$7.8 \frac{1}{6} \times 4 \frac{1}{2}$
Answer (2)
Convert the mixed numbers to improper fractions: 7 6 1 = 6 43 and 4 2 1 = 2 9 .
Multiply the improper fractions: 6 43 × 2 9 = 12 387 .
Convert the resulting improper fraction back to a mixed number: 12 387 = 32 12 3 = 32 4 1 .
The final answer is 32 4 1 , which is equal to 32.25. 32 4 1
Explanation
Understanding the Problem We are asked to calculate the product of two mixed numbers: 7 6 1 and 4 2 1 . To do this, we will first convert each mixed number to an improper fraction, then multiply the fractions, and finally convert the result back to a mixed number or decimal.
Converting to Improper Fractions First, convert the mixed number 7 6 1 to an improper fraction. To do this, we multiply the whole number part (7) by the denominator (6) and add the numerator (1). This gives us 7 × 6 + 1 = 42 + 1 = 43 . So, 7 6 1 = 6 43 .
Converting to Improper Fractions Next, convert the mixed number 4 2 1 to an improper fraction. We multiply the whole number part (4) by the denominator (2) and add the numerator (1). This gives us 4 × 2 + 1 = 8 + 1 = 9 . So, 4 2 1 = 2 9 .
Multiplying the Fractions Now, multiply the two improper fractions: 6 43 × 2 9 = 6 × 2 43 × 9 = 12 387 .
Converting Back to a Mixed Number Finally, convert the improper fraction 12 387 back to a mixed number. We divide 387 by 12 to get 387 ÷ 12 = 32 with a remainder of 3. So, 12 387 = 32 12 3 . We can simplify the fraction 12 3 by dividing both the numerator and denominator by 3, which gives us 4 1 . Therefore, 12 387 = 32 4 1 . As a decimal, this is 32.25.
Final Answer Thus, 7 6 1 × 4 2 1 = 32 4 1 = 32.25 .
Examples
Understanding how to multiply mixed numbers is useful in many real-life situations. For example, if you are baking a cake and need to triple a recipe that calls for 2 2 1 cups of flour, you would need to calculate 3 × 2 2 1 . This is the same as 3 × 2 5 = 2 15 = 7 2 1 cups of flour. Similarly, if you are calculating the area of a rectangular garden that measures 5 4 1 meters by 3 2 1 meters, you would multiply these two mixed numbers to find the area.
To multiply the mixed numbers 7.8 6 1 and 4 2 1 , we first convert each to improper fractions and then multiply them. The result is 35 20 7 after converting back to a mixed number. Thus, the final answer is 35 20 7 .
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