$\frac{4}{6} \div \frac{3}{12}$
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 by dividing both numerator and denominator by their greatest common divisor (GCD), which is 6: 18 48 = 3 8 .
The final answer 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 by finding the greatest common divisor (GCD) of 48 and 18. The GCD of 48 and 18 is 6. We divide both the numerator and the denominator by 6: 18 48 = 18 ÷ 6 48 ÷ 6 = 3 8
Final Answer The simplified fraction is 3 8 . We can also express this as a mixed number or a decimal. As a mixed number, it is 2 3 2 . As a decimal, it is approximately 2.67. Therefore, the final answer is 3 8 .
Examples
Fractions are used in everyday life, such as when baking, measuring ingredients, or splitting a pizza. Understanding how to divide fractions is essential for accurately scaling recipes or determining how much of a resource each person gets when dividing it equally. For example, if you have 6 4 of a pizza and want to divide it among 12 3 of your friends, you would use the above calculation to determine how much pizza each friend receives. The result, 3 8 , means each 'fraction of a friend' gets 3 8 of the pizza.
To solve 6 4 ÷ 12 3 , we multiply by the reciprocal to get 6 4 × 3 12 = 18 48 , which simplifies to 3 8 . The final answer is 3 8 .
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