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.

The distributive property for multiplication helps in solving expressions like a(b + c). It specifies that the result of multiplying one number by the sum or difference of two numbers can be obtained by multiplying each number individually and then totaling the results: a(b + c) = ab + ac. For example, 4(10-5) = (4 x 10) - (4 x 5) = 40 - 20 = 20.

Jennifer scored 83% on the test meaning she earned 83% of the possible points on the test. There were 180 possible points on the test so she earned 180 x 0.83 = 150 points. Each question is worth 3 points so she got \( \frac{150}{3} \) = 50 questions right.

The amount of flour you need is (1\(\frac{7}{8}\) - \(\frac{5}{8}\)) cups. Rewrite the quantities so they share a common denominator and subtract:

(\( \frac{15}{8} \) - \( \frac{5}{8} \)) cups
\( \frac{10}{8} \) cups
1\(\frac{1}{4}\) cups

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.