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.

By buying two shirts, Frank will save $12 x \( \frac{15}{100} \) = \( \frac{$12 x 15}{100} \) = \( \frac{$180}{100} \) = $1.80 on the second shirt.

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

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:

\( \frac{6 x 3}{2 x 3} \) + \( \frac{5 x 1}{6 x 1} \)

\( \frac{18}{6} \) + \( \frac{5}{6} \)

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

\( \frac{18 + 5}{6} \) = \( \frac{23}{6} \) = 3\(\frac{5}{6}\)

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