To calculate the sum of the mixed numbers [tex]\( 3 \frac{4}{12} \)[/tex] and [tex]\( 1 \frac{3}{4} \)[/tex], we will follow these steps:
1. Convert each mixed number to an improper fraction:
- For [tex]\( 3 \frac{4}{12} \)[/tex]:
[tex]\[
3 \frac{4}{12} = \frac{3 \times 12 + 4}{12} = \frac{36 + 4}{12} = \frac{40}{12}
\][/tex]
- For [tex]\( 1 \frac{3}{4} \)[/tex]:
[tex]\[
1 \frac{3}{4} = \frac{1 \times 4 + 3}{4} = \frac{4 + 3}{4} = \frac{7}{4}
\][/tex]
2. Find a common denominator:
- The denominators are 12 and 4. The least common multiple (LCM) of 12 and 4 is 12.
3. Convert the fractions to have the same denominator (12):
- Convert [tex]\(\frac{40}{12}\)[/tex] (no change needed, as its denominator is already 12)
- Convert [tex]\(\frac{7}{4}\)[/tex]:
[tex]\[
\frac{7}{4} = \frac{7 \times 3}{4 \times 3} = \frac{21}{12}
\][/tex]
4. Add the fractions:
- Now that both fractions have the same denominator, add the numerators:
[tex]\[
\frac{40}{12} + \frac{21}{12} = \frac{40 + 21}{12} = \frac{61}{12}
\][/tex]
5. Convert the improper fraction back to a mixed number:
- Divide the numerator by the denominator:
[tex]\[
\frac{61}{12} = 5 \text{ with a remainder of } 1
\][/tex]
Thus, we can write this as the mixed number:
[tex]\[
5 \frac{1}{12}
\][/tex]
6. Simplify the fractional part, if possible:
- The fraction [tex]\(\frac{1}{12}\)[/tex] is already in its simplest form as the greatest common divisor (GCD) of 1 and 12 is 1.
Therefore, the sum of [tex]\( 3 \frac{4}{12} \)[/tex] and [tex]\( 1 \frac{3}{4} \)[/tex] is:
[tex]\[
5 \frac{1}{12}
\][/tex]
