Answer :
Sure, let's go through the steps to multiply these mixed numbers and simplify the result.
1. Convert the 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, [tex]\(\frac{5}{3} \times \frac{9}{4} = \frac{45}{12}\)[/tex].
3. Simplify the Fraction:
- Find the greatest common divisor (GCD) of 45 and 12, which is 3.
- Divide both the numerator and the denominator by this GCD:
[tex]\[
\frac{45 \div 3}{12 \div 3} = \frac{15}{4}
\][/tex]
4. Convert to a Mixed Number:
- Divide the numerator by the denominator to find the whole number and the remainder:
- [tex]\(15 \div 4 = 3\)[/tex], remainder [tex]\(3\)[/tex].
- So, [tex]\(\frac{15}{4}\)[/tex] can be written as the mixed number [tex]\(3 \frac{3}{4}\)[/tex].
Thus, the simplified product of [tex]\(1 \frac{2}{3} \times 2 \frac{1}{4}\)[/tex] as a mixed number 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 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, [tex]\(\frac{5}{3} \times \frac{9}{4} = \frac{45}{12}\)[/tex].
3. Simplify the Fraction:
- Find the greatest common divisor (GCD) of 45 and 12, which is 3.
- Divide both the numerator and the denominator by this GCD:
[tex]\[
\frac{45 \div 3}{12 \div 3} = \frac{15}{4}
\][/tex]
4. Convert to a Mixed Number:
- Divide the numerator by the denominator to find the whole number and the remainder:
- [tex]\(15 \div 4 = 3\)[/tex], remainder [tex]\(3\)[/tex].
- So, [tex]\(\frac{15}{4}\)[/tex] can be written as the mixed number [tex]\(3 \frac{3}{4}\)[/tex].
Thus, the simplified product of [tex]\(1 \frac{2}{3} \times 2 \frac{1}{4}\)[/tex] as a mixed number is [tex]\(3 \frac{3}{4}\)[/tex].
