Let's find the difference [tex]\( 3 \frac{3}{8} - 1 \frac{6}{8} \)[/tex].
1. Convert the mixed numbers to improper fractions:
- For [tex]\( 3 \frac{3}{8} \)[/tex]:
- Multiply the whole number (3) by the denominator (8): [tex]\( 3 \times 8 = 24 \)[/tex].
- Add the numerator (3) to the result: [tex]\( 24 + 3 = 27 \)[/tex].
- Hence, [tex]\( 3 \frac{3}{8} = \frac{27}{8} \)[/tex].
- For [tex]\( 1 \frac{6}{8} \)[/tex]:
- Multiply the whole number (1) by the denominator (8): [tex]\( 1 \times 8 = 8 \)[/tex].
- Add the numerator (6) to the result: [tex]\( 8 + 6 = 14 \)[/tex].
- Hence, [tex]\( 1 \frac{6}{8} = \frac{14}{8} \)[/tex].
2. Subtract the improper fractions:
- The fractions [tex]\( \frac{27}{8} \)[/tex] and [tex]\( \frac{14}{8} \)[/tex] already have a common denominator, so you can subtract the numerators directly:
[tex]\[
\frac{27}{8} - \frac{14}{8} = \frac{27 - 14}{8} = \frac{13}{8}
\][/tex]
3. Convert the result back to a mixed number:
- Divide the numerator (13) by the denominator (8) to get the whole number part: [tex]\( 13 \div 8 = 1 \)[/tex] with a remainder of 5.
- The whole number part is 1, and the remainder (5) is the new numerator. The denominator remains 8.
- Therefore, [tex]\( \frac{13}{8} \)[/tex] can be expressed as the mixed number [tex]\( 1 \frac{5}{8} \)[/tex].
Thus, the difference between [tex]\( 3 \frac{3}{8} \)[/tex] and [tex]\( 1 \frac{6}{8} \)[/tex] is:
[tex]\[
1 \frac{5}{8}
\][/tex]
