$8 \frac{1}{12} \cdot 5 \frac{5}{12}$
Answer (2)
Convert the mixed numbers to improper fractions: 8 12 1 = 12 97 and 5 12 5 = 12 65 .
Multiply the improper fractions: 12 97 × 12 65 = 144 6305 .
Convert the result back to a mixed number: 144 6305 = 43 144 113 .
The final answer is: 43 144 113 .
Explanation
Understanding the Problem We are asked to compute the product of two mixed numbers: 8 12 1 and 5 12 5 .
Converting to Improper Fractions First, we convert the mixed numbers to improper fractions. To do this, we multiply the whole number part by the denominator and add the numerator. Then we put the result over the original denominator.
For 8 12 1 , we have 8 × 12 + 1 = 96 + 1 = 97 . So, 8 12 1 = 12 97 .
For 5 12 5 , we have 5 × 12 + 5 = 60 + 5 = 65 . So, 5 12 5 = 12 65 .
Multiplying the Improper Fractions Next, we multiply the two improper fractions: 12 97 ⋅ 12 65 = 12 × 12 97 × 65 = 144 6305 .
Converting Back to a Mixed Number Now, we convert the resulting improper fraction back to a mixed number. To do this, we divide the numerator by the denominator to find the whole number part and the remainder. The whole number part is the quotient, and the remainder is the numerator of the fractional part, with the original denominator.
Dividing 6305 by 144, we get a quotient of 43 and a remainder of 113. So, 144 6305 = 43 144 113 .
Final Answer Therefore, 8 12 1 ⋅ 5 12 5 = 43 144 113 .
Examples
Mixed number multiplication is useful in everyday situations, such as when you're scaling a recipe. For example, if a recipe calls for 2 2 1 cups of flour and you want to make 1 2 1 times the recipe, you would multiply these mixed numbers to find out how much flour you need. This skill is also helpful in construction, where you might need to calculate the area of a rectangular space with sides measured in mixed numbers.
The product of the mixed numbers 8 12 1 and 5 12 5 is calculated by converting them to improper fractions, multiplying them to get 144 6305 , and then converting back to a mixed number, which results in 43 144 113 .
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