[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 numerators and denominators: 6 × 3 4 × 12 = 18 48 .
Simplify the fraction by dividing both numerator and denominator by their greatest common divisor (GCD), which is 6: 18 ÷ 6 48 ÷ 6 = 3 8 .
The final simplified fraction 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 the division 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 numerators and the denominators: 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 . This is an improper fraction, which means the numerator is greater than the denominator. We can leave the answer as an improper fraction or convert it to a mixed number. In this case, we leave it as an improper fraction. Therefore, the final answer is 3 8 .
Examples
Fractions are used in everyday life, such as when cooking, measuring ingredients, or splitting a bill with friends. Understanding how to divide fractions is essential for accurately scaling recipes or determining individual shares. For example, if you have 6 4 of a pizza and want to divide it equally among 12 3 of your friends, you need to perform the division 6 4 ÷ 12 3 to find out how much pizza each friend gets.
To solve 6 4 ÷ 12 3 , we rewrite it as multiplication by the reciprocal, resulting in 3 8 after simplification. The key steps involved multiplying the fractions and then simplifying the result. The final answer is 3 8 .
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