Calculate $1 \div \frac{5}{7}$. Give your answer as a fraction in its lowest terms.
Answer (2)
To divide by a fraction, multiply by its reciprocal: 1 ÷ 7 5 = 1 × 5 7 .
Multiply: 1 × 5 7 = 5 7 .
The fraction is already in its lowest terms.
The final answer is 5 7 .
Explanation
Understanding the Problem We are asked to calculate 1 ÷ 7 5 and express the answer as a fraction in its lowest terms.
Dividing by a Fraction To divide by a fraction, we multiply by its reciprocal. The reciprocal of 7 5 is 5 7 . Therefore, 1 ÷ 7 5 = 1 × 5 7 .
Calculating the Product Now, we calculate the product: 1 × 5 7 = 5 7 .
Final Answer The fraction 5 7 is already in its lowest terms because 7 and 5 are both prime numbers, and they do not share any common factors other than 1. Therefore, the final answer is 5 7 .
Examples
Imagine you have one pizza, and you want to divide it into slices that are each 5/7 of the whole pizza. How many slices would you have? This problem is equivalent to calculating 1 ÷ 7 5 , which tells you how many 5/7 portions are in one whole pizza. The answer, 7/5, means you would have one whole slice (5/7 of the pizza) and 2/7 of the pizza left over, which is 2/5 of another slice. This kind of calculation is useful in cooking, baking, and any situation where you need to divide a whole into fractional parts.
To calculate 1 ÷ 7 5 , you multiply by the reciprocal of the fraction, resulting in 5 7 . This fraction is already in its lowest terms. So, the final answer is 5 7 .
;
