Learn how to do anything: How to Improve Mental Math Skills

Eventually, you'll find yourself in a situation where you'll have to solve a math problem without a calculator. Even if you're good at math, mental math can be incredibly difficult to do. To solve problems in your head, you'll need an entirely new set of strategies and methods that differ from what you were taught in school. Luckily, if you study the basics and use mental math strategies, you can improve your skills and solve complex calculations in your head.

EditSteps

EditUsing Mental Math Tricks

Visualize the equation in your head. 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.^[1]
Add and subtract from left to right. 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.^[2]
- 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.
Count the common zeros when adding or subtracting. 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.^[3]
- 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.
Simplify and add all the zeros when multiplying. 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.^[4]
- Another example is if you had 70x60, you could do 7x6=42 then add the zeros to get 4,200.
Round numbers up and then subtract the difference when adding. 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.^[5]
- 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.
Simplify complex numbers when multiplying. 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.^[6]
Simplify percentages into even numbers. 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.^[7]
Estimate when an exact calculation isn't necessary. 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.^[8]
- 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.
Associate equations with money to solve them. 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.

EditStudying and Practicing to Improve

Memorize your multiplication tables. When you memorize your multiplication tables, you'll have the answer to simple multiplication problems instantly. This will improve the speed at which you can solve smaller components of a more complex math problem. If you're rusty on your multiplication tables, study them until you know all single digit multiplication problems.^[9]
Memorize the first 20 squares. A squares chart will show what 1-20 is multiplied by itself. Memorizing the chart will allow you to solve simple square equations in your head. You can also use squares to help you get an estimate for more complex multiplication problems.^[10]
- For example, if you have to solve 18x19 you can use 19², then subtract 18 to get the solution.
Use flashcards. If you're struggling with your multiplication or division tables, flashcards are a great way to memorize common math problems. Determine what you're struggling with and then write down the equation on a card. On the back of the card, write the solution. Practice going through the flashcards with a partner so that you can use instant recall for more common math equations.^[11]
Practice mental math every day. Practicing two or three complex mental math equations per day will keep your mind sharp and will vastly improve your mental math skills. Make a concerted effort to do more mental math in different situations to build the skill. After a month, you should feel more comfortable doing mental math.^[12]
Take mental math quizzes online. There are apps and websites that are dedicated to sharpening your mental math skills. Look online for highly accredited apps or websites and use their online tools to help you drill common mental math equations.
- Popular mental math quizzes can be found on sites like http://preplounge.com and http://ift.tt/VpHuvo.
- Popular mental math apps include Elevate, Luminosity, and Mathemagics.

EditPracticing Mental Math when Purchasing Things

Practice basic addition and subtraction to estimate your receipt. Keep track of the cost of things that you purchase at the store before you get to the cashier. Add the cost of items together and keep a running tally of your overall costs. When you get the receipt for your goods, compare your mental math with the actual cost of what you purchased.^[13]
- For instance, if your cereal costs $3.99 and soap costs $9.49, your total cost would be $13.48.
Use multiplication to calculate the cost of gas. Wait until your tank is almost empty, then multiply the cost of gas by your tank size. For instance, if you had a 12-gallon tank, and gas was $3.50 you could multiply 12x$3.50 = $42. You can also cover up the cost of the gas on the pump while looking at the gallons and use mental math to calculate your total cost.^[14]
- You can use multiplication to figure out costs if you're buying more than one of the same item.
  - For instance, if you bought 4 candy bars for 2 dollars each, you'd have 4x$2.00 = $8.00.
Use sales and discounts to practice percents. Round the cost of the product to the nearest dollar, and calculate the percentage of the sale. For instance, if there was a 7% discount on a $9.65 item, you could round up to $10. 7% of 10 is 0.7 or 70 cents, which is approximately how much you'd save.^[15]
- Ten percent off of $9.65 is actually 0.67 cents.
- If you are buying a case of water that costs $5 and it's 25% off, your savings would be $1.25.
Use mental division to split a bill. If you need to split a bill, you can divide the bill by the number of people who have to pay to determine how much each person owes. For instance, if you had a heating bill that cost $125.36 and you have 4 roommates, you'd divide $125.36 by 4 to get $31.34.^[16]
- If you wanted to break down the equation to make it easier, work on the dollar amounts first, then the cents.
- Breakdown $125 to $100 to make it easier to divide by 4 or $100/4=25. Then divide $25/4 to get the remaining numbers that you're missing. Add the remainder or $6 to $25 to get the whole number of $31.