[tex]\frac{4}{6} \div \frac{3}{12}[/tex]
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 by dividing both numerator and denominator by their greatest common divisor (6): 18 48 = 3 8 .
The final result is 3 8 .
Explanation
Understanding the Problem We are asked to evaluate the expression 6 4 ÷ 12 3 . This involves dividing one fraction by another.
Rewriting as Multiplication Dividing by a fraction is the same as multiplying by its reciprocal. The reciprocal of 12 3 is 3 12 . Therefore, we can rewrite the expression as a multiplication: 6 4 ÷ 12 3 = 6 4 × 3 12
Multiplying the Fractions Now, we multiply the two fractions: 6 4 × 3 12 = 6 × 3 4 × 12 = 18 48
Simplifying the Fraction Next, we simplify the fraction 18 48 . Both 48 and 18 are divisible by 6. Dividing both the numerator and the denominator by 6, we get: 18 ÷ 6 48 ÷ 6 = 3 8
Final Result The simplified fraction is 3 8 . We can also express this as a mixed number: 3 8 = 2 3 2 Thus, the result of the division is 3 8 or 2 3 2 .
Examples
Fractions are used in everyday life, such as when cooking, baking, or measuring ingredients. For example, if a recipe calls for 4 3 cup of flour and you only want to make half the recipe, you need to divide 4 3 by 2, which is the same as multiplying by 2 1 . This gives you 4 3 × 2 1 = 8 3 cup of flour. Understanding how to divide fractions is essential for adjusting recipes and other real-world measurements.
To divide the fractions 6 4 ÷ 12 3 , we multiply by the reciprocal of the second fraction, resulting in 18 48 . Simplifying this gives 3 8 or 2 3 2 . Thus, the final result is 3 8 .
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