To subtract these fractions, first find the lowest common multiple of their denominators. The first few multiples of 4 are [4, 8, 12, 16, 20, 24, 28, 32, 36, 40] and the first few multiples of 8 are [8, 16, 24, 32, 40, 48, 56, 64, 72, 80]. The first few multiples they share are [8, 16, 24, 32, 40] making 8 the smallest multiple 4 and 8 share.

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

\( \frac{3 x 2}{4 x 2} \) - \( \frac{9 x 1}{8 x 1} \)

\( \frac{6}{8} \) - \( \frac{9}{8} \)

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

\( \frac{6 - 9}{8} \) = \( \frac{-3}{8} \) = -\(\frac{3}{8}\)

To fill a 15 gallon tank exactly halfway you'll need 7\(\frac{1}{2}\) gallons of fuel. Each fuel can holds 1\(\frac{1}{2}\) gallons so:

cans = \( \frac{7\frac{1}{2} \text{ gallons}}{1\frac{1}{2} \text{ gallons}} \) = 5

To add these fractions, first find the lowest common multiple of their denominators. The first few multiples of 2 are [2, 4, 6, 8, 10, 12, 14, 16, 18, 20] and the first few multiples of 4 are [4, 8, 12, 16, 20, 24, 28, 32, 36, 40]. The first few multiples they share are [4, 8, 12, 16, 20] making 4 the smallest multiple 2 and 4 share.

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

\( \frac{7 x 2}{2 x 2} \) + \( \frac{3 x 1}{4 x 1} \)

\( \frac{14}{4} \) + \( \frac{3}{4} \)

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

\( \frac{14 + 3}{4} \) = \( \frac{17}{4} \) = 4\(\frac{1}{4}\)

Christine scored 93% on the test meaning she earned 93% of the possible points on the test. There were 90 possible points on the test so she earned 90 x 0.93 = 84 points. Each question is worth 3 points so she got \( \frac{84}{3} \) = 28 questions right.

To add or subtract terms with exponents, both the base and the exponent must be the same. In this case they are so add the coefficients and retain the base and exponent:

-3z³ + 2z³
(-3 + 2)z³
-z³