# Number Sense and Percents

What is number sense and do you have it? How does this relate to percents? We’ll explore this and other questions in the below video. After you’ve mastered this, be sure to check out our other informative math videos!

## Number Sense Defined

Number sense is intuition for numbers and the patterns of arithmetic. It cannot be simply summarized and taught, it’s a collection of pattern-matching skills that you have to acquire over time. One usually gains number sense from playing with numbers and noticing patterns. Now this might be very anti-intuitive to folks who don’t like math that much.

Image by Bent Chang

If you view math as a chore, why on earth would you play with it? But you really have to get curious about math and curious about the patterns to notice these patterns. When you start noticing enough patterns, you can start using them to your advantage. So I’m gonna talk about one relatively simple pattern that you can use in this video.

## Handling Percents Using Number Sense

This method for handling percents involves using number sense. It takes a little bit of logic and creativity, but once you’re used to it, it’s considerably more efficient. Some folks will regard this approach as easy and obvious. While for other folks, this maybe a brand new way of thinking. What I’m showing in this video may be completely obvious to you.

Don’t even feel compelled to watch all the way through to the end of the video, just skip to the summary, and make sure you understand. Meanwhile, if what I’m showing here is brand new to you and you’ve never thought of this way before, you might have to watch this video a few times to really get the hang of what I’m saying here. The beginning suggestion, start thinking about 10% of the whole and work from there, sometime it also helps to find 1% of the whole.

## Problem 1

Image by ImageFlow

So work through some of the problems that appeared in the last video. What is 80% of 200? Well, one way to think about this, certainly, 10% of 200 is clearly 20. We want eight of those, 8 times 20 is 160, so that must be 80% of 200. 240 is 30% of what number? Well here is how I’d think about it.

If 30% is 240, we could divide this by 3 to get 10%. So 240 divided by 3 is 80. That’s 10%. Well clearly, if that’s 110th then the whole thing should be 800. Notice that all of these are things that we can do without a calculator. 56 is what percent of 800? Well first of all 10% of 800 is 80, we know 56 is less than that.

So we know we are dealing with less than 10%, 1% of 800 is 8, we need 7 of this last piece. So 7 times 8 is 56. That means we are dealing with 7% of 800. Again, everything here we can do without a calculator. 55% of 400, here we gonna take a clever shortcut. Certainly we know 50% of 400, well that’s 200.

That’s just half of 400, that has to be 200. Well, divide that by 10, 5% of 400 has to be 20. Well, now we can add those two, 50% plus 5% is 55%, and so 20 plus 200, that gives 220 and that has to be 55% of 400.

## Problem Two

Here’s another one, 37% of 700 You don’t even need a calculator for this, let’s just think about this. 10% that’s 70, 1% that’s 7, I can do that in my head. Well, we need 3 of the first and 7 of the second. Well 3 times 70 that’s 210, I can do that in my head. 7 times 7 that’s 49, I can do that in my head.

Then we just have to add those, that’s some I can do in my head, that’s 259. So we can do this entire calculation without a calculator.

Practice these, these are more practice problems, no calculator allowed. See if you can use the number sense method to figure out all of these, and you can pause the video to work on it. And here are the answers.

In this video, we talked about a very efficient method of handling percents using number sense. The basic approach often involves finding 10% and sometimes 1% of the number.

## Author

• Mike served as a GMAT Expert at Magoosh, helping create hundreds of lesson videos and practice questions to help guide GMAT students to success. He was also featured as "member of the month" for over two years at GMAT Club. Mike holds an A.B. in Physics (graduating magna cum laude) and an M.T.S. in Religions of the World, both from Harvard. Beyond standardized testing, Mike has over 20 years of both private and public high school teaching experience specializing in math and physics. In his free time, Mike likes smashing foosballs into orbit, and despite having no obvious cranial deficiency, he insists on rooting for the NY Mets. Learn more about the GMAT through Mike's Youtube video explanations and resources like What is a Good GMAT Score? and the GMAT Diagnostic Test.