| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.43 |
| Score | 0% | 69% |
Cooks are needed to prepare for a large party. Each cook can bake either 4 large cakes or 14 small cakes per hour. The kitchen is available for 4 hours and 21 large cakes and 390 small cakes need to be baked.
How many cooks are required to bake the required number of cakes during the time the kitchen is available?
| 7 | |
| 10 | |
| 11 | |
| 9 |
If a single cook can bake 4 large cakes per hour and the kitchen is available for 4 hours, a single cook can bake 4 x 4 = 16 large cakes during that time. 21 large cakes are needed for the party so \( \frac{21}{16} \) = 1\(\frac{5}{16}\) cooks are needed to bake the required number of large cakes.
If a single cook can bake 14 small cakes per hour and the kitchen is available for 4 hours, a single cook can bake 14 x 4 = 56 small cakes during that time. 390 small cakes are needed for the party so \( \frac{390}{56} \) = 6\(\frac{27}{28}\) cooks are needed to bake the required number of small cakes.
Because you can't employ a fractional cook, round the number of cooks needed for each type of cake up to the next whole number resulting in 2 + 7 = 9 cooks.
Simplify \( \frac{32}{52} \).
| \( \frac{4}{13} \) | |
| \( \frac{5}{19} \) | |
| \( \frac{5}{7} \) | |
| \( \frac{8}{13} \) |
To simplify this fraction, first find the greatest common factor between them. The factors of 32 are [1, 2, 4, 8, 16, 32] and the factors of 52 are [1, 2, 4, 13, 26, 52]. They share 3 factors [1, 2, 4] making 4 their greatest common factor (GCF).
Next, divide both numerator and denominator by the GCF:
\( \frac{32}{52} \) = \( \frac{\frac{32}{4}}{\frac{52}{4}} \) = \( \frac{8}{13} \)
What is the distance in miles of a trip that takes 8 hours at an average speed of 65 miles per hour?
| 450 miles | |
| 520 miles | |
| 130 miles | |
| 195 miles |
Average speed in miles per hour is the number of miles traveled divided by the number of hours:
speed = \( \frac{\text{distance}}{\text{time}} \)Solving for distance:
distance = \( \text{speed} \times \text{time} \)
distance = \( 65mph \times 8h \)
520 miles
Which of the following is an improper fraction?
\({7 \over 5} \) |
|
\({2 \over 5} \) |
|
\({a \over 5} \) |
|
\(1 {2 \over 5} \) |
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.
Solve for \( \frac{5!}{4!} \)
| 72 | |
| \( \frac{1}{42} \) | |
| 6 | |
| 5 |
A factorial is the product of an integer and all the positive integers below it. To solve a fraction featuring factorials, expand the factorials and cancel out like numbers:
\( \frac{5!}{4!} \)
\( \frac{5 \times 4 \times 3 \times 2 \times 1}{4 \times 3 \times 2 \times 1} \)
\( \frac{5}{1} \)
5