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Math 310 Exam #2

Turn all cell phones off or set to “silent.”

1. [6 pts] The average teen sleeps for 7 1/2 hours out of every 24. Express the ratio of hours
slept to hours awake in lowest terms. Show work.

2. [10 pts] Use either the unit-rate or scaling approach to solve the problem below. Clearly
explain your work verbally, and tell which of the two approaches you used:
It took Kelly 10 minutes to walk 6 laps. At this rate, how long will it take her to walk
15 laps?

3. [10 pts] The ratio of men to women in the classroom is 2 to 3. If there are 30 people in
the room, how many men must enter to change the ratio to 2 to 1? Show clear work,
but you need not explain.

4. [6 pts] Find a decimal number that satisfies all of the following clues:

• The digit in the hundreds position is one more than that in the 10^-1 position.
• The digit in the tenths position equals that in the 10⁰ position.
• There are no digits in the hundredths position or smaller.
• The ones digit is odd.
• Rounded to the nearest ten, the number equals 700.

5. [5 pts] Find a rational number that is between 2/3 and 0.667.

6.
(a) [2 pts] Perform the following division entirely by hand: 0.07 ÷ 3.5

(b) [4 pts] Verbally explain how you positioned the decimal point in the quotient, and why.

7. [5 pts] Without counting, use place value to explain what the right-most position in the
product 1.234 × 0.56789 must be.

8. [10 pts] Arrange the numbers below in decreasing order. Indicate any ties. Show work.

9. [5 pts] Make up an example of an irrational number, telling how you know.

10. [5 pts] The fraction 22/7 creates a repeating decimal. Without performing the actual
conversion, explain why this is guaranteed to happen. Be clear and articulate!

11.
(a) [4 pts] What percent is 93.6 of 40?

(b) [4 pts] 93.6 is 40% of what number?

12. [24 pts - 3, 4, or 6 each] Convert as indicated; if not possible, say so. Show work only as needed.

(a) 4.38% to a single fraction

(b) 6.7868686 . . . to a single fraction

(d) 1 3/8 to a percent; do not round

(e)21/27 to a decimal; do not round

(f) 6 1/8% to a decimal; do not round