Worksheet: Rational Numbers - Operations and Real-Life Problems

Learning Intention: Perform operations (addition, subtraction, multiplication, and division) with rational numbers and solve real-life statement problems involving rational numbers.

Instructions: Solve the following problems using the appropriate operations with rational numbers. Show all your work and write your answers in simplest form.

1. Evaluate: 3/4 + 2/3
2. Evaluate: 5/6 - 1/2
3. Evaluate: 2/5 × 3/4

4. Evaluate: 7/8 ÷ 2/3

5. Create a real-life statement problem that involves adding two rational numbers.
6. Create a real-life statement problem that involves subtracting two rational numbers.
7. Create a real-life statement problem that involves multiplying two rational numbers.

8. Create a real-life statement problem that involves dividing two rational numbers.

9. Evaluate: -2/3 + (-5/6)
10. Evaluate: -3/4 - (-1/2)
11. Evaluate: -2/5 × 3/4

12. Evaluate: -7/8 ÷ 2/3

13. Evaluate: 1/2 + (-3/4)
14. Evaluate: 2/3 - (-1/2)
15. Evaluate: 3/4 × (-2/5)

16. Evaluate: 7/8 ÷ (-2/3)

17. Evaluate: 1/3 + 2/3 + 1/4
18. Evaluate: 5/6 - 1/2 + 1/3
19. Evaluate: 2/5 × 3/4 + 1/2
20. Evaluate: 7/8 ÷ 2/3 + 1/4

Answer Key: 1. 17/12 2. 1/3 3. 3/10 4. 21/16

1. (Example answer) John has 3/4 of a pizza, and his friend has 2/3 of a pizza. How much pizza do they have in total?
2. (Example answer) Sarah had $5.50, but she spent $3.25. How much money does she have left?
3. (Example answer) A recipe requires 2/3 cup of flour, and you want to make 3 batches. How much flour do you need in total?

4. (Example answer) A car traveled 240 miles in 6 hours. What was its average speed in miles per hour?

5. -19/6
6. -1/4
7. -3/10

8. -21/16

9. -1/4
10. 7/6
11. -3/10

12. -21/16

13. 23/12
14. 7/6
15. 11/20
16. 43/24