Here are some shortcuts I learned to make basic math easier, working with base numbers 0 to 9.
When 0 is multiplied or divided by any number, the answer is 0. When 0 is added to or subtracted from any number, the answer is that number. You cannot divide by 0.
When multiplying whole numbers that end in 0, they are called base 10 numbers. You can drop the 0, multiply the remaining number, then add the 0 back to your answer. For example, if you need to multiply 150 times 30, you can drop the 0 from both numbers and multiply 15 times 3 to get 45. Then add back the 2 zeros that were dropped (1 from each number) and your final answer is 4,500. This only works when 0 is at the end of the number. For example, you cannot drop the 0 and add it back if the number is 105. If you have 1,050 times 3, you can drop the 0 at the end, multiply 105 times 3 to get 315, then add the 0 back for a final answer of 3,150.
The number 1 is pretty simple. If you can count, you can add and subtract 1. If you multiply or divide by 1, your answer is the number that you are multiplying or dividing by 1. On the other hand, if you are dividing 1 by a number, the fraction is just 1 over that number because that is in its simplest form.
If you need to divide 1 by a number and get a decimal, here are some common ones to remember. 1 divided by 2 is the same as one half. Since the first decimal place is tenth, remember that half of 10 is 5, which gives you the answer .5 (or 0.5). If you need 2 decimal places, you look at half of 100, and just as you added a 0 to 10 to get to 100, you can add a 0 to the 5 and get .50 (or 0.50). 1 divided by 3 is .3 (or 0.3) and the 3 repeats indefinitely. Whatever decimal place you round it to will not change (.3 or .33 or .333, etc.). When dividing 1 by 4, think of the 1 as a whole dollar (1.00) and the 4 as a quarter because 1 divided by 4 is one quarter (or one fourth). You know it takes 4 quarters to make a dollar, so one quarter is 25 cents, or 0.25, two quarters are 50 cents, or half of a dollar, or 0.50. Three quarters, or three fourths, is 75 cents, or 0.75. Of course 4 quarters gives you the 1 whole dollar. Typically, you do not need to add a 0 to the right of the decimal place if it is the last number on the right. For example. 0.5000 is the same as 0.5. The extra zeros add no value, unless you are required to list them in your answer, like when you are showing currency (money), which should be shown with 2 decimal places.
1 divided by 6 gives you a decimal of .16 (or 0.16) and the 6 repeats , so it will eventually need to be rounded to 7, like 0.167, or 0.166667, or 0.17 if you need to round to the nearest hundred. Finally, 1 divided by 9 is 0.1 and the 1 repeats, just like the 3 above. When you round, you will just have ones like 0.11 or 0.111111.
Let’s move on to the number 2. If you need to multiply by 2, you are just doubling the number you are multiplying by 2. You can simply add the number to itself to get the same answer. Any even number can be divided evenly by 2. No matter how long the number is, if the last digit to the right is an even number (0, 2, 4, 6, 8), it can be evenly divided by 2. It does not matter if the number is a whole number or a decimal. If you have a decimal that ends with an odd number, adding a 0 the end on the right of the decimal will allow you to divide it evenly by 2. If your odd number is a whole number, add a decimal of 0 allows you to divide it evenly by 2, like changing 45 to 45.0 or changing 6.35 to 6.350. If you need to divide by 2, your answer should be half of the number you started with. If you add your answer to itself and you don’t get the number you started with, then check your calculation because something went wrong.
If you need to check if a number can be evenly divided by 3, you can add the digits together. If the sum total is 3 or a multiple of 3, you can divide it evenly by 3. For example, 12 can be divided by 3 because 1+2=3. 111 can be divided by 3 because 1+1+1=3. At the same time, 123 can be divided by 3 because 1+2+3=6 and 6 is a multiple of 3. Another way to check is by adding the numbers separately to see if you have multiples of 3. For example, the number 259131 can be divided evenly by 3 because 2+1=3, 5+1=6, 9 is a multiple of 3, and the remaining digit is a 3. This logic also works for the number 9.
I do not have any shortcuts for the numbers 4, 6, 7, or 8. If you think of some. let me know!
There is not a lot I can say about the number 5. Any number that ends with 0 or 5 can be evenly divided by 5. Similar to the number 2, if you add a 0 on the end of a number, to the right of the decimal, you can evenly divide the number by 5.
Now for the number 9. I mentioned you can figure out if a number can be divided evenly by 9 simply by adding the digits. to each other. If the sum total of the digits is 9 or if the sum total of the digits when grouped is 9, then the whole number can be divided evenly by 9. Another trick I learned, which uses the same logic is how to remember the multiples of 9, at least up to 9×9. First, we already know about 0 and 1 because I mentioned it above (0x9=0 and 1×9=9). However, to remember the multiples of 9, starting with 2 and going all the way to 9, this is what you need to know. First of all, the answer (product) starts with the digit that is 1 less than the multiplier. For example, the answer to 9×2 starts with 1, the answer to 9×3 starts with 2, the answer to 9×5 starts with 4, the answer to 9×8 starts with 7, and so on and so forth. Second of all, once you know what the answer starts with, you can add to get to 9 for the rest of the answer. For example, 9×2 starts with 1, then the answer is 18 because 1+8=9. 9×4 starts with 3, so 9×4=36 because 3+6=9. Last one! 9×6 starts with 5, so 9×6=54 because 5+4=9. Basically, 0+9, 1+8, 2+7, 3+6, 4+5, 5+4, 6+3, 7+2, 8+1, and 9+0. So, even if you forget the scale that is being taught today, you can still use another method to figure out random calculations quickly.