| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.92 |
| Score | 0% | 58% |
Solve 4 + (5 + 4) ÷ 2 x 5 - 42
| 10\(\frac{1}{2}\) | |
| \(\frac{5}{6}\) | |
| \(\frac{4}{5}\) | |
| \(\frac{1}{4}\) |
Use PEMDAS (Parentheses, Exponents, Multipy/Divide, Add/Subtract):
4 + (5 + 4) ÷ 2 x 5 - 42
P: 4 + (9) ÷ 2 x 5 - 42
E: 4 + 9 ÷ 2 x 5 - 16
MD: 4 + \( \frac{9}{2} \) x 5 - 16
MD: 4 + \( \frac{45}{2} \) - 16
AS: \( \frac{8}{2} \) + \( \frac{45}{2} \) - 16
AS: \( \frac{53}{2} \) - 16
AS: \( \frac{53 - 32}{2} \)
\( \frac{21}{2} \)
10\(\frac{1}{2}\)
Find the average of the following numbers: 15, 11, 15, 11.
| 16 | |
| 10 | |
| 13 | |
| 14 |
To find the average of these 4 numbers add them together then divide by 4:
\( \frac{15 + 11 + 15 + 11}{4} \) = \( \frac{52}{4} \) = 13
What is \( \frac{7}{6} \) + \( \frac{7}{14} \)?
| 2 \( \frac{9}{42} \) | |
| 1\(\frac{2}{3}\) | |
| 1 \( \frac{8}{42} \) | |
| 2 \( \frac{7}{42} \) |
To add these fractions, first find the lowest common multiple of their denominators. The first few multiples of 6 are [6, 12, 18, 24, 30, 36, 42, 48, 54, 60] and the first few multiples of 14 are [14, 28, 42, 56, 70, 84, 98]. The first few multiples they share are [42, 84] making 42 the smallest multiple 6 and 14 share.
Next, convert the fractions so each denominator equals the lowest common multiple:
\( \frac{7 x 7}{6 x 7} \) + \( \frac{7 x 3}{14 x 3} \)
\( \frac{49}{42} \) + \( \frac{21}{42} \)
Now, because the fractions share a common denominator, you can add them:
\( \frac{49 + 21}{42} \) = \( \frac{70}{42} \) = 1\(\frac{2}{3}\)
On average, the center for a basketball team hits 35% of his shots while a guard on the same team hits 45% of his shots. If the guard takes 30 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?
| 25 | |
| 37 | |
| 35 | |
| 42 |
guard shots made = shots taken x \( \frac{\text{% made}}{100} \) = 30 x \( \frac{45}{100} \) = \( \frac{45 x 30}{100} \) = \( \frac{1350}{100} \) = 13 shots
The center makes 35% 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 = \( \frac{13}{\frac{35}{100}} \) = 13 x \( \frac{100}{35} \) = \( \frac{13 x 100}{35} \) = \( \frac{1300}{35} \) = 37 shots
to make the same number of shots as the guard and thus score the same number of points.
A bread recipe calls for 3\(\frac{3}{8}\) cups of flour. If you only have 1 cup, how much more flour is needed?
| 2\(\frac{5}{8}\) cups | |
| 2\(\frac{3}{8}\) cups | |
| 2\(\frac{1}{4}\) cups | |
| 1\(\frac{1}{2}\) cups |
The amount of flour you need is (3\(\frac{3}{8}\) - 1) cups. Rewrite the quantities so they share a common denominator and subtract:
(\( \frac{27}{8} \) - \( \frac{8}{8} \)) cups
\( \frac{19}{8} \) cups
2\(\frac{3}{8}\) cups