Add. 3/10 + 1/2=_____

Identify Common Denominator: Identify a common denominator for 3/10 and 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 1/2 to a fraction with the common denominator of 10. To convert 1/2 to a fraction with a denominator of 10, multiply both the numerator and the denominator by 5. 1/2 * 5/5 = 5/10Add Fractions: Add the two fractions with the common denominator. Now that both fractions have the same denominator, you can add the numerators together. 3/10 + 5/10 = (3+5)/10Perform Numerical Addition: Perform the addition of the numerators. Add the numerators 3 and 5. 3 + 5 = 8Write Result as Fraction: Write the result as a fraction with the common denominator. The sum of the numerators is 8, and the common denominator is 10. 8/10Simplify Fraction: Simplify the fraction 8/10 if possible. The fraction 8/10 can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 2. 8/10 ÷ 2/2 = 4/5

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Math Problems

Algebra 1

Add and subtract rational numbers

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 $2$ . $\newline$ $\frac{8}{10} \div \frac{2}{2} = \frac{4}{5}$