Full solution

Q. Add.

\newline

\frac{3}{10} + \frac{1}{2}=

_____

Identify Common Denominator: Identify a common denominator for $\frac{3}{10}$ and $\frac{1}{2}$ . The denominators are $10$ and $2$ . The least common denominator (LCD) for these two fractions is $10$ , since $10$ is the smallest number that both denominators can divide into without a remainder.
Convert to Common Denominator: Convert $\frac{1}{2}$ to a fraction with the common denominator of $10$ . To convert $\frac{1}{2}$ to a fraction with a denominator of $10$ , multiply both the numerator and the denominator by $5$ . $\frac{1}{2} \times \frac{5}{5} = \frac{5}{10}$
Add Fractions: Add the two fractions with the common denominator. $\newline$ Now that both fractions have the same denominator, you can add the numerators together. $\newline$ $\frac{3}{10} + \frac{5}{10} = \frac{(3+5)}{10}$
Perform Numerical Addition: Perform the addition of the numerators. $\newline$ Add the numerators $3$ and $5$ . $\newline$ $3 + 5 = 8$
Write Result as Fraction: Write the result as a fraction with the common denominator. $\newline$ The sum of the numerators is $8$ , and the common denominator is $10$ . $\newline$ $\frac{8}{10}$
Simplify Fraction: Simplify the fraction $\frac{8}{10}$ if possible. $\newline$ The fraction $\frac{8}{10}$ can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is $2$ . $\newline$ $\frac{8}{10} \div \frac{2}{2} = \frac{4}{5}$