Multiply. Write your answer as a mixed number.
$6 \times 3 \frac{5}{9}$
Answer (2)
Convert the mixed number to an improper fraction: 3 9 5 = 9 32 .
Multiply the whole number by the improper fraction: 6 × 9 32 = 9 192 .
Simplify the fraction: 9 192 = 3 64 .
Convert the improper fraction back to a mixed number: 3 64 = 21 3 1 .
The final answer is 21 3 1 .
Explanation
Understanding the problem We are asked to multiply a whole number by a mixed number and express the result as a mixed number. The whole number is 6 and the mixed number is 3 9 5 .
Converting to an improper fraction First, we convert the mixed number 3 9 5 to an improper fraction. To do this, we multiply the whole number part (3) by the denominator (9) and add the numerator (5). This gives us 3 × 9 + 5 = 27 + 5 = 32 . So, the improper fraction is 9 32 .
Multiplying the whole number by the improper fraction Next, we multiply the whole number 6 by the improper fraction 9 32 . This gives us 6 × 9 32 = 9 6 × 32 = 9 192 .
Simplifying the fraction Now, we simplify the fraction 9 192 by dividing both the numerator and the denominator by their greatest common divisor, which is 3. So, 9 192 = 9 ÷ 3 192 ÷ 3 = 3 64 .
Converting back to a mixed number Finally, we convert the improper fraction 3 64 back to a mixed number. To do this, we divide 64 by 3. The quotient is 21 and the remainder is 1. So, the mixed number is 21 3 1 .
Final Answer Therefore, 6 × 3 9 5 = 21 3 1 .
Examples
Understanding how to multiply whole numbers and 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 3 9 5 cups of flour, you would need to calculate 3 × 3 9 5 to determine the total amount of flour needed. This skill is also useful in construction, where you might need to calculate the total length of several pieces of wood that are each a mixed number length.
To multiply the whole number 6 by the mixed number 3 9 5 , first convert the mixed number to an improper fraction 9 32 . Then multiply to get 9 192 , simplify to 3 64 , and convert back to the mixed number 21 3 1 . The final answer is 21 3 1 .
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