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.

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

\( \frac{30\sqrt{25}}{6\sqrt{5}} \)
\( \frac{30}{6} \) \( \sqrt{\frac{25}{5}} \)
5 \( \sqrt{5} \)

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).

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

\( \frac{7}{100} \) x 8 = \( \frac{7 \times 8}{100} \) = \( \frac{56}{100} \) = 0.56 errors per hour

So, in an average hour, the machine will produce 8 - 0.56 = 7.4399999999999995 error free parts.

The machine ran for 24 - 7 = 17 hours yesterday so you would expect that 17 x 7.4399999999999995 = 126.5 error free parts were produced yesterday.

To multiply terms with exponents, the base of both exponents must be the same. In this case they are so multiply the coefficients and add the exponents:

9y⁷ x 2y⁷
(9 x 2)y^{(7 + 7)}
18y¹⁴