The simplicity of basic arithmetic operations can sometimes lead to confusion, especially when dealing with fractions and division. A question like "2 divided by 2/7" might seem straightforward at first glance, but it requires a clear understanding of mathematical operations and the order in which they should be performed.
In this article, we will delve into the explanation of how to solve "2 divided by 2/7," covering the fundamental concepts of division, fractions, and the order of operations. Additionally, we will provide practical examples and step-by-step solutions to make the concept more accessible.
Understanding the Basics
Before diving into the problem, let's quickly review the basics of fractions and division. A fraction is a way to express a part of a whole as a ratio of two numbers. For example, 2/7 represents two equal parts out of a total of seven parts. Division, on the other hand, is the operation of splitting a quantity into equal parts or groups.
Division of Fractions
When dividing by a fraction, it's essential to remember that division is the inverse operation of multiplication. To divide by a fraction, we multiply by its reciprocal. The reciprocal of a fraction is obtained by swapping its numerator and denominator. For instance, the reciprocal of 2/7 is 7/2.
Solving the Problem
Now, let's solve the problem step by step:
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Understanding the Division: The problem asks us to divide 2 by 2/7. To do this, we need to find the reciprocal of 2/7, which is 7/2.
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Multiplying by the Reciprocal: We then multiply 2 by the reciprocal of 2/7, which is 7/2. This can be written as 2 * (7/2).
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Simplifying the Expression: Multiplying 2 by 7/2 simplifies to (2 * 7) / 2. Following the order of operations, we first multiply 2 by 7 to get 14, and then divide by 2.
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Final Calculation: The final calculation is 14 / 2, which equals 7.
Gallery of Division Examples
Frequently Asked Questions
What is the reciprocal of a fraction?
+The reciprocal of a fraction is obtained by swapping its numerator and denominator. For example, the reciprocal of 2/7 is 7/2.
Why do we multiply by the reciprocal when dividing by a fraction?
+Multiplying by the reciprocal is essentially the same as dividing, but it makes the calculation simpler and follows the rules of arithmetic operations.
Can you give an example of dividing a number by a fraction?
+Yes, for instance, 4 divided by 1/2 is the same as 4 multiplied by 2/1, which equals 8.
Summary and Final Thoughts
In conclusion, solving "2 divided by 2/7" involves understanding the basics of fractions and division, recognizing the need to multiply by the reciprocal of the fraction, and performing the arithmetic operations in the correct order. By grasping these fundamental concepts, readers can confidently tackle more complex mathematical problems and deepen their understanding of arithmetic operations.