| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.44 |
| Score | 0% | 69% |
Which of the following is an improper fraction?
\({a \over 5} \) |
|
\({2 \over 5} \) |
|
\({7 \over 5} \) |
|
\(1 {2 \over 5} \) |
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 \( \frac{3!}{4!} \)
| \( \frac{1}{20} \) | |
| \( \frac{1}{120} \) | |
| \( \frac{1}{6} \) | |
| \( \frac{1}{4} \) |
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:
\( \frac{3!}{4!} \)
\( \frac{3 \times 2 \times 1}{4 \times 3 \times 2 \times 1} \)
\( \frac{1}{4} \)
\( \frac{1}{4} \)
If the ratio of home fans to visiting fans in a crowd is 2:1 and all 50,000 seats in a stadium are filled, how many home fans are in attendance?
| 35,833 | |
| 24,800 | |
| 33,333 | |
| 28,000 |
A ratio of 2:1 means that there are 2 home fans for every one visiting fan. So, of every 3 fans, 2 are home fans and \( \frac{2}{3} \) of every fan in the stadium is a home fan:
50,000 fans x \( \frac{2}{3} \) = \( \frac{100000}{3} \) = 33,333 fans.
What is -y7 - y7?
| -2y-7 | |
| 49 | |
| -2y7 | |
| 14 |
To add or subtract terms with exponents, both the base and the exponent must be the same. In this case they are so subtract the coefficients and retain the base and exponent:
-1y7 - 1y7
(-1 - 1)y7
-2y7
If a car travels 280 miles in 8 hours, what is the average speed?
| 35 mph | |
| 15 mph | |
| 65 mph | |
| 20 mph |
Average speed in miles per hour is the number of miles traveled divided by the number of hours:
speed = \( \frac{\text{distance}}{\text{time}} \)