To simplify this fraction, first find the greatest common factor between them. The factors of 36 are [1, 2, 3, 4, 6, 9, 12, 18, 36] and the factors of 60 are [1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60]. They share 6 factors [1, 2, 3, 4, 6, 12] making 12 their greatest common factor (GCF).

Next, divide both numerator and denominator by the GCF:

\( \frac{36}{60} \) = \( \frac{\frac{36}{12}}{\frac{60}{12}} \) = \( \frac{3}{5} \)

The factors of a number are all positive integers that divide evenly into the number. The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36.

To subtract 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:

\( \frac{5 x 5}{2 x 5} \) - \( \frac{5 x 1}{10 x 1} \)

\( \frac{25}{10} \) - \( \frac{5}{10} \)

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

\( \frac{25 - 5}{10} \) = \( \frac{20}{10} \) = 2

The distributive property for division helps in solving expressions like \({b + c \over a}\). It specifies that the result of dividing a fraction with multiple terms in the numerator and one term in the denominator can be obtained by dividing each term individually and then totaling the results: \({b + c \over a} = {b \over a} + {c \over a}\). For example, \({a^3 + 6a^2 \over a^2} = {a^3 \over a^2} + {6a^2 \over a^2} = a + 6\).

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:

\( \sqrt{\frac{36}{9}} \)
\( \frac{\sqrt{36}}{\sqrt{9}} \)
\( \frac{\sqrt{6^2}}{\sqrt{3^2}} \)
\( \frac{6}{3} \)
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