To add the mixed numbers [tex]\(1 \frac{3}{4} + 1 \frac{3}{4}\)[/tex], follow these detailed steps:
1. Convert each mixed number to an improper fraction:
- A mixed number [tex]\(1 \frac{3}{4}\)[/tex] can be converted to an improper fraction by multiplying the whole number part by the denominator of the fractional part and then adding the numerator.
- For [tex]\(1 \frac{3}{4}\)[/tex]:
[tex]\[
1 \frac{3}{4} = 1 + \frac{3}{4} = \frac{4}{4} + \frac{3}{4} = \frac{7}{4}
\][/tex]
- Repeat for the second mixed number:
[tex]\[
1 \frac{3}{4} = \frac{7}{4}
\][/tex]
2. Add the improper fractions:
- Now, add the two improper fractions:
[tex]\[
\frac{7}{4} + \frac{7}{4} = \frac{14}{4}
\][/tex]
3. Simplify the resulting fraction:
- Simplify [tex]\(\frac{14}{4}\)[/tex] by dividing both the numerator and the denominator by their greatest common divisor (GCD), which is 2:
[tex]\[
\frac{14}{4} = \frac{14 \div 2}{4 \div 2} = \frac{7}{2}
\][/tex]
4. Convert the improper fraction back to a mixed number:
- To convert [tex]\(\frac{7}{2}\)[/tex] back to a mixed number, divide the numerator by the denominator:
[tex]\[
7 \div 2 = 3 \text{ remainder } 1
\][/tex]
- Therefore, [tex]\(\frac{7}{2}\)[/tex] is equivalent to:
[tex]\[
3 \frac{1}{2}
\][/tex]
As a result, adding the mixed numbers [tex]\(1 \frac{3}{4} + 1 \frac{3}{4} \)[/tex] yields [tex]\(3 \frac{1}{2}\)[/tex].
Answer: [tex]\(3 \frac{1}{2}\)[/tex]
