Answer :
To solve the problem of multiplying the mixed numbers [tex]\(1 \frac{2}{3}\)[/tex] and [tex]\(2 \frac{1}{4}\)[/tex], and simplifying the answer as a mixed number, follow these steps:
1. Convert Mixed Numbers to Improper Fractions:
- For [tex]\(1 \frac{2}{3}\)[/tex]:
- Multiply the whole number by the denominator and add the numerator:
[tex]\[
1 \times 3 + 2 = 3 + 2 = 5
\][/tex]
- So, [tex]\(1 \frac{2}{3}\)[/tex] becomes [tex]\(\frac{5}{3}\)[/tex].
- For [tex]\(2 \frac{1}{4}\)[/tex]:
- Multiply the whole number by the denominator and add the numerator:
[tex]\[
2 \times 4 + 1 = 8 + 1 = 9
\][/tex]
- So, [tex]\(2 \frac{1}{4}\)[/tex] becomes [tex]\(\frac{9}{4}\)[/tex].
2. Multiply the Fractions:
- Multiply the numerators:
[tex]\[
5 \times 9 = 45
\][/tex]
- Multiply the denominators:
[tex]\[
3 \times 4 = 12
\][/tex]
- So, the product is [tex]\(\frac{45}{12}\)[/tex].
3. Simplify the Fraction:
- Find the greatest common divisor (GCD) of the numerator and the denominator, which is 3.
- Divide both the numerator and the denominator by their GCD (3):
[tex]\[
\frac{45 \div 3}{12 \div 3} = \frac{15}{4}
\][/tex]
4. Convert the Improper Fraction to a Mixed Number:
- Divide the numerator by the denominator:
[tex]\[
15 \div 4 = 3\ \text{remainder}\ 3
\][/tex]
- This gives a whole number of 3 and a remainder of 3.
- Therefore, [tex]\(\frac{15}{4}\)[/tex] as a mixed number is [tex]\(3 \frac{3}{4}\)[/tex].
So, the final simplified answer 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 by the denominator and add the numerator:
[tex]\[
1 \times 3 + 2 = 3 + 2 = 5
\][/tex]
- So, [tex]\(1 \frac{2}{3}\)[/tex] becomes [tex]\(\frac{5}{3}\)[/tex].
- For [tex]\(2 \frac{1}{4}\)[/tex]:
- Multiply the whole number by the denominator and add the numerator:
[tex]\[
2 \times 4 + 1 = 8 + 1 = 9
\][/tex]
- So, [tex]\(2 \frac{1}{4}\)[/tex] becomes [tex]\(\frac{9}{4}\)[/tex].
2. Multiply the Fractions:
- Multiply the numerators:
[tex]\[
5 \times 9 = 45
\][/tex]
- Multiply the denominators:
[tex]\[
3 \times 4 = 12
\][/tex]
- So, the product is [tex]\(\frac{45}{12}\)[/tex].
3. Simplify the Fraction:
- Find the greatest common divisor (GCD) of the numerator and the denominator, which is 3.
- Divide both the numerator and the denominator by their GCD (3):
[tex]\[
\frac{45 \div 3}{12 \div 3} = \frac{15}{4}
\][/tex]
4. Convert the Improper Fraction to a Mixed Number:
- Divide the numerator by the denominator:
[tex]\[
15 \div 4 = 3\ \text{remainder}\ 3
\][/tex]
- This gives a whole number of 3 and a remainder of 3.
- Therefore, [tex]\(\frac{15}{4}\)[/tex] as a mixed number is [tex]\(3 \frac{3}{4}\)[/tex].
So, the final simplified answer is [tex]\(3 \frac{3}{4}\)[/tex].
