2 1/3 times 3 1/2 As a mixed number

2 1/3 times 3 1/2 As a mixed number

The Correct Answer and Explanation is:

To multiply the mixed numbers (2 \frac{1}{3}) and (3 \frac{1}{2}), we can follow a step-by-step process to obtain the product as a mixed number.

Step 1: Convert Mixed Numbers to Improper Fractions

First, we need to convert the mixed numbers to improper fractions:

1. Convert (2 \frac{1}{3}):

• Multiply the whole number by the denominator: (2 \times 3 = 6).
• Add the numerator: (6 + 1 = 7).
• Thus, (2 \frac{1}{3} = \frac{7}{3}).

1. Convert (3 \frac{1}{2}):

• Multiply the whole number by the denominator: (3 \times 2 = 6).
• Add the numerator: (6 + 1 = 7).
• Thus, (3 \frac{1}{2} = \frac{7}{2}).

Step 2: Multiply the Improper Fractions

Now that we have both mixed numbers as improper fractions, we can multiply them:

[
\frac{7}{3} \times \frac{7}{2} = \frac{7 \times 7}{3 \times 2} = \frac{49}{6}.
]

Step 3: Convert the Improper Fraction Back to a Mixed Number

Next, we need to convert the improper fraction (\frac{49}{6}) back to a mixed number:

1. Divide the numerator by the denominator: (49 \div 6 = 8) (the whole number part).
2. Calculate the remainder: (49 – (8 \times 6) = 49 – 48 = 1).
3. Therefore, (\frac{49}{6}) can be expressed as the mixed number (8 \frac{1}{6}).

Final Answer

The product of (2 \frac{1}{3}) and (3 \frac{1}{2}) is

[
\boxed{8 \frac{1}{6}}.
]

Explanation

Multiplying mixed numbers involves converting them into improper fractions to simplify calculations. By breaking down the process into manageable steps—converting to improper fractions, multiplying, and then converting back—we can maintain clarity and accuracy. This method ensures that we account for both the whole number and fractional components of the mixed numbers effectively. The final step of converting the improper fraction back into a mixed number gives us an answer that is easy to understand and interpret, reinforcing the significance of mixed numbers in everyday calculations. This technique is not only applicable to simple multiplication but also extends to more complex operations involving fractions, making it a foundational skill in arithmetic and algebra.