Work out $3 \div \frac{17}{4}$. Give your answer in its simplest form.
Answer (2)
To divide 3 by 4 17 , multiply 3 by the reciprocal of 4 17 , which is 17 4 .
Multiply the numerators: 3 × 4 = 12 .
Keep the denominator as 17, resulting in the fraction 17 12 .
The fraction 17 12 is already in its simplest form, so the final answer is 17 12 .
Explanation
Understanding the Problem We need to divide the number 3 by the fraction 4 17 . The answer should be given in its simplest form.
Dividing by a Fraction To divide by a fraction, we multiply by its reciprocal. So, we need to calculate 3 ÷ 4 17 . This is the same as 3 × 17 4 .
Multiplying by the Reciprocal Now, we multiply the numerator: 3 × 4 = 12 . The denominator remains 17. So, the result is 17 12 .
Simplifying the Fraction Finally, we check if the fraction 17 12 can be simplified. The factors of 12 are 1, 2, 3, 4, 6, and 12. The number 17 is a prime number, so its only factors are 1 and 17. Since 12 and 17 have no common factors other than 1, the fraction is already in its simplest form. Therefore, the answer is 17 12 .
Final Answer The result of dividing 3 by 4 17 is 17 12 .
Examples
Fractions are used in everyday life, such as when baking, measuring ingredients, or splitting a bill with friends. For example, if you have 3 pizzas and want to divide them equally among 4 friends, each friend would get 4 3 of a pizza. Understanding how to divide by fractions helps in these real-world scenarios to ensure fair and accurate distribution.
To divide 3 by 4 17 , we multiply by its reciprocal, resulting in 3 × 17 4 = 17 12 , which is already in its simplest form. Hence, the answer is 17 12 .
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