| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.24 |
| Score | 0% | 65% |
What is \( \frac{4}{8} \) ÷ \( \frac{2}{6} \)?
| \(\frac{1}{16}\) | |
| 1\(\frac{1}{2}\) | |
| \(\frac{2}{35}\) | |
| \(\frac{8}{35}\) |
To divide fractions, invert the second fraction and then multiply:
\( \frac{4}{8} \) ÷ \( \frac{2}{6} \) = \( \frac{4}{8} \) x \( \frac{6}{2} \)
To multiply fractions, multiply the numerators together and then multiply the denominators together:
\( \frac{4}{8} \) x \( \frac{6}{2} \) = \( \frac{4 x 6}{8 x 2} \) = \( \frac{24}{16} \) = 1\(\frac{1}{2}\)
How many hours does it take a car to travel 210 miles at an average speed of 70 miles per hour?
| 2 hours | |
| 9 hours | |
| 3 hours | |
| 8 hours |
Average speed in miles per hour is the number of miles traveled divided by the number of hours:
speed = \( \frac{\text{distance}}{\text{time}} \)Solving for time:
time = \( \frac{\text{distance}}{\text{speed}} \)
time = \( \frac{210mi}{70mph} \)
3 hours
The total water usage for a city is 30,000 gallons each day. Of that total, 34% is for personal use and 44% is for industrial use. How many more gallons of water each day is consumed for industrial use over personal use?
| 3,000 | |
| 9,600 | |
| 2,700 | |
| 2,400 |
44% of the water consumption is industrial use and 34% is personal use so (44% - 34%) = 10% more water is used for industrial purposes. 30,000 gallons are consumed daily so industry consumes \( \frac{10}{100} \) x 30,000 gallons = 3,000 gallons.
What is \( \frac{9}{4} \) - \( \frac{8}{10} \)?
| 1 \( \frac{5}{20} \) | |
| \( \frac{3}{12} \) | |
| 1\(\frac{9}{20}\) | |
| 2 \( \frac{1}{20} \) |
To subtract 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 10 are [10, 20, 30, 40, 50, 60, 70, 80, 90]. The first few multiples they share are [20, 40, 60, 80] making 20 the smallest multiple 4 and 10 share.
Next, convert the fractions so each denominator equals the lowest common multiple:
\( \frac{9 x 5}{4 x 5} \) - \( \frac{8 x 2}{10 x 2} \)
\( \frac{45}{20} \) - \( \frac{16}{20} \)
Now, because the fractions share a common denominator, you can subtract them:
\( \frac{45 - 16}{20} \) = \( \frac{29}{20} \) = 1\(\frac{9}{20}\)
A circular logo is enlarged to fit the lid of a jar. The new diameter is 65% larger than the original. By what percentage has the area of the logo increased?
| 20% | |
| 32\(\frac{1}{2}\)% | |
| 27\(\frac{1}{2}\)% | |
| 17\(\frac{1}{2}\)% |
The area of a circle is given by the formula A = πr2 where r is the radius of the circle. The radius of a circle is its diameter divided by two so A = π(\( \frac{d}{2} \))2. If the diameter of the logo increases by 65% the radius (and, consequently, the total area) increases by \( \frac{65\text{%}}{2} \) = 32\(\frac{1}{2}\)%