Solve the math equation: (8) 4/6 + 10/16

Okay, let's solve the equation step by step: 1. Write down the equation: $$ \frac{4}{6} + \frac{10}{16} $$ 2. Simplify the fractions: * $$\frac{4}{6}$$ can be simplified by dividing both numerator and denominator by 2: $$\frac{4 \div 2}{6 \div 2} = \frac{2}{3}$$ * $$\frac{10}{16}$$ can be simplified by dividing both numerator and denominator by 2: $$\frac{10 \div 2}{16 \div 2} = \frac{5}{8}$$ So now the equation is: $$ \frac{2}{3} + \frac{5}{8} $$ 3. Find a common denominator: The least common multiple (LCM) of 3 and 8 is 24. So we will convert both fractions to have a denominator of 24. 4. Convert the fractions: * To convert $$\frac{2}{3}$$ to a fraction with a denominator of 24, multiply both the numerator and the denominator by 8: $$\frac{2 \times 8}{3 \times 8} = \frac{16}{24}$$ * To convert $$\frac{5}{8}$$ to a fraction with a denominator of 24, multiply both the numerator and the denominator by 3: $$\frac{5 \times 3}{8 \times 3} = \frac{15}{24}$$ So now the equation is: $$ \frac{16}{24} + \frac{15}{24} $$ 5. Add the fractions: Since the denominators are the same, we can add the numerators directly: $$ \frac{16 + 15}{24} = \frac{31}{24} $$ 6. Express the answer as a mixed number (optional): Since 31 is greater than 24, we can express the fraction as a mixed number. 24 goes into 31 once with a remainder of 7. So, $$\frac{31}{24} = 1 \frac{7}{24}$$ Answer: $$\frac{31}{24}$$ or $$1 \frac{7}{24}$$