To simplify this fraction, first find the greatest common factor between them. The factors of 16 are [1, 2, 4, 8, 16] and the factors of 48 are [1, 2, 3, 4, 6, 8, 12, 16, 24, 48]. They share 5 factors [1, 2, 4, 8, 16] making 16 their greatest common factor (GCF).

Next, divide both numerator and denominator by the GCF:

\( \frac{16}{48} \) = \( \frac{\frac{16}{16}}{\frac{48}{16}} \) = \( \frac{1}{3} \)

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, \({a^3 + 6a^2 \over a^2} = {a^3 \over a^2} + {6a^2 \over a^2} = a + 6\).

Use PEMDAS (Parentheses, Exponents, Multipy/Divide, Add/Subtract):

4 + (3 + 4) ÷ 2 x 4 - 2²
P: 4 + (7) ÷ 2 x 4 - 2²
E: 4 + 7 ÷ 2 x 4 - 4
MD: 4 + \( \frac{7}{2} \) x 4 - 4
MD: 4 + \( \frac{28}{2} \) - 4
AS: \( \frac{8}{2} \) + \( \frac{28}{2} \) - 4
AS: \( \frac{36}{2} \) - 4
AS: \( \frac{36 - 8}{2} \)
\( \frac{28}{2} \)
14

The least common multiple (LCM) is the smallest positive integer that is a multiple of two or more integers.

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

\( \frac{1}{8} \) ÷ \( \frac{1}{8} \) = \( \frac{1}{8} \) x \( \frac{8}{1} \)

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

\( \frac{1}{8} \) x \( \frac{8}{1} \) = \( \frac{1 x 8}{8 x 1} \) = \( \frac{8}{8} \) = 1