| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.17 |
| Score | 0% | 63% |
A triathlon course includes a 400m swim, a 30.9km bike ride, and a 14.2km run. What is the total length of the race course?
| 45.5km | |
| 32.5km | |
| 55.1km | |
| 52.3km |
To add these distances, they must share the same unit so first you need to first convert the swim distance from meters (m) to kilometers (km) before adding it to the bike and run distances which are already in km. To convert 400 meters to kilometers, divide the distance by 1000 to get 0.4km then add the remaining distances:
total distance = swim + bike + run
total distance = 0.4km + 30.9km + 14.2km
total distance = 45.5km
What is \( \frac{4}{7} \) ÷ \( \frac{4}{8} \)?
| 8 | |
| \(\frac{1}{24}\) | |
| \(\frac{8}{63}\) | |
| 1\(\frac{1}{7}\) |
To divide fractions, invert the second fraction and then multiply:
\( \frac{4}{7} \) ÷ \( \frac{4}{8} \) = \( \frac{4}{7} \) x \( \frac{8}{4} \)
To multiply fractions, multiply the numerators together and then multiply the denominators together:
\( \frac{4}{7} \) x \( \frac{8}{4} \) = \( \frac{4 x 8}{7 x 4} \) = \( \frac{32}{28} \) = 1\(\frac{1}{7}\)
What is \( \sqrt{\frac{16}{36}} \)?
| 1 | |
| \(\frac{7}{9}\) | |
| 1\(\frac{3}{5}\) | |
| \(\frac{2}{3}\) |
To take the square root of a fraction, break the fraction into two separate roots then calculate the square root of the numerator and denominator separately:
\( \sqrt{\frac{16}{36}} \)
\( \frac{\sqrt{16}}{\sqrt{36}} \)
\( \frac{\sqrt{4^2}}{\sqrt{6^2}} \)
\(\frac{2}{3}\)
What is \( \frac{9}{3} \) + \( \frac{4}{9} \)?
| \( \frac{7}{9} \) | |
| \( \frac{6}{12} \) | |
| 1 \( \frac{5}{8} \) | |
| 3\(\frac{4}{9}\) |
To add these fractions, first find the lowest common multiple of their denominators. The first few multiples of 3 are [3, 6, 9, 12, 15, 18, 21, 24, 27, 30] and the first few multiples of 9 are [9, 18, 27, 36, 45, 54, 63, 72, 81, 90]. The first few multiples they share are [9, 18, 27, 36, 45] making 9 the smallest multiple 3 and 9 share.
Next, convert the fractions so each denominator equals the lowest common multiple:
\( \frac{9 x 3}{3 x 3} \) + \( \frac{4 x 1}{9 x 1} \)
\( \frac{27}{9} \) + \( \frac{4}{9} \)
Now, because the fractions share a common denominator, you can add them:
\( \frac{27 + 4}{9} \) = \( \frac{31}{9} \) = 3\(\frac{4}{9}\)
Solve 3 + (3 + 4) ÷ 4 x 2 - 22
| 1\(\frac{4}{5}\) | |
| 2 | |
| 2\(\frac{1}{2}\) | |
| 1\(\frac{1}{2}\) |
Use PEMDAS (Parentheses, Exponents, Multipy/Divide, Add/Subtract):
3 + (3 + 4) ÷ 4 x 2 - 22
P: 3 + (7) ÷ 4 x 2 - 22
E: 3 + 7 ÷ 4 x 2 - 4
MD: 3 + \( \frac{7}{4} \) x 2 - 4
MD: 3 + \( \frac{14}{4} \) - 4
AS: \( \frac{12}{4} \) + \( \frac{14}{4} \) - 4
AS: \( \frac{26}{4} \) - 4
AS: \( \frac{26 - 16}{4} \)
\( \frac{10}{4} \)
2\(\frac{1}{2}\)