2. Rational Numbers

3. Subtracting Integers To subtract an integer, add its additive inverse. SUBTRACTING RATIONAL NUMBERS

4. Subtracting a smaller number from a larger number is the same as finding how far apart the two numbers are on a number line. Subtracting an integer is the same as adding its opposite. How do I subtract Integers? WordsNumbersAlgebra Change the subtraction sign to an addition sign and change the sign of the second number. 2 – 3 = 2 + (–3) 4 – (–5) = 4 + 5 a – b = a + (–b) a – (–b) = a + b SUBTRACTING RATIONAL NUMBERS

5. Rules: 1.Change the SUBTRACTION sign to an ADDITION sign. 2.Change the sign of the SECOND addend to its OPPOSITE sign. 3.This is now an addition problem! Follow the rules for adding integers! SUBTRACTING RATIONAL NUMBERS

6. A. –7 – 4 –7 – 4 = –7 + (–4) B. 8 – (–5) 8 – (–5) = 8 + 5 C. –6 – (–3) –6 – (–3) = –6 + 3 = –11 = 13 = –3 Add the opposite of 4. Add the opposite of –5. Add the opposite of –3. Same sign; use the sign of the integers. 6 > 3; use the sign of 6. Subtract. SUBTRACTING RATIONAL NUMBERS

7. Your Turn! A. 3 – (–6) 3 – (–6) = 3 + 6 B. –4 – 1 –4 – 1 = –4 + (–1) C. –7 – (–8) –7 – (–8) = –7 + 8 = 9 = –5 = 1 Add the opposite of –6. Add the opposite of 1. Add the opposite of –8. Same signs; use the sign of the integers. Same sign; use the sign of the integers. 8 > 7; use the sign of 8. Subtract. SUBTRACTING RATIONAL NUMBERS

8. A. 8 – j for j = –6 8 – j 8 – (–6)Substitute –6 for j. Evaluate the expression for the given value of the variable. = 8 + 6 = 14 Add the opposite of –6. Same sign; use the sign of the integers. SUBTRACTING RATIONAL NUMBERS

9. B. –9 – y for y = –4 = –9 + 4 = –5 Evaluate the expression for the given value of the variable. –9 – y –9 – (–4)Substitute –4 for y. Add the opposite of –4. 9 > 4; use the sign of 9. SUBTRACTING RATIONAL NUMBERS

10. A. 11 – m for m = –3 11 – m 11 – (–3)Substitute –3 for m. Evaluate the expression for the given value of the variable. = 11 + 3 = 14 Add the opposite of –3. Same sign; use the sign of the integers. Your Turn! SUBTRACTING RATIONAL NUMBERS

11. B. –5 – r for r = –2 = –5 + 2 = –3 Evaluate the expression for the given value of the variable. –5 – r –5 – (–2)Substitute –2 for r. Add the opposite of –2. 5 > 2; use the sign of 5. Your Turn! SUBTRACTING RATIONAL NUMBERS

12. The top of the Sears Tower in Chicago, is 1454 feet above street level, while the lowest level is 43 feet below street level. How far is it from the lowest level to the top? Architecture Application 1454 – (–43) Subtract the lowest level from the height. 1454 + 43 Add the opposite of ( – 43). = 1497 Same sign; use the sign of the integers. It is 1497 feet from the lowest level to the top. SUBTRACTING RATIONAL NUMBERS

13. The distance from the high dive to the swimming pool is 25 feet. The pool is 14 feet deep. What is the total distance from the high dive to the bottom of the pool? Your Turn! 25 – (–14) Subtract the depth of the pool from the height of the high dive. 25 + 14 Add the opposite of ( – 14). = 39 Same sign; use the sign of the integers. It is 39 feet from the diving board to the bottom of the pool. SUBTRACTING RATIONAL NUMBERS

14. Example Solve each equation. a.n = 6 – (-4) SUBTRACTING RATIONAL NUMBERS

15. Example Solve each equation. a.n = 6 – (-4) n = 6 – (-4)To subtract –4, add 4 SUBTRACTING RATIONAL NUMBERS

16. Example Solve each equation. a.n = 6 – (-4) n = 6 – (-4)To subtract –4, add 4 n = 6 + 4 SUBTRACTING RATIONAL NUMBERS

17. Example Solve each equation. a.n = 6 – (-4) n = 6 – (-4)To subtract –4, add 4 n = 6 + 4 n = 10 SUBTRACTING RATIONAL NUMBERS

18. Example Solve each equation. b.(-3) – (-7) = y SUBTRACTING RATIONAL NUMBERS

19. Example Solve each equation. b.(-3) – (-7) = y (-3) – (-7) = yTo subtract –7, add 7 SUBTRACTING RATIONAL NUMBERS

20. Example Solve each equation. b.(-3) – (-7) = y (-3) – (-7) = yTo subtract –7, add 7 (-3) + 7 = y SUBTRACTING RATIONAL NUMBERS

21. Example Solve each equation. b.(-3) – (-7) = y (-3) – (-7) = yTo subtract –7, add 7 (-3) + 7 = y 4 = y SUBTRACTING RATIONAL NUMBERS

22. You will now receive a worksheet. Turn the worksheet in when completed.

23. Do Not Disturb Work In Progress