Answer :
Sure, let's simplify these fractions step by step.
### i. [tex]\( \frac{1}{2} - \frac{3}{8} + \frac{1}{2} \)[/tex]
1. Let's simplify each fraction individually:
- [tex]\( \frac{1}{2} \)[/tex] stays as it is.
- [tex]\( \frac{3}{8} \)[/tex] stays as it is.
- [tex]\( \frac{1}{2} \)[/tex] stays as it is.
2. Find a common denominator for the fractions. Since [tex]\( 2 \times 4 = 8 \)[/tex], we'll convert [tex]\( \frac{1}{2} \)[/tex] to [tex]\( \frac{4}{8} \)[/tex].
3. Now we have:
- [tex]\( \frac{4}{8} \)[/tex]
- [tex]\( \frac{3}{8} \)[/tex]
- [tex]\( \frac{4}{8} \)[/tex]
4. Next, perform the arithmetic:
- [tex]\( \frac{4}{8} - \frac{3}{8} + \frac{4}{8} = \frac{4 - 3 + 4}{8} = \frac{5}{8} \)[/tex]
The simplified form is: [tex]\( 0.625 \)[/tex]
### ii. [tex]\( \frac{2}{3} + \frac{1}{6} - \frac{3}{5} \)[/tex]
1. Find a common denominator (LCM of 3, 6, and 5). LCM is 30.
2. Convert each fraction:
- [tex]\( \frac{2}{3} = \frac{20}{30} \)[/tex]
- [tex]\( \frac{1}{6} = \frac{5}{30} \)[/tex]
- [tex]\( \frac{3}{5} = \frac{18}{30} \)[/tex]
3. Now perform the arithmetic:
- [tex]\( \frac{20}{30} + \frac{5}{30} - \frac{18}{30} = \frac{20 + 5 - 18}{30} = \frac{7}{30} \)[/tex]
The simplified form is: [tex]\( 0.2333... \approx 0.2333 \)[/tex]
### iii. [tex]\( \frac{5}{4} - \frac{3}{2} \)[/tex]
1. Convert [tex]\( \frac{3}{2} \)[/tex] to have a common denominator with [tex]\( \frac{5}{4} \)[/tex]:
- [tex]\( \frac{3}{2} = \frac{6}{4} \)[/tex]
2. Now perform the arithmetic:
- [tex]\( \frac{5}{4} - \frac{6}{4} = \frac{5 - 6}{4} = \frac{-1}{4} \)[/tex]
The simplified form is: [tex]\( -0.25 \)[/tex]
### iv. [tex]\( \frac{7}{6} + \frac{1}{3} \)[/tex]
1. Find a common denominator. Since 6 is the LCM of 6 and 3, convert [tex]\( \frac{1}{3} \)[/tex]:
- [tex]\( \frac{1}{3} = \frac{2}{6} \)[/tex]
2. Now perform the arithmetic:
- [tex]\( \frac{7}{6} + \frac{2}{6} = \frac{7 + 2}{6} = \frac{9}{6} = \frac{3}{2} \)[/tex]
The simplified form is: [tex]\( 1.5 \)[/tex]
### v. [tex]\( \frac{4}{7} + 2\pi \)[/tex]
1. The fraction [tex]\( \frac{4}{7} \)[/tex] remains the same.
2. [tex]\( 2\pi \)[/tex] is approximately [tex]\( 2 \times 3.1416 \approx 6.2832 \)[/tex].
3. Perform the arithmetic:
- [tex]\( \frac{4}{7} \approx 0.5714 \)[/tex]
- Adding these: [tex]\( 0.5714 + 6.2832 = 6.8546 \)[/tex]
The simplified form is: [tex]\( 6.8546 \)[/tex]
This completes the step-by-step simplification of each fraction.
### i. [tex]\( \frac{1}{2} - \frac{3}{8} + \frac{1}{2} \)[/tex]
1. Let's simplify each fraction individually:
- [tex]\( \frac{1}{2} \)[/tex] stays as it is.
- [tex]\( \frac{3}{8} \)[/tex] stays as it is.
- [tex]\( \frac{1}{2} \)[/tex] stays as it is.
2. Find a common denominator for the fractions. Since [tex]\( 2 \times 4 = 8 \)[/tex], we'll convert [tex]\( \frac{1}{2} \)[/tex] to [tex]\( \frac{4}{8} \)[/tex].
3. Now we have:
- [tex]\( \frac{4}{8} \)[/tex]
- [tex]\( \frac{3}{8} \)[/tex]
- [tex]\( \frac{4}{8} \)[/tex]
4. Next, perform the arithmetic:
- [tex]\( \frac{4}{8} - \frac{3}{8} + \frac{4}{8} = \frac{4 - 3 + 4}{8} = \frac{5}{8} \)[/tex]
The simplified form is: [tex]\( 0.625 \)[/tex]
### ii. [tex]\( \frac{2}{3} + \frac{1}{6} - \frac{3}{5} \)[/tex]
1. Find a common denominator (LCM of 3, 6, and 5). LCM is 30.
2. Convert each fraction:
- [tex]\( \frac{2}{3} = \frac{20}{30} \)[/tex]
- [tex]\( \frac{1}{6} = \frac{5}{30} \)[/tex]
- [tex]\( \frac{3}{5} = \frac{18}{30} \)[/tex]
3. Now perform the arithmetic:
- [tex]\( \frac{20}{30} + \frac{5}{30} - \frac{18}{30} = \frac{20 + 5 - 18}{30} = \frac{7}{30} \)[/tex]
The simplified form is: [tex]\( 0.2333... \approx 0.2333 \)[/tex]
### iii. [tex]\( \frac{5}{4} - \frac{3}{2} \)[/tex]
1. Convert [tex]\( \frac{3}{2} \)[/tex] to have a common denominator with [tex]\( \frac{5}{4} \)[/tex]:
- [tex]\( \frac{3}{2} = \frac{6}{4} \)[/tex]
2. Now perform the arithmetic:
- [tex]\( \frac{5}{4} - \frac{6}{4} = \frac{5 - 6}{4} = \frac{-1}{4} \)[/tex]
The simplified form is: [tex]\( -0.25 \)[/tex]
### iv. [tex]\( \frac{7}{6} + \frac{1}{3} \)[/tex]
1. Find a common denominator. Since 6 is the LCM of 6 and 3, convert [tex]\( \frac{1}{3} \)[/tex]:
- [tex]\( \frac{1}{3} = \frac{2}{6} \)[/tex]
2. Now perform the arithmetic:
- [tex]\( \frac{7}{6} + \frac{2}{6} = \frac{7 + 2}{6} = \frac{9}{6} = \frac{3}{2} \)[/tex]
The simplified form is: [tex]\( 1.5 \)[/tex]
### v. [tex]\( \frac{4}{7} + 2\pi \)[/tex]
1. The fraction [tex]\( \frac{4}{7} \)[/tex] remains the same.
2. [tex]\( 2\pi \)[/tex] is approximately [tex]\( 2 \times 3.1416 \approx 6.2832 \)[/tex].
3. Perform the arithmetic:
- [tex]\( \frac{4}{7} \approx 0.5714 \)[/tex]
- Adding these: [tex]\( 0.5714 + 6.2832 = 6.8546 \)[/tex]
The simplified form is: [tex]\( 6.8546 \)[/tex]
This completes the step-by-step simplification of each fraction.
