| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.55 |
| Score | 0% | 71% |
What is \( \sqrt{\frac{9}{64}} \)?
| 1\(\frac{1}{2}\) | |
| \(\frac{3}{8}\) | |
| \(\frac{4}{9}\) | |
| 1\(\frac{2}{7}\) |
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:
\( \sqrt{\frac{9}{64}} \)
\( \frac{\sqrt{9}}{\sqrt{64}} \)
\( \frac{\sqrt{3^2}}{\sqrt{8^2}} \)
\(\frac{3}{8}\)
Frank loaned Frank $400 at an annual interest rate of 3%. If no payments are made, what is the interest owed on this loan at the end of the first year?
| $12 | |
| $54 | |
| $28 | |
| $9 |
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 $400
i = 0.03 x $400
i = $12
In a class of 32 students, 10 are taking German and 12 are taking Spanish. Of the students studying German or Spanish, 4 are taking both courses. How many students are not enrolled in either course?
| 24 | |
| 16 | |
| 14 | |
| 21 |
The number of students taking German or Spanish is 10 + 12 = 22. Of that group of 22, 4 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 22 - 4 = 18 who are taking at least one language. 32 - 18 = 14 students who are not taking either language.
Simplify \( \frac{24}{72} \).
| \( \frac{2}{3} \) | |
| \( \frac{8}{19} \) | |
| \( \frac{1}{3} \) | |
| \( \frac{8}{15} \) |
To simplify this fraction, first find the greatest common factor between them. The factors of 24 are [1, 2, 3, 4, 6, 8, 12, 24] and the factors of 72 are [1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72]. They share 8 factors [1, 2, 3, 4, 6, 8, 12, 24] making 24 their greatest common factor (GCF).
Next, divide both numerator and denominator by the GCF:
\( \frac{24}{72} \) = \( \frac{\frac{24}{24}}{\frac{72}{24}} \) = \( \frac{1}{3} \)
Which of the following is an improper fraction?
\(1 {2 \over 5} \) |
|
\({a \over 5} \) |
|
\({2 \over 5} \) |
|
\({7 \over 5} \) |
A rational number (or fraction) is represented as a ratio between two integers, a and b, and has the form \({a \over b}\) where a is the numerator and b is the denominator. An improper fraction (\({5 \over 3} \)) has a numerator with a greater absolute value than the denominator and can be converted into a mixed number (\(1 {2 \over 3} \)) which has a whole number part and a fractional part.