\frac{4}{6} \div \frac{3}{12}
Answer (2)
Rewrite the division as multiplication by the reciprocal: 6 4 ÷ 12 3 = 6 4 × 3 12 .
Multiply the fractions: 6 4 × 3 12 = 18 48 .
Simplify the fraction: 18 48 = 3 8 .
The final answer is 3 8 .
Explanation
Rewrite the division as multiplication We are asked to evaluate the expression 6 4 ÷ 12 3 . Dividing by a fraction is the same as multiplying by its reciprocal. So, we can rewrite the expression as 6 4 × 3 12 .
Multiply the fractions Now, we multiply the fractions: 6 4 × 3 12 = 6 × 3 4 × 12 = 18 48 .
Simplify the fraction Next, we simplify the fraction. Both the numerator and the denominator are divisible by 6: 18 48 = 18 ÷ 6 48 ÷ 6 = 3 8 .
Final Result The simplified fraction is 3 8 . This can also be written as a mixed number: 2 3 2 .
Examples
Understanding fraction division is crucial in many real-life scenarios. For instance, if you're baking and need to divide a certain amount of flour into equal portions for multiple recipes, knowing how to divide fractions helps you determine the exact quantity to use for each recipe. Similarly, in construction or engineering, dividing materials or resources often involves fractional quantities, making this skill essential for accurate calculations and efficient resource allocation. This concept is also applicable in financial contexts, such as splitting investments or calculating proportions of profits or losses.
To solve 6 4 ÷ 12 3 , rewrite it as 6 4 × 3 12 and multiply to get 18 48 . Simplifying gives 3 8 , which can also be expressed as 2 3 2 .
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