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

guard shots made = shots taken x \( \frac{\text{% made}}{100} \) = 10 x \( \frac{70}{100} \) = \( \frac{70 x 10}{100} \) = \( \frac{700}{100} \) = 7 shots

The center makes 50% of his shots so he'll have to take:

shots made = shots taken x \( \frac{\text{% made}}{100} \)
shots taken = \( \frac{\text{shots taken}}{\frac{\text{% made}}{100}} \)

to make as many shots as the guard. Plugging in values for the center gives us:

center shots taken = \( \frac{7}{\frac{50}{100}} \) = 7 x \( \frac{100}{50} \) = \( \frac{7 x 100}{50} \) = \( \frac{700}{50} \) = 14 shots

to make the same number of shots as the guard and thus score the same number of points.

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

2 + (4 + 2) ÷ 3 x 5 - 4²
P: 2 + (6) ÷ 3 x 5 - 4²
E: 2 + 6 ÷ 3 x 5 - 16
MD: 2 + \( \frac{6}{3} \) x 5 - 16
MD: 2 + \( \frac{30}{3} \) - 16
AS: \( \frac{6}{3} \) + \( \frac{30}{3} \) - 16
AS: \( \frac{36}{3} \) - 16
AS: \( \frac{36 - 48}{3} \)
\( \frac{-12}{3} \)
-4

To multiply terms with radicals, multiply the coefficients and radicands separately:

6\( \sqrt{8} \) x 7\( \sqrt{3} \)
(6 x 7)\( \sqrt{8 \times 3} \)
42\( \sqrt{24} \)

Now we need to simplify the radical:

42\( \sqrt{24} \)
42\( \sqrt{6 \times 4} \)
42\( \sqrt{6 \times 2^2} \)
(42)(2)\( \sqrt{6} \)
84\( \sqrt{6} \)

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.