By buying two shirts, Alex will save $32 x \( \frac{45}{100} \) = \( \frac{$32 x 45}{100} \) = \( \frac{$1440}{100} \) = $14.40 on the second shirt.

So, his total cost will be
$32.00 + ($32.00 - $14.40)
$32.00 + $17.60
$49.60

The distributive property for division helps in solving expressions like \({b + c \over a}\). It specifies that the result of dividing a fraction with multiple terms in the numerator and one term in the denominator can be obtained by dividing each term individually and then totaling the results: \({b + c \over a} = {b \over a} + {c \over a}\). For example, \({a^3 + 6a^2 \over a^2} = {a^3 \over a^2} + {6a^2 \over a^2} = a + 6\).

The ratio of football cards to baseball cards is 9:2 and the ratio of baseball cards to basketball cards is 9:1. 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 81:18 and the ratio of baseball cards to basketball cards as 18:2. So, the ratio of football cards to basketball cards is football:baseball, baseball:basketball or 81:18, 18:2 which reduces to 81:2.

A factor is a positive integer that divides evenly into a given number. For example, the factors of 8 are 1, 2, 4, and 8.

The hourly error rate for this machine is the error rate in parts per 100 multiplied by the number of parts produced per hour:

\( \frac{2}{100} \) x 7 = \( \frac{2 \times 7}{100} \) = \( \frac{14}{100} \) = 0.14 errors per hour

So, in an average hour, the machine will produce 7 - 0.14 = 6.86 error free parts.

The machine ran for 24 - 6 = 18 hours yesterday so you would expect that 18 x 6.86 = 123.5 error free parts were produced yesterday.