IDNLearn.com provides a seamless experience for finding the answers you need. Our platform provides detailed and accurate responses from experts, helping you navigate any topic with confidence.
Sagot :
Certainly! Let's solve the problem step-by-step.
We have the mixed numbers [tex]\(1 \frac{1}{9}\)[/tex] and [tex]\(2 \frac{3}{6}\)[/tex], and we need to multiply them together.
### Step 1: Convert Mixed Numbers to Improper Fractions
First, convert each mixed number to an improper fraction.
#### For [tex]\(1 \frac{1}{9}\)[/tex]:
1. Multiply the whole number by the denominator: [tex]\(1 \times 9 = 9\)[/tex].
2. Add the numerator to the result: [tex]\(9 + 1 = 10\)[/tex].
3. Place this result over the original denominator: [tex]\(\frac{10}{9}\)[/tex].
So, [tex]\(1 \frac{1}{9}\)[/tex] becomes [tex]\(\frac{10}{9}\)[/tex].
#### For [tex]\(2 \frac{3}{6}\)[/tex]:
1. Simplify the fraction [tex]\(\frac{3}{6}\)[/tex] to [tex]\(\frac{1}{2}\)[/tex], because [tex]\( \frac{3}{6} = \frac{1}{2} \)[/tex].
2. Multiply the whole number by the denominator: [tex]\(2 \times 2 = 4\)[/tex].
3. Add the numerator to the result: [tex]\(4 + 1 = 5\)[/tex].
4. Place this result over the original denominator: [tex]\(\frac{5}{2}\)[/tex].
So, [tex]\(2 \frac{1}{2}\)[/tex] becomes [tex]\(\frac{5}{2}\)[/tex].
### Step 2: Multiply the Fractions
Now multiply the two improper fractions:
[tex]\[ \frac{10}{9} \times \frac{5}{2} \][/tex]
### Step 3: Multiply the Numerators and Denominators
Multiply the numerators together and the denominators together:
[tex]\[ \text{Numerator: } 10 \times 5 = 50 \\ \text{Denominator: } 9 \times 2 = 18 \][/tex]
Therefore, the product of the fractions is:
[tex]\[ \frac{50}{18} \][/tex]
### Step 4: Simplify the Fraction (if possible)
Let's simplify [tex]\(\frac{50}{18}\)[/tex]:
1. Find the greatest common divisor (GCD) of 50 and 18. The GCD is 2.
2. Divide the numerator and the denominator by their GCD:
[tex]\[ \frac{50 \div 2}{18 \div 2} = \frac{25}{9} \][/tex]
So, [tex]\(\frac{50}{18}\)[/tex] simplifies to [tex]\(\frac{25}{9}\)[/tex].
### Step 5: Convert Back to Mixed Number (if needed)
If we want to convert [tex]\(\frac{25}{9}\)[/tex] back to a mixed number:
1. Divide the numerator by the denominator: [tex]\(25 \div 9 = 2\)[/tex] remainder 7.
2. So, [tex]\(\frac{25}{9} = 2 \frac{7}{9}\)[/tex].
Therefore, the result of multiplying [tex]\(1 \frac{1}{9} \times 2 \frac{3}{6}\)[/tex] is [tex]\(\frac{25}{9}\)[/tex] or [tex]\(2 \frac{7}{9}\)[/tex].
However, based on the numerical results from the provided data:
[tex]\[ 1.1111111111111112 \times 2.5 = 2.7777777777777777 \][/tex]
This verifies our solution.
So, the final product is approximately [tex]\(2.78\)[/tex] in decimal form or exactly [tex]\(\frac{25}{9}\)[/tex] or [tex]\(2 \frac{7}{9}\)[/tex].
We have the mixed numbers [tex]\(1 \frac{1}{9}\)[/tex] and [tex]\(2 \frac{3}{6}\)[/tex], and we need to multiply them together.
### Step 1: Convert Mixed Numbers to Improper Fractions
First, convert each mixed number to an improper fraction.
#### For [tex]\(1 \frac{1}{9}\)[/tex]:
1. Multiply the whole number by the denominator: [tex]\(1 \times 9 = 9\)[/tex].
2. Add the numerator to the result: [tex]\(9 + 1 = 10\)[/tex].
3. Place this result over the original denominator: [tex]\(\frac{10}{9}\)[/tex].
So, [tex]\(1 \frac{1}{9}\)[/tex] becomes [tex]\(\frac{10}{9}\)[/tex].
#### For [tex]\(2 \frac{3}{6}\)[/tex]:
1. Simplify the fraction [tex]\(\frac{3}{6}\)[/tex] to [tex]\(\frac{1}{2}\)[/tex], because [tex]\( \frac{3}{6} = \frac{1}{2} \)[/tex].
2. Multiply the whole number by the denominator: [tex]\(2 \times 2 = 4\)[/tex].
3. Add the numerator to the result: [tex]\(4 + 1 = 5\)[/tex].
4. Place this result over the original denominator: [tex]\(\frac{5}{2}\)[/tex].
So, [tex]\(2 \frac{1}{2}\)[/tex] becomes [tex]\(\frac{5}{2}\)[/tex].
### Step 2: Multiply the Fractions
Now multiply the two improper fractions:
[tex]\[ \frac{10}{9} \times \frac{5}{2} \][/tex]
### Step 3: Multiply the Numerators and Denominators
Multiply the numerators together and the denominators together:
[tex]\[ \text{Numerator: } 10 \times 5 = 50 \\ \text{Denominator: } 9 \times 2 = 18 \][/tex]
Therefore, the product of the fractions is:
[tex]\[ \frac{50}{18} \][/tex]
### Step 4: Simplify the Fraction (if possible)
Let's simplify [tex]\(\frac{50}{18}\)[/tex]:
1. Find the greatest common divisor (GCD) of 50 and 18. The GCD is 2.
2. Divide the numerator and the denominator by their GCD:
[tex]\[ \frac{50 \div 2}{18 \div 2} = \frac{25}{9} \][/tex]
So, [tex]\(\frac{50}{18}\)[/tex] simplifies to [tex]\(\frac{25}{9}\)[/tex].
### Step 5: Convert Back to Mixed Number (if needed)
If we want to convert [tex]\(\frac{25}{9}\)[/tex] back to a mixed number:
1. Divide the numerator by the denominator: [tex]\(25 \div 9 = 2\)[/tex] remainder 7.
2. So, [tex]\(\frac{25}{9} = 2 \frac{7}{9}\)[/tex].
Therefore, the result of multiplying [tex]\(1 \frac{1}{9} \times 2 \frac{3}{6}\)[/tex] is [tex]\(\frac{25}{9}\)[/tex] or [tex]\(2 \frac{7}{9}\)[/tex].
However, based on the numerical results from the provided data:
[tex]\[ 1.1111111111111112 \times 2.5 = 2.7777777777777777 \][/tex]
This verifies our solution.
So, the final product is approximately [tex]\(2.78\)[/tex] in decimal form or exactly [tex]\(\frac{25}{9}\)[/tex] or [tex]\(2 \frac{7}{9}\)[/tex].
We value your presence here. Keep sharing knowledge and helping others find the answers they need. This community is the perfect place to learn together. IDNLearn.com provides the best answers to your questions. Thank you for visiting, and come back soon for more helpful information.
