Question

ding and subtracting rational expressions
match the addition and subtraction problems to their solutions:
\\( \frac{5}{7} - \frac{3}{7} \\)
\\( \frac{1}{6} + \frac{3}{6} \\)
\\( \frac{1}{2} + \frac{1}{4} \\)
\\( \frac{1}{5} + \frac{1}{2} \\)
\\( \frac{1}{6} - \frac{1}{8} \\)
\\( \frac{1}{24} \\)
\\( \frac{2}{7} \\)
\\( \frac{2}{3} \\)
\\( \frac{7}{10} \\)
\\( \frac{3}{4} \\)

Explanation:

Step1: Solve $\frac{5}{7} - \frac{3}{7}$

Since the denominators are the same, subtract the numerators: $\frac{5 - 3}{7} = \frac{2}{7}$

Step2: Solve $\frac{1}{6} + \frac{3}{6}$

Denominators are the same, add numerators: $\frac{1 + 3}{6} = \frac{4}{6} = \frac{2}{3}$ (simplify by dividing numerator and denominator by 2)

Step3: Solve $\frac{1}{2} + \frac{1}{4}$

Find a common denominator (4): $\frac{2}{4} + \frac{1}{4} = \frac{2 + 1}{4} = \frac{3}{4}$

Step4: Solve $\frac{1}{5} + \frac{1}{2}$

Common denominator (10): $\frac{2}{10} + \frac{5}{10} = \frac{2 + 5}{10} = \frac{7}{10}$

Step5: Solve $\frac{1}{6} - \frac{1}{8}$

Common denominator (24): $\frac{4}{24} - \frac{3}{24} = \frac{4 - 3}{24} = \frac{1}{24}$

Answer:

• $\frac{5}{7} - \frac{3}{7}$ matches $\frac{2}{7}$
• $\frac{1}{6} + \frac{3}{6}$ matches $\frac{2}{3}$
• $\frac{1}{2} + \frac{1}{4}$ matches $\frac{3}{4}$
• $\frac{1}{5} + \frac{1}{2}$ matches $\frac{7}{10}$
• $\frac{1}{6} - \frac{1}{8}$ matches $\frac{1}{24}$