To subtract these fractions, first find the lowest common multiple of their denominators. The first few multiples of 6 are [6, 12, 18, 24, 30, 36, 42, 48, 54, 60] and the first few multiples of 14 are [14, 28, 42, 56, 70, 84, 98]. The first few multiples they share are [42, 84] making 42 the smallest multiple 6 and 14 share.

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

\( \frac{5 x 7}{6 x 7} \) - \( \frac{3 x 3}{14 x 3} \)

\( \frac{35}{42} \) - \( \frac{9}{42} \)

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

\( \frac{35 - 9}{42} \) = \( \frac{26}{42} \) = \(\frac{13}{21}\)

An integer is any whole number, including zero. An integer can be either positive or negative. Examples include -77, -1, 0, 55, 119.

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:

\( \sqrt{\frac{25}{64}} \)
\( \frac{\sqrt{25}}{\sqrt{64}} \)
\( \frac{\sqrt{5^2}}{\sqrt{8^2}} \)
\(\frac{5}{8}\)

The number of students taking German or Spanish is 12 + 6 = 18. Of that group of 18, 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 18 - 4 = 14 who are taking at least one language. 21 - 14 = 7 students who are not taking either language.

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.