Answer :
Sure! Let's solve the problem step by step:
We need to multiply the mixed numbers [tex]\(1 \frac{2}{3}\)[/tex] and [tex]\(2 \frac{1}{4}\)[/tex], and then simplify the result to write it as a mixed number.
### Step 1: Convert Mixed Numbers to Improper Fractions
1. Convert [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].
2. Convert [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].
### Step 2: Multiply the Fractions
Multiply the numerators and the denominators:
- Numerator: [tex]\(5 \times 9 = 45\)[/tex].
- Denominator: [tex]\(3 \times 4 = 12\)[/tex].
So, the product of the fractions is [tex]\(\frac{45}{12}\)[/tex].
### Step 3: Simplify the Result and Convert to a Mixed Number
1. Simplify [tex]\(\frac{45}{12}\)[/tex]:
- Divide the numerator (45) by the denominator (12) to get the whole number part: [tex]\(45 \div 12 = 3\)[/tex], with a remainder of 9.
- The remainder (9) becomes the new numerator over the original denominator (12), forming the fractional part [tex]\(\frac{9}{12}\)[/tex].
2. Simplify the Fractional Part:
- [tex]\(\frac{9}{12}\)[/tex] can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 3.
- [tex]\(\frac{9 \div 3}{12 \div 3} = \frac{3}{4}\)[/tex].
The final answer is the mixed number [tex]\(3 \frac{3}{4}\)[/tex].
We need to multiply the mixed numbers [tex]\(1 \frac{2}{3}\)[/tex] and [tex]\(2 \frac{1}{4}\)[/tex], and then simplify the result to write it as a mixed number.
### Step 1: Convert Mixed Numbers to Improper Fractions
1. Convert [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].
2. Convert [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].
### Step 2: Multiply the Fractions
Multiply the numerators and the denominators:
- Numerator: [tex]\(5 \times 9 = 45\)[/tex].
- Denominator: [tex]\(3 \times 4 = 12\)[/tex].
So, the product of the fractions is [tex]\(\frac{45}{12}\)[/tex].
### Step 3: Simplify the Result and Convert to a Mixed Number
1. Simplify [tex]\(\frac{45}{12}\)[/tex]:
- Divide the numerator (45) by the denominator (12) to get the whole number part: [tex]\(45 \div 12 = 3\)[/tex], with a remainder of 9.
- The remainder (9) becomes the new numerator over the original denominator (12), forming the fractional part [tex]\(\frac{9}{12}\)[/tex].
2. Simplify the Fractional Part:
- [tex]\(\frac{9}{12}\)[/tex] can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 3.
- [tex]\(\frac{9 \div 3}{12 \div 3} = \frac{3}{4}\)[/tex].
The final answer is the mixed number [tex]\(3 \frac{3}{4}\)[/tex].
