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FutureStarr4 3 Squared As a Fraction
What makes a quantitative analysis work? In this blog post, we explore the components of a quantitative analysis and the differences between it and qualitative analysis in order to better understand the ways in which data can inform our decision-making process.
Unlike adding and subtracting integers such as 2 and 8, fractions require a common denominator to undergo these operations. One method for finding a common denominator involves multiplying the numerators and denominators of all of the fractions involved by the product of the denominators of each fraction. Multiplying all of the denominators ensures that the new denominator is certain to be a multiple of each individual denominator. The numerators also need to be multiplied by the appropriate factors to preserve the value of the fraction as a whole. This is arguably the simplest way to ensure that the fractions have a common denominator. However, in most cases, the solutions to these equations will not appear in simplified form (the provided calculator computes the simplification automatically). Below is an example using this method.
Let's go through more exponent examples. So to warm up, let's think about taking a fraction to some power. So let's say I have 2/3, and I want to raise it to the third power here. Now, we've already learned there are two ways of thinking about this. One way is to say let's take three 2/3's. So that's one 2/3, two 2/3's, and three 2/3's. So that's one, two, three, 2/3. And then we multiply them. And we will get-- let's see, the numerator will be 2 times 2 times 2, which is 8. And the denominator's going to be 3 times 3 times 3 times 3, which is equal to 27. Now, the other way of viewing this is you start with a 1, and you multiply it by 2/3 three times. So you multiply by 2/3 once, twice, three times. You will get the exact same result here. So let's do one more example like that. So lets say I had 4/9, and I want to square it. When I raise something to the second power, people often say, you're squaring it. Also, raising something to the third power, people sometimes say, you're cubing it. But let's raise 4/9 to the second power. Let's square it. And I encourage you to pause the video and work this out yourself. Well, once again, you could view this as taking two 4/9's and multiplying them. Or you could view this as starting with a 1, and multiplying it by 4/9 two times. Either way, your numerator is going to be 4 times 4, which is 16. And your denominator is going to be 9 times 9, which is equal to 81. (Source: www.khanacademy.org)