To divide fractions, invert the second fraction and then multiply:

\( \frac{3}{6} \) ÷ \( \frac{1}{7} \) = \( \frac{3}{6} \) x \( \frac{7}{1} \)

To multiply fractions, multiply the numerators together and then multiply the denominators together:

\( \frac{3}{6} \) x \( \frac{7}{1} \) = \( \frac{3 x 7}{6 x 1} \) = \( \frac{21}{6} \) = 3\(\frac{1}{2}\)

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.

To subtract these radicals together their radicands must be the same:

6\( \sqrt{75} \) - 4\( \sqrt{3} \)
6\( \sqrt{25 \times 3} \) - 4\( \sqrt{3} \)
6\( \sqrt{5^2 \times 3} \) - 4\( \sqrt{3} \)
(6)(5)\( \sqrt{3} \) - 4\( \sqrt{3} \)
30\( \sqrt{3} \) - 4\( \sqrt{3} \)

Now that the radicands are identical, you can subtract them:

To fill a 4 gallon tank exactly halfway you'll need 2 gallons of fuel. Each fuel can holds 1 gallons so:

cans = \( \frac{2 \text{ gallons}}{1 \text{ gallons}} \) = 2

The factors of 40 are [1, 2, 4, 5, 8, 10, 20, 40] and the factors of 28 are [1, 2, 4, 7, 14, 28]. They share 3 factors [1, 2, 4] making 4 the greatest factor 40 and 28 have in common.