| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.16 |
| Score | 0% | 63% |
Simplify \( \frac{28}{72} \).
| \( \frac{7}{18} \) | |
| \( \frac{8}{11} \) | |
| \( \frac{1}{2} \) | |
| \( \frac{10}{17} \) |
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:
\( \frac{28}{72} \) = \( \frac{\frac{28}{4}}{\frac{72}{4}} \) = \( \frac{7}{18} \)
Cooks are needed to prepare for a large party. Each cook can bake either 3 large cakes or 12 small cakes per hour. The kitchen is available for 2 hours and 31 large cakes and 370 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?
| 13 | |
| 11 | |
| 10 | |
| 22 |
If a single cook can bake 3 large cakes per hour and the kitchen is available for 2 hours, a single cook can bake 3 x 2 = 6 large cakes during that time. 31 large cakes are needed for the party so \( \frac{31}{6} \) = 5\(\frac{1}{6}\) cooks are needed to bake the required number of large cakes.
If a single cook can bake 12 small cakes per hour and the kitchen is available for 2 hours, a single cook can bake 12 x 2 = 24 small cakes during that time. 370 small cakes are needed for the party so \( \frac{370}{24} \) = 15\(\frac{5}{12}\) 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 6 + 16 = 22 cooks.
Find the average of the following numbers: 12, 8, 14, 6.
| 10 | |
| 6 | |
| 15 | |
| 12 |
To find the average of these 4 numbers add them together then divide by 4:
\( \frac{12 + 8 + 14 + 6}{4} \) = \( \frac{40}{4} \) = 10
A sports card collection contains football, baseball, and basketball cards. If the ratio of football to baseball cards is 7 to 2 and the ratio of baseball to basketball cards is 7 to 1, what is the ratio of football to basketball cards?
| 49:2 | |
| 9:6 | |
| 9:8 | |
| 3:2 |
The ratio of football cards to baseball cards is 7:2 and the ratio of baseball cards to basketball cards is 7:1. To solve this problem, we need the baseball card side of each ratio to be equal so we need to rewrite the ratios in terms of a common number of baseball cards. (Think of this like finding the common denominator when adding fractions.) The ratio of football to baseball cards can also be written as 49:14 and the ratio of baseball cards to basketball cards as 14:2. So, the ratio of football cards to basketball cards is football:baseball, baseball:basketball or 49:14, 14:2 which reduces to 49:2.
A triathlon course includes a 300m swim, a 20.4km bike ride, and a 10.0km run. What is the total length of the race course?
| 63.4km | |
| 59.6km | |
| 30.7km | |
| 38.1km |
To add these distances, they must share the same unit so first you need to first convert the swim distance from meters (m) to kilometers (km) before adding it to the bike and run distances which are already in km. To convert 300 meters to kilometers, divide the distance by 1000 to get 0.3km then add the remaining distances:
total distance = swim + bike + run
total distance = 0.3km + 20.4km + 10.0km
total distance = 30.7km