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.

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

2 + (3 + 3) ÷ 3 x 2 - 2²
P: 2 + (6) ÷ 3 x 2 - 2²
E: 2 + 6 ÷ 3 x 2 - 4
MD: 2 + \( \frac{6}{3} \) x 2 - 4
MD: 2 + \( \frac{12}{3} \) - 4
AS: \( \frac{6}{3} \) + \( \frac{12}{3} \) - 4
AS: \( \frac{18}{3} \) - 4
AS: \( \frac{18 - 12}{3} \)
\( \frac{6}{3} \)
2

The area of a circle is given by the formula A = πr² where r is the radius of the circle. The radius of a circle is its diameter divided by two so A = π(\( \frac{d}{2} \))². If the diameter of the logo increases by 60% the radius (and, consequently, the total area) increases by \( \frac{60\text{%}}{2} \) = 30%

The factors of a number are all positive integers that divide evenly into the number. The factors of 40 are 1, 2, 4, 5, 8, 10, 20, 40.

If the tiger has consumed 140 pounds of food in 10 days that's \( \frac{140}{10} \) = 14 pounds of food per day. The tiger needs to consume 196 - 140 = 56 more pounds of food to reach 196 pounds total. At 14 pounds of food per day that's \( \frac{56}{14} \) = 4 more days.