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Number Sense and Percents


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, I realize this might be very anti-intuitive to folks who don't like math that much.

Math is, 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. Once you start noticing enough patterns, then 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.

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 may be a brand new way of thinking. And I'll just say, if what I'm showing in this video is 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 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.

Sometimes it also helps to find 1% of the whole. So I'll 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 8 of those.

8 times 20 is 160, so that must be 80% of 200. 240 is 30% of what number? Well, here's how I'd think about it. If 30% is 240, we can divide this by 3 to get 10%. So 240 divided by 3 is 80. That's 10%.

Well clearly, if that's one-tenth, then the whole thing should be 800. Notice that all of these are things 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're dealing with less than 10%. 1% of 800 is 8.

We need seven of this last piece. So, 7 times 8 is 56, that means we're dealing with 7% of 800. Again, everything here we can do without a calculator. 55% of 400. Here we're 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, plus 5% is 55%, and so 20 plus 200, that gives us 220.

And that has to be 55% of 400. 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 three of the first, and seven 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 something 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.

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