| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.34 |
| Score | 0% | 67% |
Which of the following is an improper fraction?
\({a \over 5} \) |
|
\(1 {2 \over 5} \) |
|
\({2 \over 5} \) |
|
\({7 \over 5} \) |
A rational number (or fraction) is represented as a ratio between two integers, a and b, and has the form \({a \over b}\) where a is the numerator and b is the denominator. An improper fraction (\({5 \over 3} \)) has a numerator with a greater absolute value than the denominator and can be converted into a mixed number (\(1 {2 \over 3} \)) which has a whole number part and a fractional part.
A machine in a factory has an error rate of 4 parts per 100. The machine normally runs 24 hours a day and produces 7 parts per hour. Yesterday the machine was shut down for 7 hours for maintenance.
How many error-free parts did the machine produce yesterday?
| 114.2 | |
| 134.4 | |
| 154.6 | |
| 78.2 |
The hourly error rate for this machine is the error rate in parts per 100 multiplied by the number of parts produced per hour:
\( \frac{4}{100} \) x 7 = \( \frac{4 \times 7}{100} \) = \( \frac{28}{100} \) = 0.28 errors per hour
So, in an average hour, the machine will produce 7 - 0.28 = 6.72 error free parts.
The machine ran for 24 - 7 = 17 hours yesterday so you would expect that 17 x 6.72 = 114.2 error free parts were produced yesterday.
Convert 0.0008386 to scientific notation.
| 8.386 x 10-4 | |
| 8.386 x 10-3 | |
| 8.386 x 105 | |
| 0.839 x 10-3 |
A number in scientific notation has the format 0.000 x 10exponent. To convert to scientific notation, move the decimal point to the right or the left until the number is a decimal between 1 and 10. The exponent of the 10 is the number of places you moved the decimal point and is positive if you moved the decimal point to the left and negative if you moved it to the right:
0.0008386 in scientific notation is 8.386 x 10-4
What is the next number in this sequence: 1, 3, 5, 7, 9, __________ ?
| 19 | |
| 11 | |
| 13 | |
| 2 |
The equation for this sequence is:
an = an-1 + 2
where n is the term's order in the sequence, an is the value of the term, and an-1 is the value of the term before an. This makes the next number:
a6 = a5 + 2
a6 = 9 + 2
a6 = 11
What is \( \frac{9}{5} \) - \( \frac{8}{9} \)?
| \(\frac{41}{45}\) | |
| \( \frac{5}{9} \) | |
| 1 \( \frac{8}{16} \) | |
| \( \frac{9}{45} \) |
To subtract these fractions, first find the lowest common multiple of their denominators. The first few multiples of 5 are [5, 10, 15, 20, 25, 30, 35, 40, 45, 50] and the first few multiples of 9 are [9, 18, 27, 36, 45, 54, 63, 72, 81, 90]. The first few multiples they share are [45, 90] making 45 the smallest multiple 5 and 9 share.
Next, convert the fractions so each denominator equals the lowest common multiple:
\( \frac{9 x 9}{5 x 9} \) - \( \frac{8 x 5}{9 x 5} \)
\( \frac{81}{45} \) - \( \frac{40}{45} \)
Now, because the fractions share a common denominator, you can subtract them:
\( \frac{81 - 40}{45} \) = \( \frac{41}{45} \) = \(\frac{41}{45}\)