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SOLUTIONS TO BASIC MATHEMATICS TEST TWO SAMPLE QUESTIONS

1. (a) Estimate the product 43.7 × 3.8 by rounding to whole Numbers.

Note that we do not find the exact product and then round . The estimate is not a
round-off of the exact product in (b), but can help confirm the placement of the decimal.

(b) Compute the exact product 43.7 × 3.8 by hand. Do not round.

Multiply , ignoring the decimal points .
Add the decimal places in the factors and place the
decimal point in the product so it has the total number
of decimal places. ( Two places , in this problem,)

(c) Estimate the quotient 43.91 ÷ 11.3 by rounding to whole numbers.

(d) Compute the quotient 43.91 ÷ 11.3, without rounding divisor or dividend,
by hand, rounding the quotient to two decimal places.

Move the decimal in the divisor just far enough to the
right to make it an integer. (One place, here.)
Move the decimal in the dividend the same number of
places
. Perform long division as usual. The decimal
in the quotient is placed directly above the new
decimal in the dividend. Continue until the digit after
the place
where we are to round is obtained.
Rounding, we get

2. (a) A machine runs for 5 hr 52 min, then runs 4 hr 45 min more.
How much total time did the machine run? Answer with a sentence. (1 hr = 60 min)
5 hr 52 min + 4 hr 45 min = 9 hr 97 min = 9 hr + 60 min + 37 min = 10 hr 37 min

The machine ran for a total of 10 hr 37 min.

(b) There was 6 lb 10 oz of flour left in a bag. Of this flour, 2 lb 12 oz is used
for a recipe. How much flour is now left in the bag? (1 lb = 16 oz)
6 lb 10 oz − (2 lb 12 oz) = 5 lb 26 oz − 2 lb − 12 oz = 3 lb 14 oz

There are 3 lb 14 oz of flour left in the bag.

3. Convert to reduced fractions .

4. (a) Convert to a decimal, showing the long division setup. Do not round.

(b) Convert to decimal form using bar notation in the simplest way.

The remainder of 25 has occurred before. (It’s the
original dividend, actually.) The process repeats
thereafter.


Comments: etc are unsimplified.
and are incorrect. They are not
equal to the fraction 25/37. is bad notation.

c) Convert to decimal form, rounded to three decimal places.
We must know the digit in the fourth decimal place to round correctly.

5. Given the numbers and , find the mixed number form of the

(a) sum
(b) difference
(c) product
(d) quotient

6. Simplify

7 (a) Write 3,080,000,000,000 in scientific notation.

(b) Write 0.00000073 in scientific notation.

(c) Write 3.5 × 10-4 in standard decimal notation.

8. (a) If a lawn can be mowed in hours, how long will it take to mow 9 lawns?

It will take 15 hours to mow 9 lawns.

(b) If a lawn can be mowed in hours, how many can be mowed in 10 hours?

Six lawns can be mowed in ten hours.

9. Given the data 55, 50, 90, 44, 95, 75, 57, 82, find

(a) the mean (to 3 decimal places)

(b) the median Arrange lowest to highest. 44, 50, 55, 57, 75, 82, 90, 95.
The number of data is even. Find the mean of the middle two numbers in size.

(c) the range

10. (a) Check the proportion , and state if it is true or false. The product of
the extremes should equal the product of the means. 2.4 × 4.5 = 3.6 × 3.2,
10.8 = 11.52 is false. The proportion is false .

(b) Solve the proportion

11. If we can drive 550 miles on 20 gallons of gas, how far can we drive on
16 gallons of gas? Set up and solve a proportion to solve the problem. Answer with a sentence.

Plan: Let the distance be X Miles

Check: true.

We can drive 440 miles on 16 gallons of gas.

12. Brand A gasoline cost $48 for 16 gallons. Brand B gasoline cost $42 for 15 gallons.
Brand C gasoline cost $52 for 18 gallons. Compare unit ratios and decide which is the
best buy, if the brands are equal in quality. Answer with a sentence.

Plan: Fewer dollars per gallon is better. Brand A:

Brand B: , Brand C: . 2.8 < 2.89 < 3
(Be sure to keep enough decimal places when rounding to see the differences .)

Brand B is the best buy.

13. (a) Simplify the ratio : 5 hr 36 min to 2 hr 33 min. Convert to common units.
The ratio is 336 minutes to 153 minutes. Cancel the minutes and reduce .

(b). Convert the units as indicated. Write down your calculator display .
1 inch = 2.54 cm, 1 cm = 0.3937 inch

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