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Subtracting Integers: Understanding Differences in Positive and Negative Values

In this lesson, we’ll explore how to subtract integers, including both positive and negative values. You will learn to find the difference between integers using various methods, such as number lines and by adding opposites. Real-world applications, like temperature differences, will provide context to these concepts. We'll go through multiple examples to solidify your understanding. By the end of this lesson, you will accurately solve subtraction problems involving integers and implement these strategies in everyday scenarios.

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Subtracting Integers: Understanding Differences in Positive and Negative Values

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  1. Preview Warm Up California Standards Lesson Presentation

  2. Warm Up Add. 1.–2 + 6 2. –3 + (–4) 3. 7 + (–5) 4. 3 + (–4) 5. –6 + (–1) 6. –6 + 1 4 –7 2 –1 –7 –5

  3. California Standards Number Sense (NS2.3) - Solve addition, subtraction, multiplication, and division problems, including those arising in concrete situations, that use positive and negative integers and combinations of these operations. Also covered: AF1.2

  4. Objective: You will learn how to subtract integers.

  5. Helpful Hint If the number being subtracted is less than the number it is being subtracted from, the answer will be positive. If the number being subtracted is greater, the answer will be negative.

  6. In Other Words…

  7. Example 1: Modeling Integer Subtraction Find the difference. 4 – 1 Team + Team -

  8. Example 2: Modeling Integer Subtraction Find the difference. –3 – 1 Team + Team -

  9. Example 3: Modeling Integer Subtraction Find the difference. –2 – (–4) Team + Team -

  10. Check It Out! Example 4 Use a number line to find the difference. 3 – 2 Team + Team -

  11. Check It Out! Example 5 Use a number line to find the difference. –2 – 4 Team + Team -

  12. Check It Out! Example 6 Use a number line to find the difference. –4 – (–2) Team + Team -

  13. You can also subtract an integer by adding its opposite. You can then use the rules for addition of integers.

  14. Example 7: Subtracting Integers by Adding the Opposite Find each difference. A. 5 – (–2) B. –3 – 7 C. – 1 – (–8)

  15. Check It Out! Example 8 Find each difference. A. 4 – 2 B. –2 – (–6) C. –1 – 4

  16. Example 9: Evaluating Expressions with Integers Evaluate x – y for each set of values. A. x = –3 and y = 2 B. x = 4 and y = –6

  17. Check It Out! Example 10 Evaluate x – y for each set of values. A. x = –4 and y = –3 B. x = –4 and y = 5

  18. Example 11: Temperature Application Find the difference between 32°F and –10°F. The difference in temperature is 42°F.

  19. Check It Out! Example 12 Find the difference between 8°F and –5°F. The difference in temperature is 13°F.

  20. Home Learning On-Line Tutoring Walkin’ The Plank!

  21. Lesson Quiz Use a number line to find the difference. 1. 3 – 9 Find each difference. 2. –7 – 4 3. –3 – (–5) 4. Evaluate x – y + z for x = –4, y = 5, and z = –10. –6 –11 2 –19 5. On January 1, 2002, the high temperature was 81F in Kona, Hawaii. The low temperature was –29F in Barrow, Alaska. What was the difference between the two temperatures? 110F

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