To add these fractions, first find the lowest common multiple of their denominators. The first few multiples of 3 are [3, 6, 9, 12, 15, 18, 21, 24, 27, 30] and the first few multiples of 11 are [11, 22, 33, 44, 55, 66, 77, 88, 99]. The first few multiples they share are [33, 66, 99] making 33 the smallest multiple 3 and 11 share.

Next, convert the fractions so each denominator equals the lowest common multiple:

\( \frac{7 x 11}{3 x 11} \) + \( \frac{4 x 3}{11 x 3} \)

\( \frac{77}{33} \) + \( \frac{12}{33} \)

Now, because the fractions share a common denominator, you can add them:

\( \frac{77 + 12}{33} \) = \( \frac{89}{33} \) = 2\(\frac{23}{33}\)

The factors of a number are all positive integers that divide evenly into the number. The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36.

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

\( \frac{6}{100} \) x 9 = \( \frac{6 \times 9}{100} \) = \( \frac{54}{100} \) = 0.54 errors per hour

So, in an average hour, the machine will produce 9 - 0.54 = 8.46 error free parts.

The machine ran for 24 - 7 = 17 hours yesterday so you would expect that 17 x 8.46 = 143.8 error free parts were produced yesterday.

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).

An integer is any whole number, including zero. An integer can be either positive or negative. Examples include -77, -1, 0, 55, 119.