$5 \frac{1}{2} \times 7$
Answer (1)
Convert the mixed number to an improper fraction: 5 a rc 1 2 = a rc 11 2 .
Multiply the improper fraction by 7: a rc 11 2 × 7 = a rc 77 2 .
Convert the improper fraction back to a mixed number: a rc 77 2 = 38 a rc 1 2 .
The result is: 38 a rc 1 2
Explanation
Understanding the problem We are asked to evaluate the expression 5 a rc 1 2 × 7 . This involves multiplying a mixed number by an integer.
Converting to an improper fraction First, we convert the mixed number 5 a rc 1 2 to an improper fraction. To do this, we multiply the whole number part (5) by the denominator (2) and add the numerator (1), then place the result over the original denominator (2). So, 5 a rc 1 2 = a rc ( 5 × 2 ) + 1 2 = a rc 10 + 1 2 = a rc 11 2 .
Multiplying the fraction Next, we multiply the improper fraction a rc 11 2 by 7: a rc 11 2 × 7 = a rc 11 × 7 2 = a rc 77 2 .
Converting back to a mixed number Finally, we convert the resulting improper fraction a rc 77 2 back to a mixed number. To do this, we divide 77 by 2. 77 d i v 2 = 38 with a remainder of 1. So, a rc 77 2 = 38 a rc 1 2 . Alternatively, we can express the answer as a decimal: a rc 77 2 = 38.5 .
Examples
Understanding how to multiply mixed numbers is useful in everyday situations, such as when you need to scale a recipe. For example, if a recipe calls for 5 a rc 1 2 cups of flour and you want to make 7 times the recipe, you need to calculate 5 a rc 1 2 × 7 to determine the total amount of flour needed. This calculation ensures you have the correct proportions for the larger batch.
