| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.16 |
| Score | 0% | 63% |
A sports card collection contains football, baseball, and basketball cards. If the ratio of football to baseball cards is 3 to 2 and the ratio of baseball to basketball cards is 3 to 1, what is the ratio of football to basketball cards?
| 1:1 | |
| 5:6 | |
| 9:2 | |
| 3:6 |
The ratio of football cards to baseball cards is 3:2 and the ratio of baseball cards to basketball cards is 3:1. 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 9:6 and the ratio of baseball cards to basketball cards as 6:2. So, the ratio of football cards to basketball cards is football:baseball, baseball:basketball or 9:6, 6:2 which reduces to 9:2.
Which of the following is an improper fraction?
\(1 {2 \over 5} \) |
|
\({2 \over 5} \) |
|
\({7 \over 5} \) |
|
\({a \over 5} \) |
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 triathlon course includes a 200m swim, a 30.3km bike ride, and a 11.9km run. What is the total length of the race course?
| 43.3km | |
| 39.7km | |
| 42.4km | |
| 49.6km |
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 200 meters to kilometers, divide the distance by 1000 to get 0.2km then add the remaining distances:
total distance = swim + bike + run
total distance = 0.2km + 30.3km + 11.9km
total distance = 42.4km
A machine in a factory has an error rate of 4 parts per 100. The machine normally runs 24 hours a day and produces 6 parts per hour. Yesterday the machine was shut down for 3 hours for maintenance.
How many error-free parts did the machine produce yesterday?
| 194 | |
| 190 | |
| 121 | |
| 102.3 |
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 6 = \( \frac{4 \times 6}{100} \) = \( \frac{24}{100} \) = 0.24 errors per hour
So, in an average hour, the machine will produce 6 - 0.24 = 5.76 error free parts.
The machine ran for 24 - 3 = 21 hours yesterday so you would expect that 21 x 5.76 = 121 error free parts were produced yesterday.
What is the least common multiple of 6 and 14?
| 42 | |
| 3 | |
| 25 | |
| 20 |
The first few multiples of 6 are [6, 12, 18, 24, 30, 36, 42, 48, 54, 60] and the first few multiples of 14 are [14, 28, 42, 56, 70, 84, 98]. The first few multiples they share are [42, 84] making 42 the smallest multiple 6 and 14 have in common.