The factors of 68 are [1, 2, 4, 17, 34, 68] and the factors of 44 are [1, 2, 4, 11, 22, 44]. They share 3 factors [1, 2, 4] making 4 the greatest factor 68 and 44 have in common.

The greatest common factor (GCF) is the greatest factor that divides two integers.

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

4 + (4 + 4) ÷ 3 x 5 - 4²
P: 4 + (8) ÷ 3 x 5 - 4²
E: 4 + 8 ÷ 3 x 5 - 16
MD: 4 + \( \frac{8}{3} \) x 5 - 16
MD: 4 + \( \frac{40}{3} \) - 16
AS: \( \frac{12}{3} \) + \( \frac{40}{3} \) - 16
AS: \( \frac{52}{3} \) - 16
AS: \( \frac{52 - 48}{3} \)
\( \frac{4}{3} \)
1\(\frac{1}{3}\)

To add these fractions, first find the lowest common multiple of their denominators. The first few multiples of 2 are [2, 4, 6, 8, 10, 12, 14, 16, 18, 20] and the first few multiples of 6 are [6, 12, 18, 24, 30, 36, 42, 48, 54, 60]. The first few multiples they share are [6, 12, 18, 24, 30] making 6 the smallest multiple 2 and 6 share.

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

\( \frac{4 x 3}{2 x 3} \) + \( \frac{8 x 1}{6 x 1} \)

\( \frac{12}{6} \) + \( \frac{8}{6} \)

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

\( \frac{12 + 8}{6} \) = \( \frac{20}{6} \) = 3\(\frac{1}{3}\)

The ratio of football cards to baseball cards is 5:2 and the ratio of baseball cards to basketball cards is 5:1. 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 25:10 and the ratio of baseball cards to basketball cards as 10:2. So, the ratio of football cards to basketball cards is football:baseball, baseball:basketball or 25:10, 10:2 which reduces to 25:2.