To add the fractions [tex]\(\frac{1}{4}\)[/tex] and [tex]\(\frac{5}{3}\)[/tex], follow these steps:
1. Identify the denominators: The denominators are 4 and 3.
2. Find a common denominator: To add fractions, we need a common denominator. The least common multiple (LCM) of 4 and 3 is 12. This will be our common denominator.
3. Adjust the numerators to the common denominator:
- For [tex]\(\frac{1}{4}\)[/tex], we need to adjust it to a denominator of 12.
[tex]\[
\frac{1}{4} = \frac{1 \times 3}{4 \times 3} = \frac{3}{12}
\][/tex]
- For [tex]\(\frac{5}{3}\)[/tex], we also adjust it to a denominator of 12.
[tex]\[
\frac{5}{3} = \frac{5 \times 4}{3 \times 4} = \frac{20}{12}
\][/tex]
4. Add the adjusted numerators: Now that both fractions have the same denominator, add the numerators together:
[tex]\[
\frac{3}{12} + \frac{20}{12} = \frac{3 + 20}{12} = \frac{23}{12}
\][/tex]
5. Express the result: The result of the addition is [tex]\(\frac{23}{12}\)[/tex]. This fraction can also be expressed as a mixed number:
[tex]\[
\frac{23}{12} = 1 \frac{11}{12}
\][/tex]
6. Convert to decimal form (for further understanding): To convert the result to decimal form, divide the numerator by the denominator:
[tex]\[
\frac{23}{12} \approx 1.9166666666666667
\][/tex]
Thus, the sum of the fractions [tex]\(\frac{1}{4}\)[/tex] and [tex]\(\frac{5}{3}\)[/tex] is [tex]\(\frac{23}{12}\)[/tex] or approximately [tex]\(1.9166666666666667\)[/tex] in decimal form.
