$3 \div \frac{2}{7}$
Answer (2)
To divide by a fraction, multiply by its reciprocal.
Rewrite the division as 3 × 2 7 .
Multiply to get 2 21 .
Simplify to get the final answer: 10.5 .
Explanation
Understanding the Problem We are asked to divide the number 3 by the fraction 7 2 .
Dividing by a Fraction To divide by a fraction, we multiply by its reciprocal. The reciprocal of 7 2 is 2 7 . Therefore, we need to calculate 3 ÷ 7 2 = 3 × 2 7 .
Performing the Multiplication Now, we multiply 3 by 2 7 : 3 × 2 7 = 2 3 × 7 = 2 21 .
Simplifying the Result To express the improper fraction 2 21 as a mixed number or decimal, we divide 21 by 2. 2 21 = 10.5 .
Final Answer Therefore, 3 ÷ 7 2 = 10.5 .
Examples
Understanding division by fractions is essential in many real-life scenarios. For example, if you have 3 cups of flour and a recipe requires 7 2 of a cup of flour per batch of cookies, you can determine how many batches of cookies you can make. In this case, you can make 10.5 batches of cookies. This concept is also useful in scaling recipes, calculating proportions, and understanding ratios in various fields like cooking, construction, and engineering.
To divide 3 by 7 2 , multiply by its reciprocal, resulting in 3 × 2 7 which equals 2 21 and simplifies to 10.5. Therefore, the final answer is 10.5.
;
