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Mastering Addition and Subtraction of Rational Numbers with Number Lines

Learn how to add and subtract real numbers using a number line. Understand the rules for moving left or right and changing directions for negative numbers. Practice various addition and subtraction exercises to improve your skills.

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Mastering Addition and Subtraction of Rational Numbers with Number Lines

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  1. Chapter 2.2 Adding and Subtracting Rational Numbers

  2. The set of all numbers that can be represented on a number line are called real numbers. You can use a number line to help you with addition and subtraction of real numbers. Addition To add a number, always move to the right. Subtraction To subtract a number, always move to the left. BUT: If adding or subtracting a NEGATIVE number, switch directions.

  3. -3 -1 0 1 2 3 4 6 8 9 -2 7 5 Add or subtract using a number line. –3 + 7 Start at 0. Move left to –3. To add 7, move right 7 units. +7 –3 –3 + 7 = 4

  4. 11 10 7 6 5 4 3 2 1 9 8 0 Add or subtract using a number line. –4 + (–7) Start at 0. Move left to –4. To add –7, move left 7 units. + (–7) –4 –4 + (–7) = –11

  5. -3 -2 -1 0 1 2 3 4 5 6 8 9 7 Add or subtract using a number line. 3 – (–6) Start at 0. Move right to 3. To subtract –6, move right6units. –(–6) + 3 3 – (–6) = 9

  6. Add or subtract using a number line. –3 – 7 Start at 0. Move left to –3. To subtract 7, move left 7 units. –7 –3 11 10 6 9 8 7 5 4 3 2 1 0 –3 – 7 = –10

  7. Subtracting can be thought of as the “opposite of”. 5 – (–4) 5 − (–4) = 5 + 4 To subtract –4, add 4. 5 − 4 = 5 + 4 (– ) (5 + 4 = 9) = 9

  8. Add or subtract using a number line. –5 – (–6.5) Start at 0. Move left to –5. To subtract –6.5, move right 6.5 units. – (–6.5) –5 8 7 6 5 2 1 0 1 2 4 3 –5 – (–6.5) = 1.5

  9. Another way to look at it: a) b) c) d) e) 7 + 12 So, try some now: 1) 2) 3) 4) –2 – 9 –13 – 4 6 – (–8) 10 – (-9) –5 + 8 –11 + 6 5 - 14 2 +(-13)

  10. Chapter 2.3 and 2.4 – Multiplying and Dividing Rational Numbers When you multiply or divide two numbers, the signs of the numbers determine whether the result is positive or negative. Numbers Product/Quotient Both positive Positive Negative One negative Both negative Positive

  11. Find the value of each expression. A. C. –5 B. 12

  12. Simplify each expression a.) 4(-3y) – 15y b.) 13x + (-6)(4x) -12y – 15y -27y 13x + (-24x) -11x

  13. The value of a company’s stock dropped by $1.25 per share. By what amount did the total value of the company’s stock change if the company has issued 500,000 shares of the stock? Stock Market Example 500,000 (1.25) = $625,000 DROP!!

  14. Two numbers are reciprocals if their product is 1. A number and its reciprocal are called multiplicativeinverses. To divide by a number, you can multiply by its multiplicative inverse.

  15. Evaluate the expression. Example 2 Dividing by Fractions

  16. Helpful Hint You can write the reciprocal of a number by switching the numerator and denominator. A number written without a denominator has a denominator of 1.

  17. Evaluate the expression

  18. Simplify each expression a.) b.) 3a + 2 – 12x + 8

  19. Lesson Review Simplify. a. -8 + 13 e. b. 7 – 19 f. c. -12 – (-15) g. h. d. -10 + (-36)

  20. Assignment • 2-2, 2-3 & 2-4 Study Guide/Skills Practice Worksheets (In-Class) Homework • Pages 823 – Lesson 2-2 Odds • Pages 823 – Lesson 2-3 Odds • Pages 824 – Lesson 2-4 Odds • Quiz on Sections 1-1, 1-2, 1-5, 2-2, 2-3, and 2-4 on Friday, September 18th!!!

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