| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.85 |
| Score | 0% | 57% |
What is \( \frac{1}{9} \) ÷ \( \frac{4}{7} \)?
| \(\frac{1}{9}\) | |
| \(\frac{8}{45}\) | |
| \(\frac{7}{36}\) | |
| \(\frac{2}{9}\) |
To divide fractions, invert the second fraction and then multiply:
\( \frac{1}{9} \) ÷ \( \frac{4}{7} \) = \( \frac{1}{9} \) x \( \frac{7}{4} \)
To multiply fractions, multiply the numerators together and then multiply the denominators together:
\( \frac{1}{9} \) x \( \frac{7}{4} \) = \( \frac{1 x 7}{9 x 4} \) = \( \frac{7}{36} \) = \(\frac{7}{36}\)
Cooks are needed to prepare for a large party. Each cook can bake either 2 large cakes or 12 small cakes per hour. The kitchen is available for 3 hours and 28 large cakes and 140 small cakes need to be baked.
How many cooks are required to bake the required number of cakes during the time the kitchen is available?
| 9 | |
| 8 | |
| 14 | |
| 10 |
If a single cook can bake 2 large cakes per hour and the kitchen is available for 3 hours, a single cook can bake 2 x 3 = 6 large cakes during that time. 28 large cakes are needed for the party so \( \frac{28}{6} \) = 4\(\frac{2}{3}\) cooks are needed to bake the required number of large cakes.
If a single cook can bake 12 small cakes per hour and the kitchen is available for 3 hours, a single cook can bake 12 x 3 = 36 small cakes during that time. 140 small cakes are needed for the party so \( \frac{140}{36} \) = 3\(\frac{8}{9}\) cooks are needed to bake the required number of small cakes.
Because you can't employ a fractional cook, round the number of cooks needed for each type of cake up to the next whole number resulting in 5 + 4 = 9 cooks.
A triathlon course includes a 400m swim, a 30.9km bike ride, and a 11.8km run. What is the total length of the race course?
| 39.8km | |
| 35km | |
| 43.1km | |
| 35.4km |
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 + 11.8km
total distance = 43.1km
If all of a roofing company's 12 workers are required to staff 4 roofing crews, how many workers need to be added during the busy season in order to send 6 complete crews out on jobs?
| 11 | |
| 6 | |
| 14 | |
| 18 |
In order to find how many additional workers are needed to staff the extra crews you first need to calculate how many workers are on a crew. There are 12 workers at the company now and that's enough to staff 4 crews so there are \( \frac{12}{4} \) = 3 workers on a crew. 6 crews are needed for the busy season which, at 3 workers per crew, means that the roofing company will need 6 x 3 = 18 total workers to staff the crews during the busy season. The company already employs 12 workers so they need to add 18 - 12 = 6 new staff for the busy season.
Solve 3 + (3 + 5) ÷ 3 x 3 - 42
| -5 | |
| \(\frac{4}{7}\) | |
| \(\frac{1}{4}\) | |
| \(\frac{2}{9}\) |
Use PEMDAS (Parentheses, Exponents, Multipy/Divide, Add/Subtract):
3 + (3 + 5) ÷ 3 x 3 - 42
P: 3 + (8) ÷ 3 x 3 - 42
E: 3 + 8 ÷ 3 x 3 - 16
MD: 3 + \( \frac{8}{3} \) x 3 - 16
MD: 3 + \( \frac{24}{3} \) - 16
AS: \( \frac{9}{3} \) + \( \frac{24}{3} \) - 16
AS: \( \frac{33}{3} \) - 16
AS: \( \frac{33 - 48}{3} \)
\( \frac{-15}{3} \)
-5