| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.20 |
| Score | 0% | 64% |
In a class of 22 students, 6 are taking German and 9 are taking Spanish. Of the students studying German or Spanish, 5 are taking both courses. How many students are not enrolled in either course?
| 18 | |
| 12 | |
| 14 | |
| 17 |
The number of students taking German or Spanish is 6 + 9 = 15. Of that group of 15, 5 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 15 - 5 = 10 who are taking at least one language. 22 - 10 = 12 students who are not taking either language.
What is \( \frac{7}{2} \) + \( \frac{7}{10} \)?
| 4\(\frac{1}{5}\) | |
| \( \frac{7}{10} \) | |
| \( \frac{7}{13} \) | |
| \( \frac{5}{10} \) |
To add these fractions, first find the lowest common multiple of their denominators. The first few multiples of 2 are [2, 4, 6, 8, 10, 12, 14, 16, 18, 20] and the first few multiples of 10 are [10, 20, 30, 40, 50, 60, 70, 80, 90]. The first few multiples they share are [10, 20, 30, 40, 50] making 10 the smallest multiple 2 and 10 share.
Next, convert the fractions so each denominator equals the lowest common multiple:
\( \frac{7 x 5}{2 x 5} \) + \( \frac{7 x 1}{10 x 1} \)
\( \frac{35}{10} \) + \( \frac{7}{10} \)
Now, because the fractions share a common denominator, you can add them:
\( \frac{35 + 7}{10} \) = \( \frac{42}{10} \) = 4\(\frac{1}{5}\)
This property states taht the order of addition or multiplication does not mater. For example, 2 + 5 and 5 + 2 are equivalent.
PEDMAS |
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associative |
|
commutative |
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distributive |
The commutative property states that, when adding or multiplying numbers, the order in which they're added or multiplied does not matter. For example, 3 + 4 and 4 + 3 give the same result, as do 3 x 4 and 4 x 3.
The __________ is the greatest factor that divides two integers.
greatest common multiple |
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absolute value |
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least common multiple |
|
greatest common factor |
The greatest common factor (GCF) is the greatest factor that divides two integers.
Bob loaned Diane $900 at an annual interest rate of 4%. If no payments are made, what is the total amount owed at the end of the first year?
| $936 | |
| $945 | |
| $972 | |
| $981 |
The yearly interest charged on this loan is the annual interest rate multiplied by the amount borrowed:
interest = annual interest rate x loan amount
i = (\( \frac{6}{100} \)) x $900
i = 0.04 x $900
No payments were made so the total amount due is the original amount + the accumulated interest:
total = $900 + $36