To add these fractions, first find the lowest common multiple of their denominators. The first few multiples of 6 are [6, 12, 18, 24, 30, 36, 42, 48, 54, 60] and the first few multiples of 14 are [14, 28, 42, 56, 70, 84, 98]. The first few multiples they share are [42, 84] making 42 the smallest multiple 6 and 14 share.

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

\( \frac{8 x 7}{6 x 7} \) + \( \frac{6 x 3}{14 x 3} \)

\( \frac{56}{42} \) + \( \frac{18}{42} \)

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

\( \frac{56 + 18}{42} \) = \( \frac{74}{42} \) = 1\(\frac{16}{21}\)

If a single cook can bake 4 large cakes per hour and the kitchen is available for 3 hours, a single cook can bake 4 x 3 = 12 large cakes during that time. 35 large cakes are needed for the party so \( \frac{35}{12} \) = 2\(\frac{11}{12}\) cooks are needed to bake the required number of large cakes.

If a single cook can bake 11 small cakes per hour and the kitchen is available for 3 hours, a single cook can bake 11 x 3 = 33 small cakes during that time. 300 small cakes are needed for the party so \( \frac{300}{33} \) = 9\(\frac{1}{11}\) cooks are needed to bake the required number of small cakes.

Because you can't employ a fractional cook, round the number of cooks needed for each type of cake up to the next whole number resulting in 3 + 10 = 13 cooks.

To simplify a radical, factor out the perfect squares:

\( \sqrt{63} \)
\( \sqrt{9 \times 7} \)
\( \sqrt{3^2 \times 7} \)
3\( \sqrt{7} \)

The commutative property states that, when adding or multiplying numbers, the order in which they're added or multiplied does not matter. For example, 3 + 4 and 4 + 3 give the same result, as do 3 x 4 and 4 x 3.

By buying two shirts, Bob will save $13 x \( \frac{50}{100} \) = \( \frac{$13 x 50}{100} \) = \( \frac{$650}{100} \) = $6.50 on the second shirt.

So, his total cost will be
$13.00 + ($13.00 - $6.50)
$13.00 + $6.50
$19.50