To add these fractions, first find the lowest common multiple of their denominators. The first few multiples of 8 are [8, 16, 24, 32, 40, 48, 56, 64, 72, 80] and the first few multiples of 16 are [16, 32, 48, 64, 80, 96]. The first few multiples they share are [16, 32, 48, 64, 80] making 16 the smallest multiple 8 and 16 share.

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

\( \frac{5 x 2}{8 x 2} \) + \( \frac{3 x 1}{16 x 1} \)

\( \frac{10}{16} \) + \( \frac{3}{16} \)

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

\( \frac{10 + 3}{16} \) = \( \frac{13}{16} \) = \(\frac{13}{16}\)

The ratio of football cards to baseball cards is 7:2 and the ratio of baseball cards to basketball cards is 7:1. To solve this problem, we need the baseball card side of each ratio to be equal so we need to rewrite the ratios in terms of a common number of baseball cards. (Think of this like finding the common denominator when adding fractions.) The ratio of football to baseball cards can also be written as 49:14 and the ratio of baseball cards to basketball cards as 14:2. So, the ratio of football cards to basketball cards is football:baseball, baseball:basketball or 49:14, 14:2 which reduces to 49:2.

Average speed in miles per hour is the number of miles traveled divided by the number of hours:

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 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:

\( \sqrt{\frac{16}{81}} \)
\( \frac{\sqrt{16}}{\sqrt{81}} \)
\( \frac{\sqrt{4^2}}{\sqrt{9^2}} \)
\(\frac{4}{9}\)