Answer :
Sure, I can help with that! Let's convert each improper fraction to a mixed number step-by-step.
### Steps to Convert Improper Fractions to Mixed Numbers:
1. Divide the numerator by the denominator to obtain the quotient and the remainder.
2. The quotient is the whole number part.
3. The remainder is the numerator of the fractional part, with the denominator remaining the same.
### Examples:
1. [tex]\(\frac{58}{15}\)[/tex]
- Divide 58 by 15:
[tex]\( \text{58 ÷ 15} = 3 \)[/tex] with a remainder of [tex]\( 13 \)[/tex].
- So, [tex]\(\frac{58}{15} = 3 \frac{13}{15}\)[/tex].
2. [tex]\(\frac{28}{5}\)[/tex]
- Divide 28 by 5:
[tex]\( \text{28 ÷ 5} = 5 \)[/tex] with a remainder of [tex]\( 3 \)[/tex].
- So, [tex]\(\frac{28}{5} = 5 \frac{3}{5}\)[/tex].
3. [tex]\(\frac{12}{8}\)[/tex]
- Divide 12 by 8:
[tex]\( \text{12 ÷ 8} = 1 \)[/tex] with a remainder of [tex]\( 4 \)[/tex].
- So, [tex]\(\frac{12}{8} = 1 \frac{4}{8} = 1 \frac{1}{2}\)[/tex].
4. [tex]\(\frac{25}{12}\)[/tex]
- Divide 25 by 12:
[tex]\( \text{25 ÷ 12} = 2 \)[/tex] with a remainder of [tex]\( 1 \)[/tex].
- So, [tex]\(\frac{25}{12} = 2 \frac{1}{12}\)[/tex].
5. [tex]\(\frac{7}{2}\)[/tex]
- Divide 7 by 2:
[tex]\( \text{7 ÷ 2} = 3 \)[/tex] with a remainder of [tex]\( 1 \)[/tex].
- So, [tex]\(\frac{7}{2} = 3 \frac{1}{2}\)[/tex].
6. [tex]\(\frac{20}{3}\)[/tex]
- Divide 20 by 3:
[tex]\( \text{20 ÷ 3} = 6 \)[/tex] with a remainder of [tex]\( 2 \)[/tex].
- So, [tex]\(\frac{20}{3} = 6 \frac{2}{3}\)[/tex].
7. [tex]\(\frac{55}{6}\)[/tex]
- Divide 55 by 6:
[tex]\( \text{55 ÷ 6} = 9 \)[/tex] with a remainder of [tex]\( 1 \)[/tex].
- So, [tex]\(\frac{55}{6} = 9 \frac{1}{6}\)[/tex].
8. [tex]\(\frac{4}{3}\)[/tex]
- Divide 4 by 3:
[tex]\( \text{4 ÷ 3} = 1 \)[/tex] with a remainder of [tex]\( 1 \)[/tex].
- So, [tex]\(\frac{4}{3} = 1 \frac{1}{3}\)[/tex].
9. [tex]\(\frac{51}{8}\)[/tex]
- Divide 51 by 8:
[tex]\( \text{51 ÷ 8} = 6 \)[/tex] with a remainder of [tex]\( 3 \)[/tex].
- So, [tex]\(\frac{51}{8} = 6 \frac{3}{8}\)[/tex].
10. [tex]\(\frac{45}{12}\)[/tex]
- Divide 45 by 12:
[tex]\( \text{45 ÷ 12} = 3 \)[/tex] with a remainder of [tex]\( 9 \)[/tex].
- So, [tex]\(\frac{45}{12} = 3 \frac{9}{12} = 3 \frac{3}{4}\)[/tex].
11. [tex]\(\frac{13}{5}\)[/tex]
- Divide 13 by 5:
[tex]\( \text{13 ÷ 5} = 2 \)[/tex] with a remainder of [tex]\( 3 \)[/tex].
- So, [tex]\(\frac{13}{5} = 2 \frac{3}{5}\)[/tex].
