Summarize the following:
The first step in solving a math problem in your head is to visualize the problem mentally. Imagine the numbers and the equation in your head. As you solve portions of the problem, visualize the new numbers that you're working with. Repeating numbers mentally or verbally, in a whisper, will also help you to remember more significant numbers in the equation. You were probably taught to add and subtract from right to left, but doing it this way is actually harder mentally. Instead, calculate the left numbers first, then subtract or add the right numbers together.The left number will form the left digit in your solution while the right number will be the second digit. For instance, to add 52+43, you can add 5+4=9 and 2+3=5, for a total sum of 95. If subtracting 93-22, subtract 9-2=7 and then 3-2=1 for a total of 71. If you have to carry over numbers, add them to the first digit solution. For instance, when adding 99+87, you could add 9+8 first to get 17, then 9+7 to get 16. Because you know you have to carry the 1 over, your first number would become 18, for a full solution of 186. When adding, you can find common zeros in the equation and remove them to solve an equation easier. For instance, if you had 120-70, you could remove the zeros to get 12-7=5, then add the common zero back on to get the solution or 50. Another example is if you had 300+200, you could remove the common zeros to get 3+2=5, then add them back on to get the answer or 500. When multiplying, you can simplify the number if zeros follow it. For instance, if you had 3000x50 you could simplify it to 3x5=15, then add together all the zeros and put it on the end of the product to get 150,000. Another example is if you had 70x60, you could do 7x6=42 then add the zeros to get 4,200. You can round numbers up, then subtract the added value to make it easier to solve complex addition problems when the value of the number is greater than 100. For instance, if you had to solve 596+380, you could add 4 to 596, so your equation looks like 600+380=980, which is easier to visualize. Then, go back and subtract 4 from your sum, 980, to get 976 or the sum of 596+380. Another example would be if you had 558+305. Round 558 to 560 so that your equation is 560+305 = 865. Then, subtract 2 to your sum of 865 to get 863. You don't always have to do the exact math that you're presented with. Complex or uneven numbers can make calculations more difficult. For example, if you have to multiply 12x36, you can simplify the numbers to make it easier to do in your head. 12 can become 10 so that you have 10x36 which equals 360. Then you can take the remainder that you didn't calculate or 2 and multiply that by 36, which equals 72. Finally, add 360+72 to equal 432. This may be easier than doing long form multiplication in your head. Break down percentages into smaller parts if at all possible. For instance, if you need to calculate a 15% of 40, you can figure out 10% of 40, which is 4. Then, because the remaining 5% is half of 10%, you can assume that 5% of 40 is 2. Add 4+2 = 6 or 15% of 40. Estimating the solution is often much easier than trying to work out an exact solution. Try rounding complex numbers to their whole numbers, then solving the equation. If you're in a situation when finding the exact solution isn't necessary or you have limited time to solve the equation, use estimation to get close to the actual number. For instance, if you had to add 7.07+8.95+10.09, you could round to the closest numbers and estimate that the solution was close to 26. Since there are 100 cents in a dollar, you can easily use this knowledge to solve math equations. For instance, you may not know what 100-25 is off the top of your head, but you probably know how much money you'd have if you removed a quarter from four quarters. Associate the numbers in the equation with money if applicable.
Visualize the equation in your head. Add and subtract from left to right. Count the common zeros when adding or subtracting. Simplify and add all the zeros when multiplying. Round numbers up and then subtract the difference when adding. Simplify complex numbers when multiplying. Simplify percentages into even numbers. Estimate when an exact calculation isn't necessary. Associate equations with money to solve them.