To subtract these fractions, first find the lowest common multiple of their denominators. The first few multiples of 5 are [5, 10, 15, 20, 25, 30, 35, 40, 45, 50] and the first few multiples of 7 are [7, 14, 21, 28, 35, 42, 49, 56, 63, 70]. The first few multiples they share are [35, 70] making 35 the smallest multiple 5 and 7 share.

Next, convert the fractions so each denominator equals the lowest common multiple:

\( \frac{9 x 7}{5 x 7} \) - \( \frac{8 x 5}{7 x 5} \)

\( \frac{63}{35} \) - \( \frac{40}{35} \)

Now, because the fractions share a common denominator, you can subtract them:

\( \frac{63 - 40}{35} \) = \( \frac{23}{35} \) = \(\frac{23}{35}\)

To divide terms with radicals, divide the coefficients and radicands separately:

\( \frac{27\sqrt{24}}{9\sqrt{6}} \)
\( \frac{27}{9} \) \( \sqrt{\frac{24}{6}} \)
3 \( \sqrt{4} \)

April scored 73% on the test meaning she earned 73% of the possible points on the test. There were 60 possible points on the test so she earned 60 x 0.73 = 44 points. Each question is worth 2 points so she got \( \frac{44}{2} \) = 22 questions right.

The number of students taking German or Spanish is 7 + 12 = 19. Of that group of 19, 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 19 - 4 = 15 who are taking at least one language. 27 - 15 = 12 students who are not taking either language.

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.