$7 \frac{1}{2} \times 5$
Answer (1)
Convert the mixed number to an improper fraction: 7 2 1 = 2 15 .
Multiply the improper fraction by 5: 2 15 × 5 = 2 75 .
Convert the improper fraction back to a mixed number: 2 75 = 37 2 1 .
Alternatively, convert the improper fraction to a decimal: 2 75 = 37.5 . The final answer is 37.5 or 37 2 1 .
Explanation
Understanding the Problem We are asked to multiply a mixed number, 7 2 1 , by an integer, 5.
Converting to an Improper Fraction First, we convert the mixed number 7 2 1 to an improper fraction. To do this, we multiply the whole number part (7) by the denominator (2) and add the numerator (1), then put the result over the original denominator (2): 7 2 1 = 2 7 × 2 + 1 = 2 14 + 1 = 2 15 .
Multiplying the Fractions Next, we multiply the improper fraction 2 15 by 5: 2 15 × 5 = 2 15 × 5 = 2 75 .
Converting Back to a Mixed Number Finally, we convert the improper fraction 2 75 back to a mixed number. To do this, we divide 75 by 2. The quotient is the whole number part, and the remainder is the numerator of the fractional part. 75 ÷ 2 = 37 with a remainder of 1 .So, 2 75 = 37 2 1 .
Converting to a Decimal Alternatively, we can express the improper fraction 2 75 as a decimal by dividing 75 by 2: 2 75 = 37.5 .
Examples
Understanding multiplication of mixed numbers is crucial in everyday scenarios, such as calculating cooking ingredient quantities. For instance, if a recipe calls for 7 2 1 cups of flour and you want to make 5 times the recipe, you need to calculate 7 2 1 × 5 to determine the total amount of flour needed. This skill ensures accurate measurements and successful cooking outcomes. It also applies to scaling other types of measurements in various practical situations.
