To add these fractions, first find the lowest common multiple of their denominators. The first few multiples of 5 are [5, 10, 15, 20, 25, 30, 35, 40, 45, 50] and the first few multiples of 9 are [9, 18, 27, 36, 45, 54, 63, 72, 81, 90]. The first few multiples they share are [45, 90] making 45 the smallest multiple 5 and 9 share.

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

\( \frac{9 x 9}{5 x 9} \) + \( \frac{7 x 5}{9 x 5} \)

\( \frac{81}{45} \) + \( \frac{35}{45} \)

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

\( \frac{81 + 35}{45} \) = \( \frac{116}{45} \) = 2\(\frac{26}{45}\)

To divide terms with exponents, the base of both exponents must be the same. In this case they are so divide the coefficients and subtract the exponents:

\( \frac{5b^6}{3b^3} \)
\( \frac{5}{3} \) b^{(6 - 3)}
1\(\frac{2}{3}\)b³

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

\( \frac{3}{6} \) x \( \frac{3}{6} \) = \( \frac{3 x 3}{6 x 6} \) = \( \frac{9}{36} \) = \(\frac{1}{4}\)

1

The absolute value is the positive magnitude of a particular number or variable and is indicated by two vertical lines: \(\left|-5\right| = 5\). In the case of a variable absolute value (\(\left|a\right| = 5\)) the value of a can be either positive or negative (a = -5 or a = 5).