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Video: Finding the Whole given Its Percentage and the Part

Kathryn Kingham

Fill in the missing value: 50% of _ is 60.

03:07

Video Transcript

Fill in the missing value: 50 percent of some number equals 60.

Let’s start by taking this problem and representing it algebraically; I’ll show you what that means. 50 percent is gonna stay exactly how it is. In math, we can translate the word “of” as multiplication. A missing number, a number that we don’t know the value of, is usually represented by a variable. I chose 𝑚 because it’s the missing value. We can translate the word “is” into an equal sign and bring down 60 exactly how it is.

We now need to turn our percentage into either a decimal or a fraction in order to operate with it. We can turn 50 percent into a fraction of 50 over 100, which reduces even further into one-half. Now I have an equation we can work with. When solving for a variable, we wanna isolate that variable; we wanna get it by itself on one side of the equal sign. So here, we’re multiplying 𝑚 by one-half. I can isolate 𝑚 — get it by itself — by multiplying one-half times two or two over one on both sides. If I multiply one-half by two on the left side of the equation, one-half times two equals one. So we’re just left with 𝑚 times one; 𝑚 times one equals 𝑚.

Now for the right side of the equation, I need to keep my equation balanced, so I multiply it by two on both sides. 60 times two over one equals 120. This means our missing value equals 120. How can I check if this is true or not? We can now check, does 60 over 120 equal 50 percent? Does 60 over 120 equal one-half? If I divide my numerator and my denominator by 60, 60 divided by 60 equals one; 120 divided by 60 equals two. And one-half equals 50 percent. So yes, 60 divided by 120 equals 50 percent. Our missing value is 120.