Question

ling 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:

1. Solve $\boldsymbol{\frac{5}{7}-\frac{3}{7}}$

Step1: Subtract numerators (same denominator)

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

Step2: Simplify the fraction

$5 - 3 = 2$, so the result is $\frac{2}{7}$

2. Solve $\boldsymbol{\frac{1}{6}+\frac{3}{6}}$

Step1: Add numerators (same denominator)

With the same denominator, add the numerators: $\frac{1 + 3}{6}$

Step2: Simplify the fraction

$1 + 3 = 4$, so $\frac{4}{6}=\frac{2}{3}$ (dividing numerator and denominator by 2)

3. Solve $\boldsymbol{\frac{1}{2}+\frac{1}{4}}$

Step1: Find a common denominator

The least common denominator of 2 and 4 is 4. Rewrite $\frac{1}{2}$ as $\frac{2}{4}$

Step2: Add the fractions

Now add: $\frac{2}{4}+\frac{1}{4}=\frac{2 + 1}{4}=\frac{3}{4}$

4. Solve $\boldsymbol{\frac{1}{5}+\frac{1}{2}}$

Answer:

(Matching Results):

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