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

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, \({a^3 + 6a^2 \over a^2} = {a^3 \over a^2} + {6a^2 \over a^2} = a + 6\).

To divide fractions, invert the second fraction and then multiply:

\( \frac{3}{7} \) ÷ \( \frac{3}{8} \) = \( \frac{3}{7} \) x \( \frac{8}{3} \)

To multiply fractions, multiply the numerators together and then multiply the denominators together:

\( \frac{3}{7} \) x \( \frac{8}{3} \) = \( \frac{3 x 8}{7 x 3} \) = \( \frac{24}{21} \) = 1\(\frac{1}{7}\)

A ratio of 5:1 means that there are 5 home fans for every one visiting fan. So, of every 6 fans, 5 are home fans and \( \frac{5}{6} \) of every fan in the stadium is a home fan:

50,000 fans x \( \frac{5}{6} \) = \( \frac{250000}{6} \) = 41,667 fans.

If the tiger has consumed 70 pounds of food in 5 days that's \( \frac{70}{5} \) = 14 pounds of food per day. The tiger needs to consume 140 - 70 = 70 more pounds of food to reach 140 pounds total. At 14 pounds of food per day that's \( \frac{70}{14} \) = 5 more days.