Step by step
Estimate with 50% first
Before solving 45% of 36, Mr DJ thinks about 50% of 36. 50% is 50 per 100, which is half, and half of 36 is 18. So 45% of 36 should be a little under 18.
▶ Watch this step 0:02Find 10% by moving the decimal
10% of a number is 1/10 of it, one part out of 10. Because our number system is base 10, dividing by 10 just moves the decimal one spot to the left. So 10% of 36 is 3.6.
▶ Watch this step 0:44Find 5% as half of 10%
45% is 10% + 10% + 10% + 10% + 5%. Write 3.6 four times for the four 10% pieces. 5% of 36 is half of 3.6, which is 1.8.
▶ Watch this step 1:27Add the pieces together
Add 3.6 + 3.6 + 3.6 + 3.6 + 1.8 to get 16.2, so 45% of 36 is 16.2 (or 16 2/10). Another way: 50% of 36 is 18 and 5% is 1.8, so 45% is 18 − 1.8 = 16.2.
▶ Watch this step 1:49Find 1% with two hops
For 32% of 120, use 10% + 10% + 10% + 1% + 1%. 10% of 120 is 12. 1% means dividing by 10 and by 10 again (dividing by 100), so move the decimal two hops: 1% of 120 is 1.2. Then 12 + 12 + 12 + 1.2 + 1.2 = 38.4.
▶ Watch this step 2:31Start from 100% for percents over 100
100% of any number is itself, so 100% of 160 is 160. For 102% of 160, add two 1% pieces: 1% of 160 is 1.6, so 160 + 1.6 + 1.6 = 163.2. That makes sense, because 102% should be a little more than 160.
▶ Watch this step 4:01Stack 100% pieces for 205%
For 205% of 80, use 100% + 100% + 5%. Two 100% pieces give 80 + 80 = 160. 10% of 80 is 8, so 5% is 4. Then 160 + 4 = 164.
▶ Watch this step 5:27
“100% of any number is itself.”
Worked example · with Digit the Fox
Try one more, step by step
Problem: What is 35% of 48?
- Estimate: 50% of 48 is 24, so 35% should be less than 24.
- Break it up: 35% = 10% + 10% + 10% + 5%.
- 10% of 48: move the decimal one spot to get 4.8.
- Three 10% pieces: 4.8 + 4.8 + 4.8 = 14.4.
- 5% is half of 10%: half of 4.8 is 2.4.
- Add: 14.4 + 2.4 = 16.8.
Answer: 35% of 48 is 16.8.
Check: 16.8 is less than 24 (50% of 48), so the answer makes sense.
Common mistakes
- Getting an answer less than 160 for 102% of 160. 100% of any number is itself, so anything over 100% must be more than the starting number. Start with 160 and add the extra 1% pieces.
- Moving the decimal only one spot for 1% and writing 1% of 120 as 12. One hop gives 10%. 1% takes two hops (divide by 100), so 1% of 120 is 1.2.
- Writing 5% of 36 as 5 instead of working it out. Find 10% first, then cut it in half. 10% of 36 is 3.6, so 5% is 1.8.
- For 205% of 80, adding only one 80 and getting 84. 205% is 100% + 100% + 5%, so you need two full 80s: 80 + 80 + 4 = 164.
Questions
What is 45% of 36?
45% of 36 is 16.2. Find 10% of 36 (3.6) four times and 5% of 36 (1.8) once, then add them. You can also take 50% of 36, which is 18, and subtract 5%: 18 − 1.8 = 16.2.
How do you find 1% of a number?
Divide by 100 by moving the decimal two spots to the left. Mr DJ calls it two hops: 1% of 120 is 1.2 and 1% of 160 is 1.6.
