Quick! What's 17% of 50?
What if I told you it's the same as 50% of 17?
Many of us were taught that to find 17% of 50, we need to convert 17% into 0.17 and then multiply 0.17 x 50. This would be correct and lead us to the answer of 8.5. However, let's consider some other ways to think about the question because math typically has many ways to solve the same question. Sometimes you may find one of the other ways more efficient.
Let's break down the math behind solving the question 17% of 50:
Finding 17% of a number is the same as taking 17/100 or 0.17 of the number. It's going to end up making the number smaller because 17% of a number is a portion of that number.
As I mentioned above, to find 17% of 50, you would multiply 0.17 x 50. Let's remember what 0.17 is: it's 17 x 0.01, or 17 hundredths of one.
THE COMMUTATIVE PROPERTY OF MULTIPLICATION
The commutative property of multiplication says that you can reorder numbers that are being multiplied without affecting the answer. In other words, if I ask you 4 x 9, that's the same as 9 x 4. Or, if I ask you 4 x 9 x 2, that's the same as 2 x 9 x 4 and 9 x 4 x 2, for example.
So, back to the problem of 0.17 x 50. This is the same as 17 x 0.01 x 50 because 0.17 is equal to 17 hundredths, or 17 x 0.01.
Instead of ordering the numbers as 17 x 0.01 x 50, I could use the commutative property of multiplication and choose to order them as 0.01 x 50 x 17. Doing it this way, I could interpret the problem as 50 hundredths of 17.
50 hundredths is equal to 50%, which many of us know is equal to 1/2.
You can also think of 50 hundredths as 50/100, which is equivalent to 1/2. Either way, the problem is now asking for 1/2 of 17 or 50% of 17. The answer is 8.5. We saw this answer before by finding 17% of 50. Both are equal to 8.5!
USING REASONING SKILLS to solve problems
I don't know about you, but finding 1/2 of 17 feels a bit more friendly of a problem to me versus multiplying 0.17 x 50 with the standard algorithm. It just took a little reasoning to get the problem into something I liked a little better.
As a side note, there is yet another way to think of the problem 17% of 50 using reasoning skills and without multiplying 0.17 x 50! Based on what percentages mean, we know that 17% of 100 is 17. Therefore, 17% of 50 would have to be half of 17% of 100, which means half of 17, which is 8.5.
Of course, this helpful trick of 17% of 50 = 50% of 17 works EVEN BETTER when the numbers are even more friendly. For example, if the question asks to find 36% of 50, this is the same as asking 0.36 x 50 or 0.01 x 36 x 50 or 0.01 x 50 x 36, or 50% of 36, which is asking to find half of 36, so the answer is 18 and we're finished!
Unfortunately, the trick doesn't always help. If the question is something like 19% of 37, swapping wouldn't really make the question any easier. It works great when you recognize a number that can be easily turned into a "friendly percent", such as 50, 25, 20, or 10 because 50% = 1/2 of a number, 25% = 1/4 of a number, 20% = 1/5 of a number, and 10% = 1/10 of a number.
For example:
68% of 25 = 25% of 68 and that's the same as 1/4 of 68 = 17
95% of 10 = 10% of 95 and that's the same as 1/10 of 95 = 9.5
35% of 20 = 20% of 35 and that's the same as 1/5 of 35 = 7
Do you have any other ways of solving these questions on percents? I'm always open to hearing other approaches. Also, if your child is struggling with percents and can use some support, I'd be happy to help. Reach out with any questions.
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Melissa Agocs
melissa@learnwithme123.com