$4 \frac{1}{2} \div \frac{21}{4}$
Answer (1)
Convert the mixed number to an improper fraction: 4 2 1 = 2 9 .
Rewrite the division as multiplication by the reciprocal: 2 9 ÷ 4 21 = 2 9 × 21 4 .
Multiply the fractions: 2 9 × 21 4 = 42 36 .
Simplify the fraction: 42 36 = 7 6 . The final answer is 7 6 .
Explanation
Understanding the Problem We are given the expression 4 2 1 ÷ 4 21 and we need to evaluate it. This involves dividing a mixed number by a fraction.
Converting to Improper Fraction First, we convert the mixed number 4 2 1 to an improper fraction. To do this, we multiply the whole number 4 by the denominator 2 and add the numerator 1, then place the result over the original denominator 2:
4 2 1 = 2 4 × 2 + 1 = 2 8 + 1 = 2 9
So, the expression becomes 2 9 ÷ 4 21 .
Rewriting as Multiplication Next, we rewrite the division as multiplication by the reciprocal of the second fraction. The reciprocal of 4 21 is 21 4 . Thus, we have:
2 9 ÷ 4 21 = 2 9 × 21 4 .
Multiplying the Fractions Now, we multiply the two fractions:
2 9 × 21 4 = 2 × 21 9 × 4 = 42 36 .
Simplifying the Fraction Finally, we simplify the resulting fraction to its lowest terms. Both the numerator and the denominator are divisible by 6:
42 36 = 42 ÷ 6 36 ÷ 6 = 7 6 .
Therefore, 4 2 1 ÷ 4 21 = 7 6 .
Final Answer The result of the division is 7 6 .
Examples
In baking, if a recipe calls for 4 2 1 cups of flour and you only want to make 4 21 of the recipe, you would calculate 4 2 1 ÷ 4 21 to find out how many cups of flour you need. This calculation ensures you maintain the correct proportions for a smaller batch. Understanding fraction division is crucial for scaling recipes accurately.
