| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.42 |
| Score | 0% | 68% |
What is \( \frac{2}{3} \) + \( \frac{6}{11} \)?
| \( \frac{1}{9} \) | |
| 1\(\frac{2}{9}\) | |
| 1 \( \frac{6}{10} \) | |
| 1 \( \frac{8}{33} \) |
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 11 are [11, 22, 33, 44, 55, 66, 77, 88, 99]. The first few multiples they share are [33, 66, 99] making 33 the smallest multiple 3 and 11 share.
Next, convert the fractions so each denominator equals the lowest common multiple:
\( \frac{2 x 11}{3 x 11} \) + \( \frac{6 x 3}{11 x 3} \)
\( \frac{22}{33} \) + \( \frac{18}{33} \)
Now, because the fractions share a common denominator, you can add them:
\( \frac{22 + 18}{33} \) = \( \frac{40}{33} \) = 1\(\frac{2}{9}\)
In a class of 29 students, 14 are taking German and 10 are taking Spanish. Of the students studying German or Spanish, 3 are taking both courses. How many students are not enrolled in either course?
| 26 | |
| 12 | |
| 20 | |
| 8 |
The number of students taking German or Spanish is 14 + 10 = 24. Of that group of 24, 3 are taking both languages so they've been counted twice (once in the German group and once in the Spanish group). Subtracting them out leaves 24 - 3 = 21 who are taking at least one language. 29 - 21 = 8 students who are not taking either language.
A tiger in a zoo has consumed 112 pounds of food in 8 days. If the tiger continues to eat at the same rate, in how many more days will its total food consumtion be 196 pounds?
| 2 | |
| 6 | |
| 11 | |
| 10 |
If the tiger has consumed 112 pounds of food in 8 days that's \( \frac{112}{8} \) = 14 pounds of food per day. The tiger needs to consume 196 - 112 = 84 more pounds of food to reach 196 pounds total. At 14 pounds of food per day that's \( \frac{84}{14} \) = 6 more days.
Simplify \( \frac{36}{44} \).
| \( \frac{7}{17} \) | |
| \( \frac{4}{15} \) | |
| \( \frac{9}{11} \) | |
| \( \frac{7}{16} \) |
To simplify this fraction, first find the greatest common factor between them. The factors of 36 are [1, 2, 3, 4, 6, 9, 12, 18, 36] 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:
\( \frac{36}{44} \) = \( \frac{\frac{36}{4}}{\frac{44}{4}} \) = \( \frac{9}{11} \)
If a car travels 70 miles in 2 hours, what is the average speed?
| 35 mph | |
| 60 mph | |
| 65 mph | |
| 70 mph |
Average speed in miles per hour is the number of miles traveled divided by the number of hours:
speed = \( \frac{\text{distance}}{\text{time}} \)