| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.98 |
| Score | 0% | 60% |
What is \( \frac{1}{5} \) x \( \frac{1}{9} \)?
| \(\frac{1}{45}\) | |
| \(\frac{4}{27}\) | |
| \(\frac{3}{16}\) | |
| \(\frac{3}{10}\) |
To multiply fractions, multiply the numerators together and then multiply the denominators together:
\( \frac{1}{5} \) x \( \frac{1}{9} \) = \( \frac{1 x 1}{5 x 9} \) = \( \frac{1}{45} \) = \(\frac{1}{45}\)
What is \( \frac{2}{9} \) - \( \frac{3}{15} \)?
| \( \frac{3}{45} \) | |
| 2 \( \frac{6}{45} \) | |
| \(\frac{1}{45}\) | |
| \( \frac{7}{45} \) |
To subtract these fractions, first find the lowest common multiple of their denominators. The first few multiples of 9 are [9, 18, 27, 36, 45, 54, 63, 72, 81, 90] and the first few multiples of 15 are [15, 30, 45, 60, 75, 90]. The first few multiples they share are [45, 90] making 45 the smallest multiple 9 and 15 share.
Next, convert the fractions so each denominator equals the lowest common multiple:
\( \frac{2 x 5}{9 x 5} \) - \( \frac{3 x 3}{15 x 3} \)
\( \frac{10}{45} \) - \( \frac{9}{45} \)
Now, because the fractions share a common denominator, you can subtract them:
\( \frac{10 - 9}{45} \) = \( \frac{1}{45} \) = \(\frac{1}{45}\)
Which of the following statements about exponents is false?
b1 = 1 |
|
all of these are false |
|
b1 = b |
|
b0 = 1 |
A number with an exponent (be) consists of a base (b) raised to a power (e). The exponent indicates the number of times that the base is multiplied by itself. A base with an exponent of 1 equals the base (b1 = b) and a base with an exponent of 0 equals 1 ( (b0 = 1).
A menswear store is having a sale: "Buy one shirt at full price and get another shirt for 30% off." If Frank buys two shirts, each with a regular price of $28, how much money will he save?
| $2.80 | |
| $8.40 | |
| $11.20 | |
| $1.40 |
By buying two shirts, Frank will save $28 x \( \frac{30}{100} \) = \( \frac{$28 x 30}{100} \) = \( \frac{$840}{100} \) = $8.40 on the second shirt.
A machine in a factory has an error rate of 4 parts per 100. The machine normally runs 24 hours a day and produces 8 parts per hour. Yesterday the machine was shut down for 2 hours for maintenance.
How many error-free parts did the machine produce yesterday?
| 87.4 | |
| 149 | |
| 169 | |
| 120.1 |
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 8 = \( \frac{4 \times 8}{100} \) = \( \frac{32}{100} \) = 0.32 errors per hour
So, in an average hour, the machine will produce 8 - 0.32 = 7.68 error free parts.
The machine ran for 24 - 2 = 22 hours yesterday so you would expect that 22 x 7.68 = 169 error free parts were produced yesterday.