Question

1. give the answer as a mixed number when appropriate. simplify before multiplying.

a) \\(\frac{3}{5} + \frac{-4}{3}\\)
b) \\(2\frac{5}{6} \div \frac{-20}{18}\\)

Explanation:

Add the fractions in part a

Using the Integer Arithmetic knowledge point, find a common denominator for the fractions:

$$ \frac{3}{5} + \frac{-4}{3} = \frac{3 \times 3}{5 \times 3} + \frac{-4 \times 5}{3 \times 5} = \frac{9}{15} + \frac{-20}{15} $$

Combine the numerators:

$$ \frac{9 + (-20)}{15} = \frac{-11}{15} = -\frac{11}{15} $$

Convert mixed number and simplify in part b

Convert the mixed number to an improper fraction:

$$ 2\frac{5}{6} = \frac{2 \times 6 + 5}{6} = \frac{17}{6} $$

Simplify the second fraction before performing the operation:

$$ \frac{-20}{18} = \frac{-10}{9} $$

Divide the fractions in part b

Multiply by the reciprocal of the divisor:

$$ \frac{17}{6} \div \frac{-10}{9} = \frac{17}{6} \times \frac{9}{-10} $$

Simplify by cross-canceling common factors:

$$ \frac{17}{2} \times \frac{3}{-10} = \frac{51}{-20} = -\frac{51}{20} $$

Convert to a mixed number

Convert the improper fraction to a mixed number:

$$ -\frac{51}{20} = -2\frac{11}{20} $$

Answer:

Question a

\(-\frac{11}{15}\)

Question b

\(-2\frac{11}{20}\)