Practice: Operations with Rational Numbers

Part A: Adding Integers

Directions: Find each sum. Remember: Same signs - add and keep the sign. Different signs - subtract and keep sign of larger absolute value.

1. (-8) + (-5)

2. (-12) + 7

3. 9 + (-14)

4. (-6) + 6

5. 15 + (-8)

6. (-20) + (-15)

Part B: Subtracting Integers

Directions: Find each difference. Remember: Keep, Change, Change! (Keep first number, Change subtraction to addition, Change sign of second number)

7. 8 - (-3)

8. (-5) - 9

9. (-7) - (-4)

10. 12 - 18

11. (-15) - (-15)

12. 0 - (-7)

Part C: Multiplying and Dividing Integers

Directions: Find each product or quotient. Remember: Same signs = positive, Different signs = negative.

13. (-7) x 6 =

14. (-9) x (-8) =

15. 5 x (-12) =

16. (-4) x (-4) x (-4) =

17. (-48) / 8 =

18. (-56) / (-7) =

19. 63 / (-9) =

20. (-100) / (-25) =

Part D: Operations with Fractions and Decimals

Directions: Solve each problem. Show your work for fractions.

21. (-1/2) + (-3/4) =

22. (-2/3) + 5/6 =

23. (3/4) - (-1/4) =

24. (-2/5) x (5/8) =

25. (-3.5) + 2.8 =

26. (-4.2) - (-1.7) =

27. (-2.5) x 1.6 =

28. (-7.2) / (-0.9) =

Part E: Word Problems

Directions: Read each problem carefully. Show your work.

29. The temperature at midnight was -8°F. By noon, it had risen 15 degrees. What was the temperature at noon?

Answer: _______________ °F

30. A submarine is at -350 feet (below sea level). It descends another 125 feet. What is its new position?

Answer: _______________ feet

31. Marcus has $45 in his bank account. He withdraws $62. What is his new balance? (Use negative to show debt)

Answer: $ _______________

32. A stock price changes by -$2.50 each day for 4 days. What is the total change in price?

Answer: $ _______________

33. The temperature dropped 3.5 degrees each hour for 6 hours. If it started at 12°F, what is the final temperature?

Answer: _______________ °F

Challenge: Multi-Step Problems

34. Evaluate: (-3) + (-5) x 2 - (-8)

(Remember order of operations!)

Answer: _______________

35. A hiker starts at an elevation of -45 feet (below sea level). She climbs up 120 feet, then descends 85 feet, then climbs another 65 feet. What is her final elevation?