| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.27 |
| Score | 0% | 65% |
Which of the following is an improper fraction?
\(1 {2 \over 5} \) |
|
\({a \over 5} \) |
|
\({7 \over 5} \) |
|
\({2 \over 5} \) |
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.
If a mayor is elected with 77% of the votes cast and 31% of a town's 12,000 voters cast a vote, how many votes did the mayor receive?
| 3,162 | |
| 2,864 | |
| 2,195 | |
| 3,311 |
If 31% of the town's 12,000 voters cast ballots the number of votes cast is:
(\( \frac{31}{100} \)) x 12,000 = \( \frac{372,000}{100} \) = 3,720
The mayor got 77% of the votes cast which is:
(\( \frac{77}{100} \)) x 3,720 = \( \frac{286,440}{100} \) = 2,864 votes.
A triathlon course includes a 400m swim, a 20.3km bike ride, and a 8.100000000000001km run. What is the total length of the race course?
| 50.2km | |
| 28.8km | |
| 53km | |
| 44.2km |
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 400 meters to kilometers, divide the distance by 1000 to get 0.4km then add the remaining distances:
total distance = swim + bike + run
total distance = 0.4km + 20.3km + 8.100000000000001km
total distance = 28.8km
What is \( \frac{4}{5} \) + \( \frac{8}{9} \)?
| 1 \( \frac{2}{45} \) | |
| 1\(\frac{31}{45}\) | |
| 2 \( \frac{1}{45} \) | |
| \( \frac{1}{4} \) |
To add these fractions, first find the lowest common multiple of their denominators. The first few multiples of 5 are [5, 10, 15, 20, 25, 30, 35, 40, 45, 50] and the first few multiples of 9 are [9, 18, 27, 36, 45, 54, 63, 72, 81, 90]. The first few multiples they share are [45, 90] making 45 the smallest multiple 5 and 9 share.
Next, convert the fractions so each denominator equals the lowest common multiple:
\( \frac{4 x 9}{5 x 9} \) + \( \frac{8 x 5}{9 x 5} \)
\( \frac{36}{45} \) + \( \frac{40}{45} \)
Now, because the fractions share a common denominator, you can add them:
\( \frac{36 + 40}{45} \) = \( \frac{76}{45} \) = 1\(\frac{31}{45}\)
Simplify \( \frac{16}{52} \).
| \( \frac{4}{13} \) | |
| \( \frac{7}{16} \) | |
| \( \frac{5}{18} \) | |
| \( \frac{5}{7} \) |
To simplify this fraction, first find the greatest common factor between them. The factors of 16 are [1, 2, 4, 8, 16] 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:
\( \frac{16}{52} \) = \( \frac{\frac{16}{4}}{\frac{52}{4}} \) = \( \frac{4}{13} \)