The factors of 52 are [1, 2, 4, 13, 26, 52] and the factors of 24 are [1, 2, 3, 4, 6, 8, 12, 24]. They share 3 factors [1, 2, 4] making 4 the greatest factor 52 and 24 have in common.

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.

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.

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.

To add these radicals together their radicands must be the same:

7\( \sqrt{32} \) + 5\( \sqrt{2} \)
7\( \sqrt{16 \times 2} \) + 5\( \sqrt{2} \)
7\( \sqrt{4^2 \times 2} \) + 5\( \sqrt{2} \)
(7)(4)\( \sqrt{2} \) + 5\( \sqrt{2} \)
28\( \sqrt{2} \) + 5\( \sqrt{2} \)

Now that the radicands are identical, you can add them together: