$4 \frac{1}{2} \div 2 \frac{1}{4}$
Answer (2)
Convert the mixed numbers to improper fractions: 4 2 1 = 2 9 and 2 4 1 = 4 9 .
Divide the first improper fraction by the second: 2 9 ÷ 4 9 = 2 9 × 9 4 .
Multiply the fractions: 2 9 × 9 4 = 18 36 .
Simplify the fraction: 18 36 = 2 . The final answer is 2 .
Explanation
Understanding the Problem We are asked to divide two mixed numbers: 4 2 1 and 2 4 1 .
Converting to Improper Fractions First, we convert the mixed numbers to improper fractions. 4 2 1 = 2 4 × 2 + 1 = 2 8 + 1 = 2 9 2 4 1 = 4 2 × 4 + 1 = 4 8 + 1 = 4 9
Dividing the Fractions Now, we divide the first improper fraction by the second improper fraction. This is equivalent to multiplying the first fraction by the reciprocal of the second fraction. 2 9 ÷ 4 9 = 2 9 × 9 4
Multiplying the Fractions Next, we simplify the resulting fraction: 2 9 × 9 4 = 2 × 9 9 × 4 = 18 36
Simplifying the Fraction Finally, we reduce the fraction to its simplest form: 18 36 = 2
Final Answer Therefore, 4 2 1 ÷ 2 4 1 = 2 .
Examples
Imagine you are baking a cake and the recipe calls for 4 2 1 cups of flour. You only have a measuring cup that holds 2 4 1 cups. Dividing 4 2 1 by 2 4 1 tells you how many times you need to fill the smaller measuring cup to get the required amount of flour. In this case, you would need to fill the 2 4 1 cup measuring cup exactly 2 times.
To find 4 2 1 ÷ 2 4 1 , convert each to improper fractions: 2 9 ÷ 4 9 . Multiplying by the reciprocal gives 18 36 , which simplifies to 2 .
;
