Jennifer scored 83% on the test meaning she earned 83% of the possible points on the test. There were 120 possible points on the test so she earned 120 x 0.83 = 99 points. Each question is worth 3 points so she got \( \frac{99}{3} \) = 33 questions right.

To divide fractions, invert the second fraction and then multiply:

\( \frac{4}{9} \) ÷ \( \frac{4}{5} \) = \( \frac{4}{9} \) x \( \frac{5}{4} \)

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

\( \frac{4}{9} \) x \( \frac{5}{4} \) = \( \frac{4 x 5}{9 x 4} \) = \( \frac{20}{36} \) = \(\frac{5}{9}\)

1

To add 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 10 are [10, 20, 30, 40, 50, 60, 70, 80, 90]. The first few multiples they share are [20, 40, 60, 80] making 20 the smallest multiple 4 and 10 share.

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

\( \frac{5 x 5}{4 x 5} \) + \( \frac{5 x 2}{10 x 2} \)

\( \frac{25}{20} \) + \( \frac{10}{20} \)

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

\( \frac{25 + 10}{20} \) = \( \frac{35}{20} \) = 1\(\frac{3}{4}\)

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