Read the full transcript
0:02 Welcome back to Math with Mr. DJ. Today, in this video, we are going to talk about how to find the percent of a number. Let's start off with what is 45% of 36? What is 50% of 36? Well, that's half, right? 50% is 50 per 100, so that's half of 36. Half of 36 is 18. So, if we're looking for 45% of 36, we need to think about a number that's a little under 18 if we were estimating, thinking about our answer. A strategy that you could use to find 45% of 36 is what I like to call the the 10 5 1% rule. If you know to how to find 10% of a number, you can find 1% of a number, and you can
0:47 find 5% of a number. So, remember, 10% of a number is just 1/10 of that number. So, one part out of 10 of 36. And because our number system is in base 10, 1/10 of a number is just moving the decimal over one spot. So, for example, in the number 36, you're just simply moving it over one spot because you're dividing that number by 10. 36 broken up into 10 parts is 3.6. Okay, so if you know how to find 10% of a number, 10% of 36 is equal to 3.6. So, you can do another 10% = 3.6,
1:35 and then another 10% of 36 = 3.6, and we can do another 10% that's of 36 = 3.6. 5% of 36 5% of 36 is half of 3.6, which is 1.8. So, now we We have to add all of that together. 16.2 or 16 and 2/10. 45% of 36 is 16.2 or 16 and 2/10. Another strategy that I've seen students do instead of doing the 10% 10% 10% 10% 5% you could say, "Well, you know that 50% of 36 is 18
2:20 and you know 5% of 36 is 1.8. So, 45% must be the 50% minus that 5%. So, you could do 18 minus 1.8 and that would give you 16.2 or 16 and 2/10. All right, let's move on to the next one. What is 32% of 120? Now again, think about what is 10% 5% 1%? So, we're trying to find 32% of 120. So, I'm going to do 10% 10% 10% 1% 1%. 10% of 120. 10% of 120 would be 12. Okay, we need three of those. So, we need another 10% is 12. Another
3:06 10% of 120 is 12. So, that's 10% 10% 10%. That's 30% so far. But now, how do I find 1% of 120? Well, 1% of 120 is just two hops to the left cuz it's divided by 10 divided by 10 or divided by 100. So, we're just moving it over one more spot to find 1%. 1.2. And then we need one more 1%. 1.2. Now, we have to add all this up. What is 32% of 120? Well, it's 38.4 or 38 and 4/10. Because we found 10% 10% 10% 1% 1%. That's 32% of 120. All right, let's move
3:51 on to the next one, problem number three. What is 102% of 160? For this problem, you're asking for what is a number greater than 100% of 160 here. So, what is 102% of 160? What's 100% of 160, right? Or what's 100% of any number? 100% of any number is itself. 100% of 160 is 160. So, we're looking for 102% of 160. So, we need to figure out what is 1% of 160, double that, and add that to 160. So, we know how to do that cuz we know the 10 5 1, 10%, 5%, 1%. So, 1% of 160
4:39 is equal to Let's see here. Remember the decimals right here, even though we can't see it. Now, we move it over one spot, that's 10% of 160. So, 1% is divided by another 10, it'd be 1.6. Okay? Now, we need to find another 1% of 160 cuz we're looking for 102% in all equals 1.6. We're doing 100% of 160, then we're doing 1% of 160, and then another 1% of 160, and we're adding that all together. 102% of 160 is 163.2 or 163 and 2/10, which makes sense because 100% of 160 is 160. So, 102% of 160 is a little bit more
5:27 than 160, and 163 and 2/10 is a little bit more than 160. Our answer makes sense. All right, let's move on to the fourth problem. Let's keep going. The fourth problem is what is 205% of 80? So, remember, 100% of 80 equals 80. We're looking for 205% of 80. So, another 100% of 80 is 80. So, so far that's 200% of 80, which would be 80 + 80, which is 160. So, we know 200% of 80 is 160. So, we're looking for now 205%. Well, what is 10% of 80? 10% Knowing 10% of 80 will help us find 5% of 80, cuz we can just cut that number in half. So, 10% of 80 is just going to be moving
6:12 the decimal over one spot. So, 10% of 80 is 8, because 8 is one part out of 10 parts of 80. If 10% of 80 is 8, that means 5% of 80 must equal 4. And 100% + 100% + 5% that's 205%. We just add all of this up. We get 80 + 80 is 160 + 4, 164. So, what is 205% of 80? It is 164. Awesome. If you found value in this video, please take a moment and share it with your friends. And don't forget to like and subscribe, and we'll see you in the next video. Thank you so much.
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