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.

The factors of 36 are [1, 2, 3, 4, 6, 9, 12, 18, 36] and the factors of 72 are [1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72]. They share 9 factors [1, 2, 3, 4, 6, 9, 12, 18, 36] making 36 the greatest factor 36 and 72 have in common.

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

\( \frac{2}{100} \) x 7 = \( \frac{2 \times 7}{100} \) = \( \frac{14}{100} \) = 0.14 errors per hour

So, in an average hour, the machine will produce 7 - 0.14 = 6.86 error free parts.

The machine ran for 24 - 3 = 21 hours yesterday so you would expect that 21 x 6.86 = 144.1 error free parts were produced yesterday.

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

2 + (3 + 5) ÷ 2 x 5 - 4²
P: 2 + (8) ÷ 2 x 5 - 4²
E: 2 + 8 ÷ 2 x 5 - 16
MD: 2 + \( \frac{8}{2} \) x 5 - 16
MD: 2 + \( \frac{40}{2} \) - 16
AS: \( \frac{4}{2} \) + \( \frac{40}{2} \) - 16
AS: \( \frac{44}{2} \) - 16
AS: \( \frac{44 - 32}{2} \)
\( \frac{12}{2} \)
6

A number with an exponent (b^e) consists of a base (b) raised to a power (e). The exponent indicates the number of times that the base is multiplied by itself. A base with an exponent of 1 equals the base (b¹ = b) and a base with an exponent of 0 equals 1 ( (b⁰ = 1).