Complete the following multiplication and division calculations involving fractions (show all the steps).
4.1.1. [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 (6): 18 ÷ 6 48 ÷ 6 = 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 need to rewrite the division as a multiplication.
Find the reciprocal The reciprocal of 12 3 is 3 12 . Therefore, the expression becomes 6 4 × 3 12 .
Multiply fractions Now, we multiply the numerators and the denominators: 6 4 × 3 12 = 6 × 3 4 × 12 = 18 48
Simplify 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 ÷ 6 48 ÷ 6 = 3 8
Convert to mixed number (optional) The fraction 3 8 is an improper fraction, which means the numerator is greater than the denominator. We can convert it to a mixed number by dividing 8 by 3. 8 divided by 3 is 2 with a remainder of 2. So, 3 8 = 2 3 2 . However, the question does not ask for a mixed number, so we can leave the answer as an improper fraction.
Final Answer Therefore, the final answer is 3 8 .
Examples
Fractions are used in everyday life, such as when cooking, baking, or measuring ingredients. For example, if a recipe calls for 2 1 cup of flour and you only want to make half of the recipe, you would need to divide 2 1 by 2, which is the same as multiplying 2 1 by 2 1 , resulting in 4 1 cup of flour. Understanding how to divide fractions is essential for accurately adjusting recipes and measurements.
To calculate 6 4 ÷ 12 3 , we rewrite the division as multiplication by the reciprocal, which gives us 6 4 × 3 12 = 18 48 . Simplifying 18 48 by dividing both terms by their greatest common divisor (6) results in 3 8 .
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