Answer :
Let's solve each expression step-by-step.
1. Expression: [tex]\(-\frac{6}{10} + \frac{17}{10}\)[/tex]
- Unit Form:
Both fractions have the same denominator, so we can combine the numerators:
[tex]\(-6 + 17 = 11\)[/tex].
- Improper Fraction:
Combine the numerators over the common denominator:
[tex]\(\frac{11}{10}\)[/tex].
- Mixed Number:
Divide the numerator by the denominator to find the whole number part:
[tex]\[11 \div 10 = 1 \text{ with a remainder of } 1.\][/tex]
So, the mixed number is [tex]\(1 \frac{1}{10}\)[/tex].
2. Expression: [tex]\(\frac{70}{8} - \frac{32}{8}\)[/tex]
- Unit Form:
Both fractions have the same denominator, so we can subtract the numerators:
[tex]\(70 - 32 = 38\)[/tex].
- Improper Fraction:
Combine the numerators over the common denominator:
[tex]\(\frac{38}{8}\)[/tex].
- Mixed Number:
Divide the numerator by the denominator to find the whole number part:
[tex]\[38 \div 8 = 4 \text{ with a remainder of } 6.\][/tex]
So, the mixed number is [tex]\(4 \frac{6}{8}\)[/tex], which simplifies to [tex]\(4 \frac{3}{4}\)[/tex] after reducing the fraction.
3. Expression: [tex]\(\frac{9}{6} + \frac{47}{6} + \frac{3}{6}\)[/tex]
- Unit Form:
All fractions have the same denominator, so we can add the numerators:
[tex]\(9 + 47 + 3 = 59\)[/tex].
- Improper Fraction:
Combine the numerators over the common denominator:
[tex]\(\frac{59}{6}\)[/tex].
- Mixed Number:
Divide the numerator by the denominator to find the whole number part:
[tex]\[59 \div 6 = 9 \text{ with a remainder of } 5.\][/tex]
So, the mixed number is [tex]\(9 \frac{5}{6}\)[/tex].
Each solution involves understanding how to combine or subtract fractions with the same denominator, and how to convert an improper fraction into a mixed number.
1. Expression: [tex]\(-\frac{6}{10} + \frac{17}{10}\)[/tex]
- Unit Form:
Both fractions have the same denominator, so we can combine the numerators:
[tex]\(-6 + 17 = 11\)[/tex].
- Improper Fraction:
Combine the numerators over the common denominator:
[tex]\(\frac{11}{10}\)[/tex].
- Mixed Number:
Divide the numerator by the denominator to find the whole number part:
[tex]\[11 \div 10 = 1 \text{ with a remainder of } 1.\][/tex]
So, the mixed number is [tex]\(1 \frac{1}{10}\)[/tex].
2. Expression: [tex]\(\frac{70}{8} - \frac{32}{8}\)[/tex]
- Unit Form:
Both fractions have the same denominator, so we can subtract the numerators:
[tex]\(70 - 32 = 38\)[/tex].
- Improper Fraction:
Combine the numerators over the common denominator:
[tex]\(\frac{38}{8}\)[/tex].
- Mixed Number:
Divide the numerator by the denominator to find the whole number part:
[tex]\[38 \div 8 = 4 \text{ with a remainder of } 6.\][/tex]
So, the mixed number is [tex]\(4 \frac{6}{8}\)[/tex], which simplifies to [tex]\(4 \frac{3}{4}\)[/tex] after reducing the fraction.
3. Expression: [tex]\(\frac{9}{6} + \frac{47}{6} + \frac{3}{6}\)[/tex]
- Unit Form:
All fractions have the same denominator, so we can add the numerators:
[tex]\(9 + 47 + 3 = 59\)[/tex].
- Improper Fraction:
Combine the numerators over the common denominator:
[tex]\(\frac{59}{6}\)[/tex].
- Mixed Number:
Divide the numerator by the denominator to find the whole number part:
[tex]\[59 \div 6 = 9 \text{ with a remainder of } 5.\][/tex]
So, the mixed number is [tex]\(9 \frac{5}{6}\)[/tex].
Each solution involves understanding how to combine or subtract fractions with the same denominator, and how to convert an improper fraction into a mixed number.
