Let's tackle each fraction addition and subtraction step by step:
### Problem 1: [tex]\( \frac{9}{10} + \frac{5}{12} - \frac{11}{15} \)[/tex]
1. Find the least common multiple (LCM) of the denominators 10, 12, and 15.
2. Adjust each numerator to correspond with the common denominator.
3. perform the addition/subtraction of the adjusted numerators.
4. Simplify the fraction if possible.
Following these steps, we end up with:
[tex]\[ \frac{9}{10} + \frac{5}{12} - \frac{11}{15} = \frac{7}{12} = 0.5833333333333334 \][/tex]
### Problem 2: [tex]\( \frac{8}{25} - \frac{9}{20} + \frac{1}{22} \)[/tex]
1. Find the LCM of the denominators 25, 20, and 22.
2. Adjust each numerator to correspond with the common denominator.
3. perform the addition/subtraction of the adjusted numerators.
4. Simplify the fraction if possible.
Following these steps, we end up with:
[tex]\[ \frac{8}{25} - \frac{9}{20} + \frac{1}{22} = -0.08454545454545455 \][/tex]
### Problem 3: [tex]\( \frac{12}{12} + \frac{7}{21} - \frac{13}{22} \)[/tex]
1. Find the LCM of the denominators 12, 21, and 22.
2. Adjust each numerator to correspond with the common denominator.
3. perform the addition/subtraction of the adjusted numerators.
4. Simplify the fraction if possible.
Following these steps, we end up with:
[tex]\[ \frac{12}{12} + \frac{7}{21} - \frac{13}{22} = 0.7424242424242424 \][/tex]
### Problem 4: [tex]\( \frac{3}{26} + \frac{3}{28} + \frac{4}{36} \)[/tex]
1. Find the LCM of the denominators 26, 28, and 36.
2. Adjust each numerator to correspond with the common denominator.
3. perform the addition of the adjusted numerators.
4. Simplify the fraction if possible.
Following these steps, we end up with:
[tex]\[ \frac{3}{26} + \frac{3}{28} + \frac{4}{36} = 0.3336385836385836 \][/tex]
These comprehensive calculations yield the following results:
1. [tex]\( \frac{9}{10} + \frac{5}{12} - \frac{11}{15} = 0.5833333333333334 \)[/tex]
2. [tex]\( \frac{8}{25} - \frac{9}{20} + \frac{1}{22} = -0.08454545454545455 \)[/tex]
3. [tex]\( \frac{12}{12} + \frac{7}{21} - \frac{13}{22} = 0.7424242424242424 \)[/tex]
4. [tex]\( \frac{3}{26} + \frac{3}{28} + \frac{4}{36} = 0.3336385836385836 \)[/tex]