12. [tex]\(\frac{69}{8}\)[/tex]
- Divide 69 by 8:
[tex]\( \text{69 ÷ 8} = 8 \)[/tex] with a remainder of [tex]\( 5 \)[/tex].
- So, [tex]\(\frac{69}{8} = 8 \frac{5}{8}\)[/tex].
13. [tex]\(\frac{11}{10}\)[/tex]
- Divide 11 by 10:
[tex]\( \text{11 ÷ 10} = 1 \)[/tex] with a remainder of [tex]\( 1 \)[/tex].
- So, [tex]\(\frac{11}{10} = 1 \frac{1}{10}\)[/tex].
14. [tex]\(\frac{28}{4}\)[/tex]
- Divide 28 by 4:
[tex]\( \text{28 ÷ 4} = 7 \)[/tex].
- So, [tex]\(\frac{28}{4} = 7\)[/tex].
- No fractional part since remainder is zero.
15. [tex]\(\frac{29}{6}\)[/tex]
- Divide 29 by 6:
[tex]\( \text{29 ÷ 6} = 4 \)[/tex] with a remainder of [tex]\( 5 \)[/tex].
- So, [tex]\(\frac{29}{6} = 4 \frac{5}{6}\)[/tex].
16. [tex]\(\frac{29}{5}\)[/tex]
- Divide 29 by 5:
[tex]\( \text{29 ÷ 5} = 5 \)[/tex] with a remainder of [tex]\( 4 \)[/tex].
- So, [tex]\(\frac{29}{5} = 5 \frac{4}{5}\)[/tex].
17. [tex]\(\frac{32}{12}\)[/tex]
- Divide 32 by 12:
[tex]\( \text{32 ÷ 12} = 2 \)[/tex] with a remainder of [tex]\( 8 \)[/tex].
- So, [tex]\(\frac{32}{12} = 2 \frac{8}{12} = 2 \frac{2}{3}\)[/tex].
So, these are the mixed numbers for the given improper fractions. If you have any more questions or need further explanations, feel free to ask!
### Steps to Convert Improper Fractions to Mixed Numbers:
1. Divide the numerator by the denominator to obtain the quotient and the remainder.
2. The quotient is the whole number part.
3. The remainder is the numerator of the fractional part, with the denominator remaining the same.
### Examples:
1. [tex]\(\frac{58}{15}\)[/tex]
- Divide 58 by 15:
[tex]\( \text{58 ÷ 15} = 3 \)[/tex] with a remainder of [tex]\( 13 \)[/tex].
- So, [tex]\(\frac{58}{15} = 3 \frac{13}{15}\)[/tex].
2. [tex]\(\frac{28}{5}\)[/tex]
- Divide 28 by 5:
[tex]\( \text{28 ÷ 5} = 5 \)[/tex] with a remainder of [tex]\( 3 \)[/tex].
- So, [tex]\(\frac{28}{5} = 5 \frac{3}{5}\)[/tex].
3. [tex]\(\frac{12}{8}\)[/tex]
- Divide 12 by 8:
[tex]\( \text{12 ÷ 8} = 1 \)[/tex] with a remainder of [tex]\( 4 \)[/tex].
- So, [tex]\(\frac{12}{8} = 1 \frac{4}{8} = 1 \frac{1}{2}\)[/tex].
4. [tex]\(\frac{25}{12}\)[/tex]
- Divide 25 by 12:
[tex]\( \text{25 ÷ 12} = 2 \)[/tex] with a remainder of [tex]\( 1 \)[/tex].
- So, [tex]\(\frac{25}{12} = 2 \frac{1}{12}\)[/tex].
5. [tex]\(\frac{7}{2}\)[/tex]
- Divide 7 by 2:
[tex]\( \text{7 ÷ 2} = 3 \)[/tex] with a remainder of [tex]\( 1 \)[/tex].
- So, [tex]\(\frac{7}{2} = 3 \frac{1}{2}\)[/tex].
