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Back to: Steve's Place - For Students Page
MATH SURVEY
Directions: Work each problem. Reduce all common fractions to lowest
terms.
(These questions were taken from real employers' tests.)
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They want you to add up the columns and show that you can carry numbers to the next column. You may not be allowed to use a calculator during the test, but this type of problem is easy. If you missed the answer, you need practice. |
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You probably will not be allowed to use a calculator, so you will have to mulitply the numbers the old-fashioned way. |
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Multiplying decimal numbers is easy. Just pretend there is no decimal, multiply as you would normally, then count the number of total decimal places to the right of the decimal point in both numbers (in this case six) and count over that many places from the right in the answer. |
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Adding whole numbers and fractions. You will need to find a common denominator and then reduce the result. See the presentation on this. |
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Multiplying with fractions. Check out the review on how to do this. |
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We are dealing with pounds and ounces. So remember that there are 16 ounces in a pound. Also remember that you must only add ounces to ounces and pounds to pounds. |
8. Change 0.80 to a fraction. 4/5
0.80 is 80/100. Reduce this and you end up with 4/5.
9. Select the number that has the greatest value.
0.3047 0.3470 3.047 [ans: 3.047]
Watch out for the decimal point.
10. What is 4 percent of 150? [ans: 6 ]
Use proportions to help with percentages. 4 percent is 4/100.
Solve for X.
11. 12 ¼ - 6 ½ [ans: 5 3/4 ]
Find a common denominator. In this case 1/4 - 2/4. You need to borrow 1 (4/4) from 12 so the problem then becomes: 11 5/4 - 6 2/4. Subtract fractions from fractions, whole numbers from whole numbers.
12. Change 20% to a fraction. [ans: 1/5 ]
20 % is 20/100. Then reduce to get the final answer.
13. Change 45/90 to a percent. [ans: 50% ]
Use proportions again, remembering that percentages are always per-cent or per one-hundred.
Solve for X.
14. 60% of the parts in a lot are blue. If there are 135 blue parts, how many total parts are in the lot?
[ans: 225 ]
Use those proportions again. 60% of the blue parts is 60/100. Which can be read as " there are 60 blue parts in 100 total parts. The second half of the question tells us that there are 135 blue parts and we want to know the total parts. Read this problem as: 60 is to 100 as 135 is to X.
Solve for X.
15. The time now is 11:45. What will the time be 4 hours and 18 minutes from now?
[ans: 4:03 ]
45 minutes plus 18 minutes is 63 minutes. But there are only 60 minutes in an hour, so we have 1 hour 3 minutes. 11 hours plus 4 hours is 15 hours. But there are only 12 hours in a clock cycle, so 15 minus12 is 3 hours. 3 hours plus 1 hour 3 minutes is 4 hours 3 minutes.
16. 9 ÷ ¾ = [ ans: 12 ]
You may remember that dividing is the same as multiplying by the reciprocal (you better remember or else you are going to make things hard for yourself.) So the problem becomes: 9 x 4/3. 9 x 4 is 36. 36/3 is 12.
17. How many seconds are there in a day? [ans: 86400 ]
Use dimensional analysis to do all conversions. Express conversion factors as units variations of the number ONE.
all these multipliers are forms of the number ONE. Remember, you can multiply or divide ANYTHING by the number ONE and it will remain unchanged. In conversions, you want an equivalent form with different units.
18. What is the average of the following numbers?
1344
1567
1432
1567[ans: 1477.5 ]
The sum of the numbers (5910) divided by 4.
19. The above numbers represent daily production of a certain part. How many parts would need to be produced on the next day to make a 5-day average of 1480? [ans: 1490 ]
If the 5-day average is 1480, then the total amount of production for the week is 7400 (5 x 1480). The first four days of production are 5910 (from the problem above). Therefore, we will need to produce 1490 parts on the fifth day (7400 - 5910) to have a daily average for the week of 1480.
20. 43.81 ÷ 3.5 = [ans: 12.52 ]
Move the decimal in both the divisor and the dividend the same amount so that the divisor becomes a whole number.
438.1 ÷ 35. This problem, like most in real life, doesn't work out to a tidy answer. In fact you can keep on dividing all day and get 12.51714285714... etc. When do you stop and just approximate the answer by rounding off after a while? A good rule of thumb is to carry out the operation to as many decimal places as are in the original question. In this case 43.81 has two decimal places, so unless there is a reason, don't bother to carry the operation out for more than three decimal places and round off to two. So, in this case 12.517 becomes 12.52. But always remember the context of the problem. In this case there is no context, it just asks you to do the operation, so use the rule of thumb. If you get it wrong, make an arguement. But if the context is something like converting 45.81 millimeters to inches you'll have to carry the operation out until you have at least as much accuracy as in the original number.