# Test of Mathematical Reasoning

You need paper and pencil to write your answers. There are 15 questions. You will want to show your work on several problems but when possible, use mental math. Doing the problems in your head probably means you understand the reasoning involved.

** **1. When you add fractions, you add the numbers on top but not the numbers on the bottom. Explain why.

2. The decimal .25 is equal to 25 %. Why do we move the decimal two places when changing from a decimal to a percent?

3. Add 2 weeks plus 3 days.

4. Tom and Dick and Mary were each given 5 pieces of candy. Tom and Dick each ate 2 pieces. Mary ate 3 pieces. How many pieces have not been eaten.

**This problem is much harder.** ** I have watched fourth graders solve it, but many high school seniors still have trouble with it.**

5. The farmer is raising Chickens and Rabbits. He can count 10 heads and 26 legs on his animals. How many chickens does he have? How many rabbits?

**Do the rest of the problems mentally. If you aren’t sure, then guess. **

6. You want to multiply .53729 x 4.22971 Don’t do the math. First stop and think. Which answer makes the most sense? .022713 2.2713 22.713 2271.3 Explain why.

7. What is 25% of 4?

8. What is 16% of 50?

9. What is 200% of 7?

10. A game costs $20. Today it is on sale for 20% off the regular price. What does it cost today?

11. What is 3 + ½ + ¼ ?

12. What is one-third of ¾ ?

13. What is 8 times ¼ ?

14. What is (½ of ½) plus ¾ ?

15. Add the following: ½ + ¼ + 2½ +¾

Check your answers: Answers to Math Problems and Explanations