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].
