Perform the indicated operations and express your answers in simplest form:

1. [tex]\[\frac{5}{12} + \frac{1}{4} + \frac{1}{18} =\][/tex]

2. [tex]\[4 \frac{3}{8} + 3 \frac{3}{12} + 9 \frac{1}{4} =\][/tex]

3. [tex]\[2 \frac{3}{5} + 6 \frac{7}{15} + 10 \frac{2}{9} =\][/tex]

4. [tex]\[16 \frac{7}{14} - 12 \frac{8}{21} =\][/tex]

5. [tex]\[5 \frac{3}{4} - 3 \frac{1}{8} =\][/tex]

6. [tex]\[20 \frac{3}{4} - 18 \frac{2}{3} + 3 \frac{5}{11} =\][/tex]

7. [tex]\[\left(8 \frac{1}{4} - 3 \frac{2}{5}\right) - \left(2 \frac{1}{3} - \frac{1}{4}\right) =\][/tex]

8. [tex]\[\left(32 \frac{3}{4} - 12 \frac{7}{12}\right) - 2 =\][/tex]



Answer :

To solve the problem [tex]\( 5 \frac{3}{4} - 3 \frac{1}{8} \)[/tex], we need to follow the steps below:

1. Convert the mixed numbers to improper fractions:

For [tex]\( 5 \frac{3}{4} \)[/tex]:
- Multiply the whole number part (5) by the denominator (4): [tex]\( 5 \times 4 = 20 \)[/tex].
- Add the numerator (3): [tex]\( 20 + 3 = 23 \)[/tex].
- So, [tex]\( 5 \frac{3}{4} \)[/tex] as an improper fraction is [tex]\( \frac{23}{4} \)[/tex].

For [tex]\( 3 \frac{1}{8} \)[/tex]:
- Multiply the whole number part (3) by the denominator (8): [tex]\( 3 \times 8 = 24 \)[/tex].
- Add the numerator (1): [tex]\( 24 + 1 = 25 \)[/tex].
- So, [tex]\( 3 \frac{1}{8} \)[/tex] as an improper fraction is [tex]\( \frac{25}{8} \)[/tex].

2. Find a common denominator for the fractions:

- The denominators are 4 and 8. The least common denominator (LCD) is 8.

Convert [tex]\( \frac{23}{4} \)[/tex] into a fraction with a denominator of 8:
- Multiply both the numerator and the denominator by 2: [tex]\( \frac{23 \times 2}{4 \times 2} = \frac{46}{8} \)[/tex].

The fraction [tex]\( \frac{25}{8} \)[/tex] already has the denominator of 8.

3. Subtract the fractions:

Now, we subtract [tex]\( \frac{25}{8} \)[/tex] from [tex]\( \frac{46}{8} \)[/tex]:
[tex]\[ \frac{46}{8} - \frac{25}{8} = \frac{46 - 25}{8} = \frac{21}{8} \][/tex]

4. Convert the result back to a mixed number if necessary:

To convert [tex]\( \frac{21}{8} \)[/tex] to a mixed number:
- Divide the numerator by the denominator to get the whole number part: [tex]\( 21 \div 8 = 2 \)[/tex] with a remainder of 5.
- So, the mixed number is [tex]\( 2 \frac{5}{8} \)[/tex].

5. Final answer:

Hence, [tex]\( 5 \frac{3}{4} - 3 \frac{1}{8} = 2 \frac{5}{8} \)[/tex].