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Answer :
To solve the problem of multiplying the mixed numbers [tex]\(1 \frac{2}{3}\)[/tex] and [tex]\(2 \frac{1}{4}\)[/tex], and then simplify the result to a mixed number, follow these steps:
1. Convert Mixed Numbers to Improper Fractions:
- For [tex]\(1 \frac{2}{3}\)[/tex]:
- Multiply the whole number (1) by the denominator (3): [tex]\(1 \times 3 = 3\)[/tex].
- Add the numerator (2): [tex]\(3 + 2 = 5\)[/tex].
- The improper fraction is [tex]\(\frac{5}{3}\)[/tex].
- For [tex]\(2 \frac{1}{4}\)[/tex]:
- Multiply the whole number (2) by the denominator (4): [tex]\(2 \times 4 = 8\)[/tex].
- Add the numerator (1): [tex]\(8 + 1 = 9\)[/tex].
- The improper fraction is [tex]\(\frac{9}{4}\)[/tex].
2. Multiply the Improper Fractions:
- Multiply the numerators: [tex]\(5 \times 9 = 45\)[/tex].
- Multiply the denominators: [tex]\(3 \times 4 = 12\)[/tex].
- The product of the fractions is [tex]\(\frac{45}{12}\)[/tex].
3. Simplify the Fraction to a Mixed Number:
- Divide the numerator by the denominator to find the whole number: [tex]\(45 \div 12 = 3\)[/tex] with a remainder of 9.
- Thus, the whole number part is 3.
- The remainder forms the new numerator for the fractional part: [tex]\(\frac{9}{12}\)[/tex].
4. Simplify the Fractional Part:
- Simplify [tex]\(\frac{9}{12}\)[/tex] by finding the greatest common divisor (GCD) of 9 and 12, which is 3.
- Divide both the numerator and the denominator by 3: [tex]\(\frac{9 \div 3}{12 \div 3} = \frac{3}{4}\)[/tex].
5. Write the Final Answer as a Mixed Number:
- Combine the whole number and the simplified fraction: [tex]\(3 \frac{3}{4}\)[/tex].
Therefore, the result of multiplying [tex]\(1 \frac{2}{3}\)[/tex] by [tex]\(2 \frac{1}{4}\)[/tex] and simplifying it as a mixed number is [tex]\(3 \frac{3}{4}\)[/tex].
1. Convert Mixed Numbers to Improper Fractions:
- For [tex]\(1 \frac{2}{3}\)[/tex]:
- Multiply the whole number (1) by the denominator (3): [tex]\(1 \times 3 = 3\)[/tex].
- Add the numerator (2): [tex]\(3 + 2 = 5\)[/tex].
- The improper fraction is [tex]\(\frac{5}{3}\)[/tex].
- For [tex]\(2 \frac{1}{4}\)[/tex]:
- Multiply the whole number (2) by the denominator (4): [tex]\(2 \times 4 = 8\)[/tex].
- Add the numerator (1): [tex]\(8 + 1 = 9\)[/tex].
- The improper fraction is [tex]\(\frac{9}{4}\)[/tex].
2. Multiply the Improper Fractions:
- Multiply the numerators: [tex]\(5 \times 9 = 45\)[/tex].
- Multiply the denominators: [tex]\(3 \times 4 = 12\)[/tex].
- The product of the fractions is [tex]\(\frac{45}{12}\)[/tex].
3. Simplify the Fraction to a Mixed Number:
- Divide the numerator by the denominator to find the whole number: [tex]\(45 \div 12 = 3\)[/tex] with a remainder of 9.
- Thus, the whole number part is 3.
- The remainder forms the new numerator for the fractional part: [tex]\(\frac{9}{12}\)[/tex].
4. Simplify the Fractional Part:
- Simplify [tex]\(\frac{9}{12}\)[/tex] by finding the greatest common divisor (GCD) of 9 and 12, which is 3.
- Divide both the numerator and the denominator by 3: [tex]\(\frac{9 \div 3}{12 \div 3} = \frac{3}{4}\)[/tex].
5. Write the Final Answer as a Mixed Number:
- Combine the whole number and the simplified fraction: [tex]\(3 \frac{3}{4}\)[/tex].
Therefore, the result of multiplying [tex]\(1 \frac{2}{3}\)[/tex] by [tex]\(2 \frac{1}{4}\)[/tex] and simplifying it as a mixed number is [tex]\(3 \frac{3}{4}\)[/tex].
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