To add the fractions [tex]\( \frac{2}{3} \)[/tex] and [tex]\( \frac{3}{4} \)[/tex], follow this step-by-step solution:
1. Find a common denominator:
- The denominators are 3 and 4. A common denominator is the product of these two numbers: [tex]\(3 \times 4 = 12\)[/tex].
2. Convert each fraction to an equivalent fraction with the common denominator:
- Convert [tex]\( \frac{2}{3} \)[/tex]:
[tex]\[
\frac{2}{3} = \frac{2 \times 4}{3 \times 4} = \frac{8}{12}
\][/tex]
- Convert [tex]\( \frac{3}{4} \)[/tex]:
[tex]\[
\frac{3}{4} = \frac{3 \times 3}{4 \times 3} = \frac{9}{12}
\][/tex]
3. Add the numerators, keeping the common denominator:
[tex]\[
\frac{8}{12} + \frac{9}{12} = \frac{8 + 9}{12} = \frac{17}{12}
\][/tex]
4. Simplify the fraction if possible:
- The fraction [tex]\( \frac{17}{12} \)[/tex] is already in its simplest form.
5. Convert the fraction to a mixed number (optional):
- The fraction [tex]\( \frac{17}{12} \)[/tex] can be written as a mixed number by dividing the numerator by the denominator:
[tex]\[
17 \div 12 = 1 \text{ (quotient)} \quad \text{and} \quad 5 \text{ (remainder)}
\][/tex]
Therefore, [tex]\( \frac{17}{12} = 1 \frac{5}{12} \)[/tex].
So, the sum of [tex]\( \frac{2}{3} + \frac{3}{4} \)[/tex] is [tex]\( \frac{17}{12} \)[/tex] or [tex]\( 1 \frac{5}{12} \)[/tex], which is approximately [tex]\( 1.4166666666666667 \)[/tex].
