To add these fractions, first find the lowest common multiple of their denominators. The first few multiples of 3 are [3, 6, 9, 12, 15, 18, 21, 24, 27, 30] and the first few multiples of 5 are [5, 10, 15, 20, 25, 30, 35, 40, 45, 50]. The first few multiples they share are [15, 30, 45, 60, 75] making 15 the smallest multiple 3 and 5 share.

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

\( \frac{6 x 5}{3 x 5} \) + \( \frac{9 x 3}{5 x 3} \)

\( \frac{30}{15} \) + \( \frac{27}{15} \)

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

\( \frac{30 + 27}{15} \) = \( \frac{57}{15} \) = 3\(\frac{4}{5}\)

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

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

The factors of 48 are [1, 2, 3, 4, 6, 8, 12, 16, 24, 48] and the factors of 28 are [1, 2, 4, 7, 14, 28]. They share 3 factors [1, 2, 4] making 4 the greatest factor 48 and 28 have in common.

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