (-7) is the same as 2 + (+7) 2 + 7 = 9!
- 29. Let’s try some problems: -6 - (3) = -9 6 - (-3) = 9
- 30. Another? 4 – (-2) = +6 -4 – (-2) = -2
- 31. Same signs add and keep Different signs subtract Keep the sign of the higher number Then you’ll be exact
- 32. Change the minus to a plus Change the sign of next Then all you do is add them up As if they were a plus
- 33. Same signs add and keep Different signs subtract Keep the sign of the higher number Then you’ll be exact Change the minus to a plus Change the sign of the next Then all you do is add them up As if they were a plus