6. [tex]\(\frac{20}{3}\)[/tex]
- Divide 20 by 3:
[tex]\( \text{20 ÷ 3} = 6 \)[/tex] with a remainder of [tex]\( 2 \)[/tex].
- So, [tex]\(\frac{20}{3} = 6 \frac{2}{3}\)[/tex].
7. [tex]\(\frac{55}{6}\)[/tex]
- Divide 55 by 6:
[tex]\( \text{55 ÷ 6} = 9 \)[/tex] with a remainder of [tex]\( 1 \)[/tex].
- So, [tex]\(\frac{55}{6} = 9 \frac{1}{6}\)[/tex].
8. [tex]\(\frac{4}{3}\)[/tex]
- Divide 4 by 3:
[tex]\( \text{4 ÷ 3} = 1 \)[/tex] with a remainder of [tex]\( 1 \)[/tex].
- So, [tex]\(\frac{4}{3} = 1 \frac{1}{3}\)[/tex].
9. [tex]\(\frac{51}{8}\)[/tex]
- Divide 51 by 8:
[tex]\( \text{51 ÷ 8} = 6 \)[/tex] with a remainder of [tex]\( 3 \)[/tex].
- So, [tex]\(\frac{51}{8} = 6 \frac{3}{8}\)[/tex].
10. [tex]\(\frac{45}{12}\)[/tex]
- Divide 45 by 12:
[tex]\( \text{45 ÷ 12} = 3 \)[/tex] with a remainder of [tex]\( 9 \)[/tex].
- So, [tex]\(\frac{45}{12} = 3 \frac{9}{12} = 3 \frac{3}{4}\)[/tex].
11. [tex]\(\frac{13}{5}\)[/tex]
- Divide 13 by 5:
[tex]\( \text{13 ÷ 5} = 2 \)[/tex] with a remainder of [tex]\( 3 \)[/tex].
- So, [tex]\(\frac{13}{5} = 2 \frac{3}{5}\)[/tex].
12. [tex]\(\frac{69}{8}\)[/tex]
- Divide 69 by 8:
[tex]\( \text{69 ÷ 8} = 8 \)[/tex] with a remainder of [tex]\( 5 \)[/tex].
- So, [tex]\(\frac{69}{8} = 8 \frac{5}{8}\)[/tex].
13. [tex]\(\frac{11}{10}\)[/tex]
- Divide 11 by 10:
[tex]\( \text{11 ÷ 10} = 1 \)[/tex] with a remainder of [tex]\( 1 \)[/tex].
- So, [tex]\(\frac{11}{10} = 1 \frac{1}{10}\)[/tex].
14. [tex]\(\frac{28}{4}\)[/tex]
- Divide 28 by 4:
[tex]\( \text{28 ÷ 4} = 7 \)[/tex].
- So, [tex]\(\frac{28}{4} = 7\)[/tex].
- No fractional part since remainder is zero.
15. [tex]\(\frac{29}{6}\)[/tex]
- Divide 29 by 6:
[tex]\( \text{29 ÷ 6} = 4 \)[/tex] with a remainder of [tex]\( 5 \)[/tex].
- So, [tex]\(\frac{29}{6} = 4 \frac{5}{6}\)[/tex].
16. [tex]\(\frac{29}{5}\)[/tex]
- Divide 29 by 5:
[tex]\( \text{29 ÷ 5} = 5 \)[/tex] with a remainder of [tex]\( 4 \)[/tex].
- So, [tex]\(\frac{29}{5} = 5 \frac{4}{5}\)[/tex].
17. [tex]\(\frac{32}{12}\)[/tex]
- Divide 32 by 12:
[tex]\( \text{32 ÷ 12} = 2 \)[/tex] with a remainder of [tex]\( 8 \)[/tex].
- So, [tex]\(\frac{32}{12} = 2 \frac{8}{12} = 2 \frac{2}{3}\)[/tex].
So, these are the mixed numbers for the given improper fractions. If you have any more questions or need further explanations, feel free to ask!
