To multiply fractions, multiply the numerators together and then multiply the denominators together:

\( \frac{1}{5} \) x \( \frac{2}{8} \) = \( \frac{1 x 2}{5 x 8} \) = \( \frac{2}{40} \) = \(\frac{1}{20}\)

To add these radicals together their radicands must be the same:

2\( \sqrt{12} \) + 6\( \sqrt{3} \)
2\( \sqrt{4 \times 3} \) + 6\( \sqrt{3} \)
2\( \sqrt{2^2 \times 3} \) + 6\( \sqrt{3} \)
(2)(2)\( \sqrt{3} \) + 6\( \sqrt{3} \)
4\( \sqrt{3} \) + 6\( \sqrt{3} \)

Now that the radicands are identical, you can add them together:

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

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 10 = \( \frac{7 \times 10}{100} \) = \( \frac{70}{100} \) = 0.7 errors per hour

So, in an average hour, the machine will produce 10 - 0.7 = 9.3 error free parts.

The machine ran for 24 - 2 = 22 hours yesterday so you would expect that 22 x 9.3 = 204.6 error free parts were produced yesterday.

The distributive property for multiplication helps in solving expressions like a(b + c). It specifies that the result of multiplying one number by the sum or difference of two numbers can be obtained by multiplying each number individually and then totaling the results: a(b + c) = ab + ac. For example, 4(10-5) = (4 x 10) - (4 x 5) = 40 - 20 = 20.