| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.17 |
| Score | 0% | 63% |
4! = ?
5 x 4 x 3 x 2 x 1 |
|
4 x 3 |
|
3 x 2 x 1 |
|
4 x 3 x 2 x 1 |
A factorial has the form n! and is the product of the integer (n) and all the positive integers below it. For example, 5! = 5 x 4 x 3 x 2 x 1 = 120.
A bread recipe calls for 3 cups of flour. If you only have 1\(\frac{1}{8}\) cups, how much more flour is needed?
| 1\(\frac{7}{8}\) cups | |
| 2\(\frac{1}{8}\) cups | |
| 1\(\frac{5}{8}\) cups | |
| 1\(\frac{1}{4}\) cups |
The amount of flour you need is (3 - 1\(\frac{1}{8}\)) cups. Rewrite the quantities so they share a common denominator and subtract:
(\( \frac{24}{8} \) - \( \frac{9}{8} \)) cups
\( \frac{15}{8} \) cups
1\(\frac{7}{8}\) cups
How many 2\(\frac{1}{2}\) gallon cans worth of fuel would you need to pour into an empty 25 gallon tank to fill it exactly halfway?
| 9 | |
| 10 | |
| 5 | |
| 7 |
To fill a 25 gallon tank exactly halfway you'll need 12\(\frac{1}{2}\) gallons of fuel. Each fuel can holds 2\(\frac{1}{2}\) gallons so:
cans = \( \frac{12\frac{1}{2} \text{ gallons}}{2\frac{1}{2} \text{ gallons}} \) = 5
The total water usage for a city is 35,000 gallons each day. Of that total, 22% is for personal use and 52% is for industrial use. How many more gallons of water each day is consumed for industrial use over personal use?
| 2,500 | |
| 4,750 | |
| 3,400 | |
| 10,500 |
52% of the water consumption is industrial use and 22% is personal use so (52% - 22%) = 30% more water is used for industrial purposes. 35,000 gallons are consumed daily so industry consumes \( \frac{30}{100} \) x 35,000 gallons = 10,500 gallons.
What is \( \frac{4}{4} \) + \( \frac{4}{8} \)?
| \( \frac{2}{10} \) | |
| 2 \( \frac{7}{11} \) | |
| 1\(\frac{1}{2}\) | |
| \( \frac{1}{8} \) |
To add these fractions, first find the lowest common multiple of their denominators. The first few multiples of 4 are [4, 8, 12, 16, 20, 24, 28, 32, 36, 40] and the first few multiples of 8 are [8, 16, 24, 32, 40, 48, 56, 64, 72, 80]. The first few multiples they share are [8, 16, 24, 32, 40] making 8 the smallest multiple 4 and 8 share.
Next, convert the fractions so each denominator equals the lowest common multiple:
\( \frac{4 x 2}{4 x 2} \) + \( \frac{4 x 1}{8 x 1} \)
\( \frac{8}{8} \) + \( \frac{4}{8} \)
Now, because the fractions share a common denominator, you can add them:
\( \frac{8 + 4}{8} \) = \( \frac{12}{8} \) = 1\(\frac{1}{2}\)