Answer :
Sure, let's go through each part step by step.
### a) [tex]\(\frac{2}{3} + \frac{3}{4}\)[/tex]
1. Find a common denominator for the two fractions. The denominators are 3 and 4. The least common denominator (LCD) is [tex]\(3 \times 4 = 12\)[/tex].
2. Convert each fraction to an equivalent fraction with the common denominator:
- [tex]\(\frac{2}{3}\)[/tex] can be rewritten as [tex]\(\frac{2 \times 4}{3 \times 4} = \frac{8}{12}\)[/tex]
- [tex]\(\frac{3}{4}\)[/tex] can be rewritten as [tex]\(\frac{3 \times 3}{4 \times 3} = \frac{9}{12}\)[/tex]
3. Add the fractions by adding the numerators:
[tex]\[ \frac{8}{12} + \frac{9}{12} = \frac{8 + 9}{12} = \frac{17}{12} \][/tex]
4. The fraction [tex]\(\frac{17}{12}\)[/tex] can also be expressed as a mixed number:
[tex]\[ 17 \div 12 = 1 \text{ R } 5 \implies 1 \frac{5}{12} \][/tex]
If simplified as a decimal, it would be approximately [tex]\(1.4167\)[/tex].
### b) [tex]\(1 \frac{1}{2} + 2 \frac{3}{4}\)[/tex]
1. Convert the mixed numbers to improper fractions:
[tex]\[ 1 \frac{1}{2} = \frac{3}{2} \][/tex]
[tex]\[ 2 \frac{3}{4} = \frac{8+3}{4} = \frac{11}{4} \][/tex]
2. Find a common denominator. The denominators are 2 and 4. The least common denominator is 4.
3. Convert each fraction to an equivalent fraction with the common denominator:
- [tex]\(\frac{3}{2}\)[/tex] can be rewritten as [tex]\(\frac{3 \times 2}{2 \times 2} = \frac{6}{4}\)[/tex]
- [tex]\(\frac{11}{4}\)[/tex] remains the same.
4. Add the fractions by adding the numerators:
[tex]\[ \frac{6}{4} + \frac{11}{4} = \frac{6 + 11}{4} = \frac{17}{4} \][/tex]
5. The fraction [tex]\(\frac{17}{4}\)[/tex] can also be expressed as a mixed number:
[tex]\[ 17 \div 4 = 4 \text{ R } 1 \implies 4 \frac{1}{4} \][/tex]
If simplified as a decimal, it would be [tex]\(4.25\)[/tex].
### c) [tex]\(\frac{5}{6} -\)[/tex]
For part c), there isn't enough information provided to fully solve the problem. We need to know the fraction from which [tex]\(\frac{5}{6}\)[/tex] is being subtracted in order to proceed.
### Summary:
- a) [tex]\(\frac{2}{3} + \frac{3}{4} = 1.4167\)[/tex]
- b) [tex]\(1 \frac{1}{2} + 2 \frac{3}{4} = 4.25\)[/tex]
- c) [tex]\(\frac{5}{6} -\)[/tex] (needs additional information)
These are the solutions to the given problems a) and b). For c), you would need to provide the missing term to proceed.
### a) [tex]\(\frac{2}{3} + \frac{3}{4}\)[/tex]
1. Find a common denominator for the two fractions. The denominators are 3 and 4. The least common denominator (LCD) is [tex]\(3 \times 4 = 12\)[/tex].
2. Convert each fraction to an equivalent fraction with the common denominator:
- [tex]\(\frac{2}{3}\)[/tex] can be rewritten as [tex]\(\frac{2 \times 4}{3 \times 4} = \frac{8}{12}\)[/tex]
- [tex]\(\frac{3}{4}\)[/tex] can be rewritten as [tex]\(\frac{3 \times 3}{4 \times 3} = \frac{9}{12}\)[/tex]
3. Add the fractions by adding the numerators:
[tex]\[ \frac{8}{12} + \frac{9}{12} = \frac{8 + 9}{12} = \frac{17}{12} \][/tex]
4. The fraction [tex]\(\frac{17}{12}\)[/tex] can also be expressed as a mixed number:
[tex]\[ 17 \div 12 = 1 \text{ R } 5 \implies 1 \frac{5}{12} \][/tex]
If simplified as a decimal, it would be approximately [tex]\(1.4167\)[/tex].
### b) [tex]\(1 \frac{1}{2} + 2 \frac{3}{4}\)[/tex]
1. Convert the mixed numbers to improper fractions:
[tex]\[ 1 \frac{1}{2} = \frac{3}{2} \][/tex]
[tex]\[ 2 \frac{3}{4} = \frac{8+3}{4} = \frac{11}{4} \][/tex]
2. Find a common denominator. The denominators are 2 and 4. The least common denominator is 4.
3. Convert each fraction to an equivalent fraction with the common denominator:
- [tex]\(\frac{3}{2}\)[/tex] can be rewritten as [tex]\(\frac{3 \times 2}{2 \times 2} = \frac{6}{4}\)[/tex]
- [tex]\(\frac{11}{4}\)[/tex] remains the same.
4. Add the fractions by adding the numerators:
[tex]\[ \frac{6}{4} + \frac{11}{4} = \frac{6 + 11}{4} = \frac{17}{4} \][/tex]
5. The fraction [tex]\(\frac{17}{4}\)[/tex] can also be expressed as a mixed number:
[tex]\[ 17 \div 4 = 4 \text{ R } 1 \implies 4 \frac{1}{4} \][/tex]
If simplified as a decimal, it would be [tex]\(4.25\)[/tex].
### c) [tex]\(\frac{5}{6} -\)[/tex]
For part c), there isn't enough information provided to fully solve the problem. We need to know the fraction from which [tex]\(\frac{5}{6}\)[/tex] is being subtracted in order to proceed.
### Summary:
- a) [tex]\(\frac{2}{3} + \frac{3}{4} = 1.4167\)[/tex]
- b) [tex]\(1 \frac{1}{2} + 2 \frac{3}{4} = 4.25\)[/tex]
- c) [tex]\(\frac{5}{6} -\)[/tex] (needs additional information)
These are the solutions to the given problems a) and b). For c), you would need to provide the missing term to proceed.
