Complete the equation. Write the sum as a mixed number. $\newline$ $\frac{3}{4}+\frac{5}{6}=\frac{18}{\square}+\frac{20}{\square}=\square \frac{\square}{\square}$

Full solution

Q. Complete the equation. Write the sum as a mixed number.

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\frac{3}{4}+\frac{5}{6}=\frac{18}{\square}+\frac{20}{\square}=\square \frac{\square}{\square}

Find Common Denominator: Find a common denominator for $\frac{3}{4}$ and $\frac{5}{6}$ . $\newline$ To add fractions, they must have the same denominator. The least common multiple of $4$ and $6$ is $12$ . $\newline$ $\frac{3}{4} = \frac{(3\times3)}{(4\times3)} = \frac{9}{12}$ $\newline$ $\frac{5}{6} = \frac{(5\times2)}{(6\times2)} = \frac{10}{12}$
Add Fractions: Add the fractions with the common denominator. $\newline$ Now that both fractions have the same denominator, add them: $\newline$ $\frac{9}{12} + \frac{10}{12} = \frac{19}{12}$
Convert to Mixed Number: Convert the improper fraction to a mixed number. $\newline$ $\frac{19}{12}$ is an improper fraction (the numerator is larger than the denominator). $\newline$ To convert it, divide $19$ by $12$ . $\newline$ $19 \div 12 = 1$ remainder $7$ $\newline$ So, $\frac{19}{12} = 1 \frac{7}{12}$
Write Sum as Mixed Number: Write the sum as a mixed number with the common denominator. $\newline$ The sum of the fractions is $1\frac{7}{12}$ . To express it with the common denominator: $\newline$ $1\frac{7}{12} = \frac{12}{12} + \frac{7}{12} = \frac{19}{12}$