Knowledge of the meaning of numbers with zeros behind them allows students to quickly calculate large numbers. Numbers with zeros in them are really "root" numbers that have been multiplied by ten, one hundred, one thousand or even more. This means that the number 80 is really the root number 8 multiplied by ten (one zero). The number 8000 is the root number 8 multiplied by one thousand (three zeros). To multiply with a large number that ends in zeros, multiply the root numbers and then add the zeros to the end of the result. For instance, when multiplying 80 times 20, multiply 8 times 2 to get 16. Then, add a total of two zeroes (one zero from 80 and one zero from 20) to the end of the 16 to get 1600.
The distributive property of operations allows you to change the order of the numbers being multiplied and added. When multiplying numbers, you can rewrite the operation to multiply the easier numbers first. For instance, if the problem calls for multiplying 56 times 6 then, you can change that problem to (50 times 6) + (6 times 6) which is equal to 300 + 36 or 336. This is easier than using traditional multiplication that requires you to multiply and carry over numbers.
To divide large numbers, students can use knowledge of even (divisible by 2) and odd (not divisible by 2) numbers to ultimately divide numbers more efficient. Use smaller numbers to observe which ones are divisible by 2, divisible by 3, divisible by 4, divisible by 5 and so on. For instance, even numbers or those that are divisible by 2 end in an even number such as 0,2,4,6,8 and so forth. So the number 16 is even and thus is divisible by 2.
If you had to divide 8448 by 32 without using a calculator, first look at the factors of 8448. The number 8448 is even because it ends in 8, which is divisible by 2. Next, looking at the number 32 would yield even-numbered factors of 2, 4 and 8 since 32 is divisible by 2. So you can simplify the original division problem of 8448 / 32 by dividing 8448 / 8 to get 1056. Then, divide 1056 by 4 to get 256.
Dividing a big number by its multiples makes the division much easier by breaking down the dividend, or the number that is divided. The KidzWorld website gives specific rules for determining whether given numbers are multiples of 2, 3, 4, 5, 6, 7, 8, 9 and 10 and thus are divisible by them.
For example, to divide 2376 by 27, first sum 2376 to get 2 + 3 + 7 + 6 = 18. The numbers 18 and 27 are both multiples by 9, or are divisible by 9. So rewrite the problem into two simpler divisions. First divide 2376 by 9 to get 264. Then divide 27 by 9 to get 3. Finally divide 264 by 3 to get 88, which is the answer to the original problem, 2376 divided by 27.