How to Find 1/2 of 2/3

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  • 0:02 Steps to Solve
  • 1:07 Checking Your Work
  • 2:50 Real-Life Applications
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Lesson Transcript
Instructor: Laura Pennington

Laura received her Master's degree in Pure Mathematics from Michigan State University. She has 15 years of experience teaching collegiate mathematics at various institutions.

Let's examine how to find 1/2 of 2/3. In doing so, we'll see how to find 1/2 of a number in general. We'll also look at how to check our work and a couple of practical applications for this particular problem.

Steps to Solve

We want to find 1/2 of 2/3. There are two ways we can look at this problem. First, we want to split the fraction into two equal parts, or divide it by 2. The steps for this method involve dividing 2/3 by 2 and then simplifying as shown:

one half 1

The second way to look at this problem involves understanding that dividing a number by 2 is the same as multiplying it by 1/2. If we want to find 1/2 of 2/3 we can multiply 2/3 by 1/2. To multiply fractions, first multiply the numerators together and then multiply the denominators together. Then, simplify as shown:

one half 2


In both of our solving methods, we see that 1/2 of 2/3 is 1/3.

Checking Your Work

If we want to make sure that our calculations are correct, we can check our work using the fact that multiplication and division are opposites of each other. In a way, they undo each other. For instance, if we divide 15 by 5 to get 3, we can undo the operation by multiplying 3 by 5 to get 15. In general, the following two facts allow us to check our work in both of our solving methods.

  1. If a * b = c and a and b are not equal to 0, then c / a = b and c / b = a
  2. If r / s = t, then r = ts

If we choose to find 1/2 of 2/3 by multiplying 2/3 by 1/2, we have that 1/2 * 2/3 = 1/3. We can use the first fact to check this. Since 1/2 * 2/3 = 1/3, it should be the case that 1/3 divided by 2/3 gives 1/2 and that 1/3 divided by 1/2 gives 2/3. To divide fractions, we multiply the numerator by the reciprocal of the denominator, where the reciprocal of a number just interchanges the numerator and denominator of the number.

one half 3

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