$18.4 \frac{1}{2} \div 2 \frac{1}{4}$
Answer (1)
Convert mixed fractions to improper fractions: 4 2 1 = 2 9 and 2 4 1 = 4 9 .
Divide the improper fractions: 2 9 ÷ 4 9 = 2 .
Multiply the result by 18: 18 × 2 = 36 .
The final answer is 36 .
Explanation
Understanding the Expression We are asked to evaluate the expression 18 , 4 2 1 ÷ 2 4 1 . Let's assume that '18,' is a typo and should be interpreted as multiplication. Thus, the expression becomes 18 × ( 4 2 1 ÷ 2 4 1 ) .
Converting Mixed Fractions to Improper Fractions First, we need to convert the mixed fractions to improper fractions. We have: 4 2 1 = 4 + 2 1 = 2 8 + 2 1 = 2 9 2 4 1 = 2 + 4 1 = 4 8 + 4 1 = 4 9
Dividing the Improper Fractions Now, we divide the improper fractions: 2 9 ÷ 4 9 = 2 9 × 9 4 = 2 × 9 9 × 4 = 18 36 = 2
Multiplying by 18 Finally, we multiply the result of the division by 18: 18 × 2 = 36
Final Answer Therefore, the value of the expression 18 , 4 2 1 ÷ 2 4 1 is 36.
Examples
Understanding fraction division is crucial in many real-life scenarios, such as scaling recipes. For instance, if a recipe calls for 2 4 1 cups of flour and you only want to make half the recipe, you would divide 2 4 1 by 2. Similarly, if you have 18 batches of cookies to bake and each batch requires 4 2 1 ÷ 2 4 1 cups of sugar, calculating the total sugar needed involves multiplying 18 by the result of the division, which is 36 cups of sugar.
