Question

1. solve the following and express your answer in both improper and

a)
b) $1 + \frac{2}{5}$
c) $2 + \frac{3}{4}$

1. solve the following and express your answer in reduced form:

a) $\frac{4}{5} - \frac{3}{8}$
b) $\frac{3}{2} - \frac{2}{5}$
c) $\frac{5}{3} - \frac{4}{5}$

1. solve the following and put into reduced (simplest) form:

a) $\frac{4}{7} \times \frac{3}{5}$
b) $\frac{1}{3} \times \frac{3}{7}$
c) $\frac{4}{5} \times \frac{5}{8}$

1. solve the following and put into reduced (simplest) form:

a) $\frac{3}{11} \div \frac{1}{3}$
b) $\frac{2}{7} \div \frac{4}{3}$
c) $\frac{3}{2} \div \frac{3}{4}$

1. express as a decimal:

Explanation:

Problem 2 (assuming part a is incomplete, solving b and c)

Part b: \(1+\frac{2}{5}\)

Step1: Convert 1 to fraction with denominator 5

\(1 = \frac{5}{5}\)

Step2: Add the fractions

\(\frac{5}{5}+\frac{2}{5}=\frac{5 + 2}{5}=\frac{7}{5}\) (improper), \(1\frac{2}{5}\) (mixed)

Step1: Convert 2 to fraction with denominator 4

\(2=\frac{8}{4}\)

Step2: Add the fractions

\(\frac{8}{4}+\frac{3}{4}=\frac{8 + 3}{4}=\frac{11}{4}\) (improper), \(2\frac{3}{4}\) (mixed)

Step1: Find common denominator (LCM of 5 and 8 is 40)

\(\frac{4}{5}=\frac{4\times8}{5\times8}=\frac{32}{40}\), \(\frac{3}{8}=\frac{3\times5}{8\times5}=\frac{15}{40}\)

Step2: Subtract the fractions

\(\frac{32}{40}-\frac{15}{40}=\frac{32 - 15}{40}=\frac{17}{40}\)

Answer:

Improper: \(\frac{7}{5}\), Mixed: \(1\frac{2}{5}\)

Part c: \(2+\frac{3}{4}\)