To simplify a radical, factor out the perfect squares:

\( \sqrt{112} \)
\( \sqrt{16 \times 7} \)
\( \sqrt{4^2 \times 7} \)
4\( \sqrt{7} \)

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

\( \frac{4}{100} \) x 8 = \( \frac{4 \times 8}{100} \) = \( \frac{32}{100} \) = 0.32 errors per hour

So, in an average hour, the machine will produce 8 - 0.32 = 7.68 error free parts.

The machine ran for 24 - 3 = 21 hours yesterday so you would expect that 21 x 7.68 = 161.3 error free parts were produced yesterday.

The greatest common factor (GCF) is the greatest factor that divides two integers.

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

3 + (2 + 4) ÷ 3 x 2 - 3²
P: 3 + (6) ÷ 3 x 2 - 3²
E: 3 + 6 ÷ 3 x 2 - 9
MD: 3 + \( \frac{6}{3} \) x 2 - 9
MD: 3 + \( \frac{12}{3} \) - 9
AS: \( \frac{9}{3} \) + \( \frac{12}{3} \) - 9
AS: \( \frac{21}{3} \) - 9
AS: \( \frac{21 - 27}{3} \)
\( \frac{-6}{3} \)
-2

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.