Multiply the whole number and fraction. Simplify your answer and write it as a mixed number.
3 * $1 \frac{6}{9}$
Answer (2)
Convert the mixed number to an improper fraction: 1 9 6 = 9 15 .
Multiply the whole number by the improper fraction: 3 × 9 15 = 9 45 .
Simplify the resulting fraction: 9 45 = 5 .
Write the result as a mixed number: 5 .
Explanation
Understanding the problem We are asked to multiply the whole number 3 by the mixed number 1 9 6 , simplify the result, and write it as a mixed number.
Converting to an improper fraction First, we convert the mixed number 1 9 6 to an improper fraction. To do this, we multiply the whole number part (1) by the denominator (9) and add the numerator (6):
1 × 9 + 6 = 9 + 6 = 15 .
So, 1 9 6 = 9 15 .
Multiplying the whole number and fraction Next, we multiply the whole number 3 by the improper fraction 9 15 :
3 × 9 15 = 9 3 × 15 = 9 45 .
Simplifying the fraction Now, we simplify the fraction 9 45 . We can divide both the numerator and the denominator by their greatest common divisor, which is 9:
9 45 = 9 ÷ 9 45 ÷ 9 = 1 5 = 5 .
Converting to a mixed number Since the result is a whole number, we can write it as a mixed number with a whole number part of 5 and a fractional part of 0. So, the simplified mixed number is 5.
Final Answer Therefore, the final answer is 5.
Examples
In baking, if a recipe calls for 1 9 6 cups of flour and you want to triple the recipe, you would multiply 3 by 1 9 6 . This problem shows you how to calculate the new amount of flour needed, which is 5 cups. Understanding how to multiply whole numbers and mixed numbers is essential for adjusting recipes and ensuring accurate measurements in cooking.
To multiply 3 by the mixed number 1 9 6 , we first convert the mixed number to the improper fraction 9 15 . After multiplying and simplifying, we find that the result is 5 , which can be written as a mixed number. Therefore, the final answer is 5 .
;
