| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.13 |
| Score | 0% | 63% |
What is \( \frac{7}{3} \) + \( \frac{4}{7} \)?
| \( \frac{1}{21} \) | |
| 2\(\frac{19}{21}\) | |
| \( \frac{2}{7} \) | |
| 2 \( \frac{3}{21} \) |
To add these fractions, first find the lowest common multiple of their denominators. The first few multiples of 3 are [3, 6, 9, 12, 15, 18, 21, 24, 27, 30] and the first few multiples of 7 are [7, 14, 21, 28, 35, 42, 49, 56, 63, 70]. The first few multiples they share are [21, 42, 63, 84] making 21 the smallest multiple 3 and 7 share.
Next, convert the fractions so each denominator equals the lowest common multiple:
\( \frac{7 x 7}{3 x 7} \) + \( \frac{4 x 3}{7 x 3} \)
\( \frac{49}{21} \) + \( \frac{12}{21} \)
Now, because the fractions share a common denominator, you can add them:
\( \frac{49 + 12}{21} \) = \( \frac{61}{21} \) = 2\(\frac{19}{21}\)
What is \( \frac{3}{5} \) ÷ \( \frac{2}{8} \)?
| 4\(\frac{4}{5}\) | |
| \(\frac{4}{81}\) | |
| 2\(\frac{2}{5}\) | |
| \(\frac{1}{10}\) |
To divide fractions, invert the second fraction and then multiply:
\( \frac{3}{5} \) ÷ \( \frac{2}{8} \) = \( \frac{3}{5} \) x \( \frac{8}{2} \)
To multiply fractions, multiply the numerators together and then multiply the denominators together:
\( \frac{3}{5} \) x \( \frac{8}{2} \) = \( \frac{3 x 8}{5 x 2} \) = \( \frac{24}{10} \) = 2\(\frac{2}{5}\)
Simplify \( \frac{28}{72} \).
| \( \frac{9}{19} \) | |
| \( \frac{4}{15} \) | |
| \( \frac{7}{18} \) | |
| \( \frac{1}{4} \) |
To simplify this fraction, first find the greatest common factor between them. The factors of 28 are [1, 2, 4, 7, 14, 28] and the factors of 72 are [1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72]. They share 3 factors [1, 2, 4] making 4 their greatest common factor (GCF).
Next, divide both numerator and denominator by the GCF:
\( \frac{28}{72} \) = \( \frac{\frac{28}{4}}{\frac{72}{4}} \) = \( \frac{7}{18} \)
A machine in a factory has an error rate of 8 parts per 100. The machine normally runs 24 hours a day and produces 10 parts per hour. Yesterday the machine was shut down for 7 hours for maintenance.
How many error-free parts did the machine produce yesterday?
| 156.4 | |
| 93 | |
| 70.5 | |
| 129.4 |
The hourly error rate for this machine is the error rate in parts per 100 multiplied by the number of parts produced per hour:
\( \frac{8}{100} \) x 10 = \( \frac{8 \times 10}{100} \) = \( \frac{80}{100} \) = 0.8 errors per hour
So, in an average hour, the machine will produce 10 - 0.8 = 9.2 error free parts.
The machine ran for 24 - 7 = 17 hours yesterday so you would expect that 17 x 9.2 = 156.4 error free parts were produced yesterday.
A menswear store is having a sale: "Buy one shirt at full price and get another shirt for 5% off." If Frank buys two shirts, each with a regular price of $47, how much will he pay for both shirts?
| $70.50 | |
| $91.65 | |
| $44.65 | |
| $61.10 |
By buying two shirts, Frank will save $47 x \( \frac{5}{100} \) = \( \frac{$47 x 5}{100} \) = \( \frac{$235}{100} \) = $2.35 on the second shirt.
So, his total cost will be
$47.00 + ($47.00 - $2.35)
$47.00 + $44.65
$91.65