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Answer :
Sure! Let's solve the problem step-by-step:
1. Convert the Mixed Numbers to Improper Fractions
- For [tex]\(1 \frac{2}{3}\)[/tex]:
- Multiply the whole number (1) by the denominator (3) and add the numerator (2).
- [tex]\(1 \times 3 + 2 = 3 + 2 = 5\)[/tex]
- So, [tex]\(1 \frac{2}{3} = \frac{5}{3}\)[/tex].
- For [tex]\(2 \frac{1}{4}\)[/tex]:
- Multiply the whole number (2) by the denominator (4) and add the numerator (1).
- [tex]\(2 \times 4 + 1 = 8 + 1 = 9\)[/tex]
- So, [tex]\(2 \frac{1}{4} = \frac{9}{4}\)[/tex].
2. Multiply the Improper Fractions
- Multiply the numerators: [tex]\(5 \times 9 = 45\)[/tex].
- Multiply the denominators: [tex]\(3 \times 4 = 12\)[/tex].
- Therefore, [tex]\(\frac{5}{3} \times \frac{9}{4} = \frac{45}{12}\)[/tex].
3. Simplify the Fraction
- Simplify [tex]\(\frac{45}{12}\)[/tex] by finding the greatest common divisor (GCD) of 45 and 12, which is 3.
- Divide both the numerator and denominator by the GCD:
- Numerator: [tex]\(45 ÷ 3 = 15\)[/tex]
- Denominator: [tex]\(12 ÷ 3 = 4\)[/tex]
- So, [tex]\(\frac{45}{12}\)[/tex] simplifies to [tex]\(\frac{15}{4}\)[/tex].
4. Convert the Improper Fraction to a Mixed Number
- Divide the numerator by the denominator: [tex]\(15 ÷ 4 = 3\)[/tex] with a remainder of 3.
- So, [tex]\(\frac{15}{4} = 3 \frac{3}{4}\)[/tex].
Thus, the answer is [tex]\(3 \frac{3}{4}\)[/tex].
1. Convert the Mixed Numbers to Improper Fractions
- For [tex]\(1 \frac{2}{3}\)[/tex]:
- Multiply the whole number (1) by the denominator (3) and add the numerator (2).
- [tex]\(1 \times 3 + 2 = 3 + 2 = 5\)[/tex]
- So, [tex]\(1 \frac{2}{3} = \frac{5}{3}\)[/tex].
- For [tex]\(2 \frac{1}{4}\)[/tex]:
- Multiply the whole number (2) by the denominator (4) and add the numerator (1).
- [tex]\(2 \times 4 + 1 = 8 + 1 = 9\)[/tex]
- So, [tex]\(2 \frac{1}{4} = \frac{9}{4}\)[/tex].
2. Multiply the Improper Fractions
- Multiply the numerators: [tex]\(5 \times 9 = 45\)[/tex].
- Multiply the denominators: [tex]\(3 \times 4 = 12\)[/tex].
- Therefore, [tex]\(\frac{5}{3} \times \frac{9}{4} = \frac{45}{12}\)[/tex].
3. Simplify the Fraction
- Simplify [tex]\(\frac{45}{12}\)[/tex] by finding the greatest common divisor (GCD) of 45 and 12, which is 3.
- Divide both the numerator and denominator by the GCD:
- Numerator: [tex]\(45 ÷ 3 = 15\)[/tex]
- Denominator: [tex]\(12 ÷ 3 = 4\)[/tex]
- So, [tex]\(\frac{45}{12}\)[/tex] simplifies to [tex]\(\frac{15}{4}\)[/tex].
4. Convert the Improper Fraction to a Mixed Number
- Divide the numerator by the denominator: [tex]\(15 ÷ 4 = 3\)[/tex] with a remainder of 3.
- So, [tex]\(\frac{15}{4} = 3 \frac{3}{4}\)[/tex].
Thus, the answer is [tex]\(3 \frac{3}{4}\)[/tex].
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