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 6 = \( \frac{4 \times 6}{100} \) = \( \frac{24}{100} \) = 0.24 errors per hour

So, in an average hour, the machine will produce 6 - 0.24 = 5.76 error free parts.

The machine ran for 24 - 4 = 20 hours yesterday so you would expect that 20 x 5.76 = 115.2 error free parts were produced yesterday.

The factors of 24 are [1, 2, 3, 4, 6, 8, 12, 24] and the factors of 56 are [1, 2, 4, 7, 8, 14, 28, 56]. They share 4 factors [1, 2, 4, 8] making 8 the greatest factor 24 and 56 have in common.

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 convert a negative exponent to a positive exponent, calculate the positive exponent then take the reciprocal.

To take the square root of a fraction, break the fraction into two separate roots then calculate the square root of the numerator and denominator separately:

\( \sqrt{\frac{36}{81}} \)
\( \frac{\sqrt{36}}{\sqrt{81}} \)
\( \frac{\sqrt{6^2}}{\sqrt{9^2}} \)
\(\frac{2}{3}\)