1. Multiplying by 10, 100, 1000, etc. If you want to multiply a number by 10, just add a 0 to its (right) end. So, 3726 x 10 = 37260. And 34255245 x 10 = 342552450. If you want to multiply by 100, you add two zeros to the end. 65 x 100 = 6500. If you want to multiply by one million, you add six zeros to the end. 200 x 1 million = 200 000 000.
2. Adding 9, 99, 999, etc. to a number We know that 9 = 10 - 1. Adding 10 is easy, and taking away 1 is easy, so we just do those two steps instead of adding 9. So, 3 + 9 is done in two stages. First, we add 10 to 3, to get 13. Next, we take away 1 from 13, to get 12. And that’s our answer, 3 + 9 = 12. This works for more complex sums as well. 653427 + 9 = (653427 + 10) - 1 = 653437 - 1 = 653436. Adding 99 is similar. We first add 100, and then take away 1. So, 352 + 99 sees us adding 100 to 352 first, to get 452. We then take 1 away from 452, to get 451 (our answer). If someone came to you and asked you to add 998 to 4532, you could first add 1000 to 4532 to get 5532. Then, you could take 2 away from 5532 (because 998 = 1000 - 2) to get 5530. This technique is incredibly versatile, and converts difficult addition sums to simple combinations of addition and subtraction.
3. Multiplying by 5 This is already quite easy to do by hand, but there’s a way that makes it even faster! We know that 5 = 10 / 2, so multiplying by 5 is the same as multiplying by 10, and then dividing by 2. Dividing by 2 is perhaps the easiest thing you can do with long division, and takes less time than it would have taken you to read this sentence. Let’s say you need to multiply 486 by 5. First, you multiply 486 by 10 to get 4860. You then divide 4860 to get 2430.
To quickly divide a number by 2 when all its digits are even, you just need to write down the quotients on division by 2 of each digit, from left to right. If you have to divide 24680246802 by 2, you use the facts that (2 / 2 = 1, 4 / 2 = 2, 6 / 2 = 3, 8 / 2 = 4, and 0 / 2 = 0) to write 24680246802 / 2 = 12340123401.
4. Dividing by 10 To divide a number that ends in a string of zeros on the right by 10, you just take away one of the zeros from the rightmost end. So, 234000 / 10 = 23400. If the number doesn’t end in zero, you can still divide by 10, but you’ll end up with a decimal. So, 6523 / 10 = 652.3. Dividing by 100 or 1000 is similar, but you will take away two zeros (if you’re dividing by 100) or shift the decimal point two steps to the left (if the number doesn’t end with a string of zeros, and you need to divide by 100). For example, 98700 / 100 = 987. 987 / 100 = 9.87. And 9870 / 100 = 98.7. In the last case, you take away one zero, and then shift the decimal point one place to the left.
5. Dividing by 5 Dividing by 5 is the same as dividing by 10, and then multiplying by 2 (because 5 = 10 / 2). So, if you need to divide 12340 by 5, you first divide it by 10 to get 1234. You then multiply 1234 by 2 to get 2468, and that’s your answer! You can use similar techniques to divide a number by 50, 500, etc. So, 2500 / 50 = (2500 / 100) x 2 = 25 x 2 = 50.
6. Subtracting one big number from another, especially when there is a lot of borrowing There are two things that might help you. First, if your sum involves a number that is close to a ‘nice’ number, you can use that to convert your hard subtraction problem into a combination of an easy subtraction problem and an easy addition problem. So, if you need to find 1234 - 991, you observe that, since 991 = 1000 - 9, you have 1234 - 991 = (1234 - 1000) + 9 = 234 + 9 = 243. But this is not always possible - though, when it is possible, it makes life very very easy. When you can’t simplify matters like this, you just have to resign yourself to the fact that this will take time, and either approximate the answer if you’re in a situation where that’s acceptable (for example, if you need to know approximately what 12345 - 6789 is, you can note that this is close to 12000 - 7000 = 5000. And it’s even closer to 12300 - 6800 = 5500), or check the answer (through addition) in case accuracy is very important.
7. Percentages These occur everywhere in daily life, and it’s often all about training our brains to quickly identify what multiplication or division problem a particular percentage talks about. For example, if you need to find 10% of a certain number, you just need to divide that number by 10 (and section 4 taught us just how to do that!). If you need to find 5% of a number, you need to divide it by 20 (first divide by 10, and then divide by 2). If you are asked to find 80% of a number, you need to divide it by 5 (easy!) and then multiply it by 2, and then multiply it again by 2.
8. Multiplying a number by 11 Just multiply it by 10, and add that result to the number itself. For example, if you need to find 53 x 11, you take 530, and add it to 53, to get 583. And 23656 x 11 = 236560 + 23656 = 260216.
9. BODMAS If you have a long, complicated string of numbers, separated by multiplication, division, addition, and subtraction signs, you will agree that the value of the expression depends on which order you do the calculations in. Math has a rule for that. In the complicated expression, you first solve the division and multiplication problems, and then the addition and subtraction ones. For instance: 1 - 2 + 3 x 4 / 6 - 7 + 8 = 1 - 2 + 12 / 6 - 7 + 8 (we first solve 3 x 4 = 12) = 1 - 2 + 2 - 7 + 8 (we solve 12 / 6 = 2) = 1 + 0 + 1 (we solve 2 - 2 = 0 and 8 - 7 = 1) = 2
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