# Math 201 Test 3 Review

1. Know how to represent integers using color counters and the number line.

2. Know the definition and how to compute the absolute value.

3. Be able to add and subtract integers using color counters and the number line.

4. Be able to multiply integers using color counters and
the number line. Know the definition for division

and be able to compute quotients.

5. Know how to add, subtract, and multiply on a clock. Be
comfortable enough with this that you could

work on a clock other than a 12-hour clock.

6. Be able to describe and work with fractions using the
colored regions model, fraction strips, and the

number line.

7. Be able to determine whether two fractions are equivalent or not.

8. Be able to add and subtract fractions and be prepared
to explain why, using any conceptual model,

the addition algorithm works the way it does (i.e. finding a common
denominator).

9. Be able to convert from an “improper” fraction to a mixed number and vice versa.

10. Be able to multiply fractions using a rectangular
array. Be able to use this model to explain the

algorithm for multiplying fractions.

11. Be able to divide fractions using the algorithm.

12. Be able to solve conceptual word problems that involve
division of fractions (like the math club pizza

problem from class where we drew pictures).

13. Be able to write word problems that correspond to fraction multiplication and division problems.

14. Know the definition of a rational number.

15. Know the density property for rational numbers.

16. Be able to find a rational number between two given rationals.

Practice Problems

1. Order the following rational numbers from least to greatest.

2. Find three rational numbers between

3. For the following, explain how to compute the problem
using the indicated conceptual model.

(a) Model using colored regions.

(b) Model using fraction strips.

(c) Model using a rectangular array.

4. Use a conceptual model (i.e. draw a diagram) to show
how to solve the following problem. Explain

your picture using complete sentences.

Each quart of soup calls for 2/3 cup of pinto beans. How many quarts of soup can
be made with 3 cups

of beans?

5. The length of a day on Neptune is about 16 hours. The
Neptunian children were doing arithmetic on

their 16 hour clock. Help them solve the following problems.

(d) What is the additive identity on the Neptunian clock?

6. Mark the following statements True or False

(a) and
are equivalent fractions.

(b) The integers are closed under addition, subtraction, multiplication, and
division.

(c) If the rational numbers x and y are additive inverses of each other, then x
× y = 1.

(d) If x is negative, then |x| = −x.

7. Explain, using complete sentences and color counters, why 3 − (−2) is the same as 3 + 2.

8. Use a number line to model the following problems.

(a) 5 + (−7)

(b) 5 − 7

(c) 5 − (−7)

(d) 2 × −3

9. Replace 5/6 and 7/9 by equivalent fractions with the least common denominator.

10. Use the GCD to find the simplest form of the fraction 24/60 .