(b) [tex]$10 \frac{3}{8} \times 3 \frac{1}{9}$[/tex]
Answer (1)
Convert the mixed numbers to improper fractions: 10 8 3 = 8 83 and 3 9 1 = 9 28 .
Multiply the improper fractions: 8 83 × 9 28 = 72 2324 .
Convert the resulting improper fraction back to a mixed number: 72 2324 = 32 72 20 .
Simplify the mixed number: 32 72 20 = 32 18 5 . The final answer is 32 18 5 .
Explanation
Problem Analysis We are asked to multiply two mixed numbers: 10 8 3 and 3 9 1 . To do this, we will first convert each mixed number to an improper fraction. Then, we will multiply the two improper fractions, and finally, convert the result back to a mixed number.
Converting to Improper Fraction First, convert the mixed number 10 8 3 to an improper fraction. To do this, we multiply the whole number part (10) by the denominator (8) and add the numerator (3). This gives us 10 × 8 + 3 = 80 + 3 = 83 . So, 10 8 3 = 8 83 .
Converting to Improper Fraction Next, convert the mixed number 3 9 1 to an improper fraction. We multiply the whole number part (3) by the denominator (9) and add the numerator (1). This gives us 3 × 9 + 1 = 27 + 1 = 28 . So, 3 9 1 = 9 28 .
Multiplying Improper Fractions Now, we multiply the two improper fractions: 8 83 × 9 28 = 8 × 9 83 × 28 = 72 2324
Converting Back to Mixed Number Now, we convert the improper fraction 72 2324 back to a mixed number. To do this, we divide 2324 by 72. 2324 ÷ 72 = 32 with a remainder of 20 So, 72 2324 = 32 72 20 . We can simplify the fraction 72 20 by dividing both the numerator and the denominator by their greatest common divisor, which is 4. So, 72 20 = 72 ÷ 4 20 ÷ 4 = 18 5 . Therefore, 72 2324 = 32 18 5 .
Final Answer Therefore, 10 8 3 × 3 9 1 = 32 18 5 .
Examples
Mixed number multiplication is useful in everyday situations, such as when you're scaling a recipe. For example, if a recipe calls for 2 2 1 cups of flour and you want to triple the recipe, you would multiply 2 2 1 by 3. This is the same as multiplying 2 5 by 3, which equals 2 15 or 7 2 1 cups of flour. Understanding mixed number multiplication helps ensure accurate measurements and successful cooking outcomes.
