| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.86 |
| Score | 0% | 57% |
Simplify \( \frac{28}{44} \).
| \( \frac{5}{16} \) | |
| \( \frac{7}{11} \) | |
| \( \frac{6}{13} \) | |
| \( \frac{1}{2} \) |
To simplify this fraction, first find the greatest common factor between them. The factors of 28 are [1, 2, 4, 7, 14, 28] and the factors of 44 are [1, 2, 4, 11, 22, 44]. They share 3 factors [1, 2, 4] making 4 their greatest common factor (GCF).
Next, divide both numerator and denominator by the GCF:
\( \frac{28}{44} \) = \( \frac{\frac{28}{4}}{\frac{44}{4}} \) = \( \frac{7}{11} \)
How many 2\(\frac{1}{2}\) gallon cans worth of fuel would you need to pour into an empty 10 gallon tank to fill it exactly halfway?
| 77 | |
| 9 | |
| 4 | |
| 2 |
To fill a 10 gallon tank exactly halfway you'll need 5 gallons of fuel. Each fuel can holds 2\(\frac{1}{2}\) gallons so:
cans = \( \frac{5 \text{ gallons}}{2\frac{1}{2} \text{ gallons}} \) = 2
A circular logo is enlarged to fit the lid of a jar. The new diameter is 55% larger than the original. By what percentage has the area of the logo increased?
| 15% | |
| 27\(\frac{1}{2}\)% | |
| 22\(\frac{1}{2}\)% | |
| 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 55% the radius (and, consequently, the total area) increases by \( \frac{55\text{%}}{2} \) = 27\(\frac{1}{2}\)%
On average, the center for a basketball team hits 40% of his shots while a guard on the same team hits 55% of his shots. If the guard takes 15 shots during a game, how many shots will the center have to take to score as many points as the guard assuming each shot is worth the same number of points?
| 17 | |
| 23 | |
| 36 | |
| 20 |
guard shots made = shots taken x \( \frac{\text{% made}}{100} \) = 15 x \( \frac{55}{100} \) = \( \frac{55 x 15}{100} \) = \( \frac{825}{100} \) = 8 shots
The center makes 40% of his shots so he'll have to take:
shots made = shots taken x \( \frac{\text{% made}}{100} \)
shots taken = \( \frac{\text{shots taken}}{\frac{\text{% made}}{100}} \)
to make as many shots as the guard. Plugging in values for the center gives us:
center shots taken = \( \frac{8}{\frac{40}{100}} \) = 8 x \( \frac{100}{40} \) = \( \frac{8 x 100}{40} \) = \( \frac{800}{40} \) = 20 shots
to make the same number of shots as the guard and thus score the same number of points.
What is \( \frac{8}{2} \) - \( \frac{3}{6} \)?
| 3\(\frac{1}{2}\) | |
| 1 \( \frac{5}{6} \) | |
| \( \frac{5}{6} \) | |
| 1 \( \frac{5}{14} \) |
To subtract these fractions, first find the lowest common multiple of their denominators. The first few multiples of 2 are [2, 4, 6, 8, 10, 12, 14, 16, 18, 20] and the first few multiples of 6 are [6, 12, 18, 24, 30, 36, 42, 48, 54, 60]. The first few multiples they share are [6, 12, 18, 24, 30] making 6 the smallest multiple 2 and 6 share.
Next, convert the fractions so each denominator equals the lowest common multiple:
\( \frac{8 x 3}{2 x 3} \) - \( \frac{3 x 1}{6 x 1} \)
\( \frac{24}{6} \) - \( \frac{3}{6} \)
Now, because the fractions share a common denominator, you can subtract them:
\( \frac{24 - 3}{6} \) = \( \frac{21}{6} \) = 3\(\frac{1}{2}\)