To add the fractions [tex]\(\frac{3}{4}\)[/tex] and [tex]\(\frac{5}{10}\)[/tex], follow these steps:
1. Find a Common Denominator:
The denominators of the fractions are 4 and 10. To combine the fractions, we need a common denominator. The least common denominator (LCD) of 4 and 10 is 20.
2. Adjust the Numerators:
Convert each fraction to an equivalent fraction with the common denominator:
- For [tex]\(\frac{3}{4}\)[/tex], multiply both the numerator and the denominator by 5 to get:
[tex]\[
\frac{3 \times 5}{4 \times 5} = \frac{15}{20}
\][/tex]
- For [tex]\(\frac{5}{10}\)[/tex], multiply both the numerator and the denominator by 2 to get:
[tex]\[
\frac{5 \times 2}{10 \times 2} = \frac{10}{20}
\][/tex]
3. Add the Fractions:
Now that the fractions have the same denominator, you can add the numerators directly:
[tex]\[
\frac{15}{20} + \frac{10}{20} = \frac{15 + 10}{20} = \frac{25}{20}
\][/tex]
4. Simplify the Fraction:
Simplify [tex]\(\frac{25}{20}\)[/tex] by finding the greatest common divisor (GCD) of 25 and 20, which is 5. Divide both the numerator and the denominator by their GCD:
[tex]\[
\frac{25 \div 5}{20 \div 5} = \frac{5}{4}
\][/tex]
Therefore, the sum of the fractions [tex]\(\frac{3}{4}\)[/tex] and [tex]\(\frac{5}{10}\)[/tex] is [tex]\(\frac{5}{4}\)[/tex].
