Answer :
Sure! Let's go through the process step by step to convert between mixed numbers and improper fractions.
### Part 1: Convert Mixed Numbers to Improper Fractions
1. [tex]\(2 \frac{1}{3}\)[/tex]:
- Multiply the whole number by the denominator: [tex]\(2 \times 3 = 6\)[/tex].
- Add the numerator to this product: [tex]\(6 + 1 = 7\)[/tex].
- Place this result over the original denominator: [tex]\(\frac{7}{3}\)[/tex].
2. [tex]\(1 \frac{5}{8}\)[/tex]:
- Multiply the whole number by the denominator: [tex]\(1 \times 8 = 8\)[/tex].
- Add the numerator to this product: [tex]\(8 + 5 = 13\)[/tex].
- Place this result over the original denominator: [tex]\(\frac{13}{8}\)[/tex].
3. [tex]\(3 \frac{2}{5}\)[/tex]:
- Multiply the whole number by the denominator: [tex]\(3 \times 5 = 15\)[/tex].
- Add the numerator to this product: [tex]\(15 + 2 = 17\)[/tex].
- Place this result over the original denominator: [tex]\(\frac{17}{5}\)[/tex].
4. [tex]\(5 \frac{1}{6}\)[/tex]:
- Multiply the whole number by the denominator: [tex]\(5 \times 6 = 30\)[/tex].
- Add the numerator to this product: [tex]\(30 + 1 = 31\)[/tex].
- Place this result over the original denominator: [tex]\(\frac{31}{6}\)[/tex].
5. [tex]\(3 \frac{3}{5}\)[/tex]:
- Multiply the whole number by the denominator: [tex]\(3 \times 5 = 15\)[/tex].
- Add the numerator to this product: [tex]\(15 + 3 = 18\)[/tex].
- Place this result over the original denominator: [tex]\(\frac{18}{5}\)[/tex].
### Part 2: Convert Improper Fractions to Mixed Numbers
6. [tex]\(\frac{21}{8}\)[/tex]:
- Divide the numerator by the denominator: [tex]\(21 \div 8 = 2\)[/tex] with a remainder of [tex]\(5\)[/tex].
- The quotient is the whole number, and the remainder becomes the numerator: [tex]\(2 \frac{5}{8}\)[/tex].
7. [tex]\(\frac{15}{6}\)[/tex]:
- Divide the numerator by the denominator: [tex]\(15 \div 6 = 2\)[/tex] with a remainder of [tex]\(3\)[/tex].
- The quotient is the whole number, and the remainder becomes the numerator: [tex]\(2 \frac{3}{6}\)[/tex]. Simplify to [tex]\(2 \frac{1}{2}\)[/tex].
8. [tex]\(\frac{12}{4}\)[/tex]:
- Divide the numerator by the denominator: [tex]\(12 \div 4 = 3\)[/tex] with no remainder.
- This is a whole number: [tex]\(3\)[/tex].
9. [tex]\(\frac{11}{9}\)[/tex]:
- Divide the numerator by the denominator: [tex]\(11 \div 9 = 1\)[/tex] with a remainder of [tex]\(2\)[/tex].
- The quotient is the whole number, and the remainder becomes the numerator: [tex]\(1 \frac{2}{9}\)[/tex].
10. [tex]\(\frac{45}{12}\)[/tex]:
- Divide the numerator by the denominator: [tex]\(45 \div 12 = 3\)[/tex] with a remainder of [tex]\(9\)[/tex].
- The quotient is the whole number, and the remainder becomes the numerator: [tex]\(3 \frac{9}{12}\)[/tex]. Simplify to [tex]\(3 \frac{3}{4}\)[/tex].
These calculations allow us to confidently convert between mixed numbers and improper fractions. Let me know if you have any more questions!
### Part 1: Convert Mixed Numbers to Improper Fractions
1. [tex]\(2 \frac{1}{3}\)[/tex]:
- Multiply the whole number by the denominator: [tex]\(2 \times 3 = 6\)[/tex].
- Add the numerator to this product: [tex]\(6 + 1 = 7\)[/tex].
- Place this result over the original denominator: [tex]\(\frac{7}{3}\)[/tex].
2. [tex]\(1 \frac{5}{8}\)[/tex]:
- Multiply the whole number by the denominator: [tex]\(1 \times 8 = 8\)[/tex].
- Add the numerator to this product: [tex]\(8 + 5 = 13\)[/tex].
- Place this result over the original denominator: [tex]\(\frac{13}{8}\)[/tex].
3. [tex]\(3 \frac{2}{5}\)[/tex]:
- Multiply the whole number by the denominator: [tex]\(3 \times 5 = 15\)[/tex].
- Add the numerator to this product: [tex]\(15 + 2 = 17\)[/tex].
- Place this result over the original denominator: [tex]\(\frac{17}{5}\)[/tex].
4. [tex]\(5 \frac{1}{6}\)[/tex]:
- Multiply the whole number by the denominator: [tex]\(5 \times 6 = 30\)[/tex].
- Add the numerator to this product: [tex]\(30 + 1 = 31\)[/tex].
- Place this result over the original denominator: [tex]\(\frac{31}{6}\)[/tex].
5. [tex]\(3 \frac{3}{5}\)[/tex]:
- Multiply the whole number by the denominator: [tex]\(3 \times 5 = 15\)[/tex].
- Add the numerator to this product: [tex]\(15 + 3 = 18\)[/tex].
- Place this result over the original denominator: [tex]\(\frac{18}{5}\)[/tex].
### Part 2: Convert Improper Fractions to Mixed Numbers
6. [tex]\(\frac{21}{8}\)[/tex]:
- Divide the numerator by the denominator: [tex]\(21 \div 8 = 2\)[/tex] with a remainder of [tex]\(5\)[/tex].
- The quotient is the whole number, and the remainder becomes the numerator: [tex]\(2 \frac{5}{8}\)[/tex].
7. [tex]\(\frac{15}{6}\)[/tex]:
- Divide the numerator by the denominator: [tex]\(15 \div 6 = 2\)[/tex] with a remainder of [tex]\(3\)[/tex].
- The quotient is the whole number, and the remainder becomes the numerator: [tex]\(2 \frac{3}{6}\)[/tex]. Simplify to [tex]\(2 \frac{1}{2}\)[/tex].
8. [tex]\(\frac{12}{4}\)[/tex]:
- Divide the numerator by the denominator: [tex]\(12 \div 4 = 3\)[/tex] with no remainder.
- This is a whole number: [tex]\(3\)[/tex].
9. [tex]\(\frac{11}{9}\)[/tex]:
- Divide the numerator by the denominator: [tex]\(11 \div 9 = 1\)[/tex] with a remainder of [tex]\(2\)[/tex].
- The quotient is the whole number, and the remainder becomes the numerator: [tex]\(1 \frac{2}{9}\)[/tex].
10. [tex]\(\frac{45}{12}\)[/tex]:
- Divide the numerator by the denominator: [tex]\(45 \div 12 = 3\)[/tex] with a remainder of [tex]\(9\)[/tex].
- The quotient is the whole number, and the remainder becomes the numerator: [tex]\(3 \frac{9}{12}\)[/tex]. Simplify to [tex]\(3 \frac{3}{4}\)[/tex].
These calculations allow us to confidently convert between mixed numbers and improper fractions. Let me know if you have any more questions!
