| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.18 |
| Score | 0% | 64% |
A factor is a positive __________ that divides evenly into a given number.
improper fraction |
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fraction |
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integer |
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mixed number |
A factor is a positive integer that divides evenly into a given number. For example, the factors of 8 are 1, 2, 4, and 8.
Diane scored 86% on her final exam. If each question was worth 2 points and there were 100 possible points on the exam, how many questions did Diane answer correctly?
| 43 | |
| 51 | |
| 47 | |
| 52 |
Diane scored 86% on the test meaning she earned 86% of the possible points on the test. There were 100 possible points on the test so she earned 100 x 0.86 = 86 points. Each question is worth 2 points so she got \( \frac{86}{2} \) = 43 questions right.
In a class of 29 students, 14 are taking German and 7 are taking Spanish. Of the students studying German or Spanish, 7 are taking both courses. How many students are not enrolled in either course?
| 25 | |
| 17 | |
| 15 | |
| 14 |
The number of students taking German or Spanish is 14 + 7 = 21. Of that group of 21, 7 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 21 - 7 = 14 who are taking at least one language. 29 - 14 = 15 students who are not taking either language.
A tiger in a zoo has consumed 84 pounds of food in 6 days. If the tiger continues to eat at the same rate, in how many more days will its total food consumtion be 154 pounds?
| 10 | |
| 5 | |
| 9 | |
| 7 |
If the tiger has consumed 84 pounds of food in 6 days that's \( \frac{84}{6} \) = 14 pounds of food per day. The tiger needs to consume 154 - 84 = 70 more pounds of food to reach 154 pounds total. At 14 pounds of food per day that's \( \frac{70}{14} \) = 5 more days.
What is \( \frac{9}{3} \) - \( \frac{8}{11} \)?
| 2\(\frac{3}{11}\) | |
| 1 \( \frac{7}{13} \) | |
| \( \frac{4}{33} \) | |
| \( \frac{3}{33} \) |
To subtract 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:
\( \frac{9 x 11}{3 x 11} \) - \( \frac{8 x 3}{11 x 3} \)
\( \frac{99}{33} \) - \( \frac{24}{33} \)
Now, because the fractions share a common denominator, you can subtract them:
\( \frac{99 - 24}{33} \) = \( \frac{75}{33} \) = 2\(\frac{3}{11}\)