Sooner or later you will find yourself in a situation where you have to solve math problems without a calculator. Even if you are good at math, mental math can be really difficult. To solve a problem in your head, you need strategies and methods that are different from the ones you learned in school. Fortunately, by studying the basics and use of mental math, you can improve your skills and solve complex equations using just your head.
Steps
Method 1 of 3: Using Mental Math Tricks
Step 1. Visualize the equation in your head
The first step in solving a math problem in mind is to visualize it. Imagine the numbers and the equation. As you troubleshoot parts of the problem, view the numbers you are using. Repeat them in your head or verbally, whispering, to make it easier for you to remember the most important figures.
Step 2. Add and subtract from right to left
You've probably been taught to add and subtract from right to left, but this process is harder to do in mind. Instead, try calculating the numbers on the left first, then the numbers on the right. The number on the left will form the left digit of the solution, while the one on the right the second digit.
- For example, to add 52 + 43, you can do the operations 5 + 4 = 9 and 2 + 3 = 5, for a total of 95.
- To solve 93-22, subtract 9-2 = 7, then 3-2 = 1 for a total of 71.
- If you need to report numbers, add them to the first digit. For example, for the sum 99 + 87, you can first do 9 + 8 to get 17, then 9 + 7 to get 16. Since you have to report 1, the first number will become 18, giving the solution 186.
Step 3. Count common zeros when adding or subtracting
For sums, you can find common zeros in the equation and eliminate them to solve it more easily. For example, in the case of 120-70, you can eliminate the zeros and get 12-7 = 5, then put the zero back to calculate the solution, 50.
Another example is 300 + 200, which you can turn into 3 + 2 = 5 by removing the zeros. Put them back to get 500
Step 4. Simplify and add all zeros when multiplying
For multiplications, you can simplify numbers followed by zero. For example, you can turn 3000x50 into 3x5 = 15, then put the zeros back at the end of the product to get 150,000.
Another example is 70x60. You can think 7x6 = 42, then add zeros to get 4200
Step 5. In the sums, round the numbers up, then subtract the difference
To make certain calculations with numbers greater than 100 easier, you can round the digits, then subtract the value you added. For example, to solve 596 + 380, you can add 4 to 596, which makes the equation 600 + 380 = 980, which is easier to visualize. At that point, go back and subtract 4 from the sum, 980, to get the result 976.
Another example is 558 + 305. Round 558 to 560 so that the equation becomes 560 + 305 = 865. Next, subtract 2 from 865 to get 863
Step 6. Simplify the numbers in multiplications
You don't always have to try to solve the exact problem in front of you. Difficult or irregular numbers make the calculations more complicated. For example, if you need to multiply 12x36, you can simplify the equation to make it easier for you to do it in your head. 12 can become 10, so you have 10x36 which is 360. You can then add the remainder you didn't calculate and multiply 36x2, getting 72. Finally, add 360 + 72, which is 432. This operation is simpler than a long multiplication in mind.
Step 7. Simplify the percentages into simpler numbers by breaking them down into the smallest possible parts
For example, if you have to calculate 15% of 40, you can start from 10% of 40 = 4. At that point, the remaining 5% is half of 10%, so you can assume that 5% of 40 is 2. Add 4 + 2 = 6, i.e. 15% of 40.
Step 8. Estimate when you don't need an exact calculation
Approximating a solution is often much easier than finding the exact one. Try rounding the complex numbers to the nearest integer, then solving the equation. If you find yourself in a situation where the precise solution is not required or if you have little time available, approximations allow you to get closer to the real number.
For example, if you need to calculate 7, 07 + 8, 95 + 10, 09 you can round all digits to the nearest integer and estimate that the solution is about 26
Step 9. Associate equations with money to solve them
Since one euro is made up of 100 cents, you can use this information to solve mathematical equations. For example, you may not know right away how much 100-25 is, but you probably know how much money you have left if you pay twenty-five cents with one euro. If you can, associate the numbers with the coins.
Method 2 of 3: Study and Practice to Improve
Step 1. Memorize the multiplication tables
This way, you will instantly know the answer to all the simplest multiplication problems. This allows you to solve the various small components of more complex math problems faster. If you don't remember the times tables, study them until you know them perfectly.
Step 2. Memorize the first 20 squares
The table of squares shows the result of multiplying the first 20 numbers by themselves. Knowing it by heart will be able to solve the simplest equations in mind. You can also use squares to estimate the solutions of more complex problems.
For example, to calculate 18x19 you can calculate 19² and subtract 19
Step 3. Use cards
If you have trouble with multiplication and division tables, cards are great for memorizing common math problems. Determine which calculations give you the most trouble, then write those equations on a card. Write the solution on the back of the card. Practice solving equations with a partner, so you can learn how to do the most common calculations in a short time.
Step 4. Practice every day
Solving two or three complex math equations in mind every day helps you keep your mind sharp and improve your mental math skills a lot. Engage in mental calculations in various situations to get better at it. After a month, mental math shouldn't bother you anymore.
Step 5. Take mental math quizzes on the internet
There are apps and websites dedicated to improving your math skills. Search online for top rated apps and sites, then use their tools to solve common math problems.
- You can find widely used mind calculations quizzes on sites like https://preplounge.com and
- The most downloaded mental math apps include Elevate, Luminosity, and Mathemagics.
Method 3 of 3: Practice Mind Calculations When Shopping
Step 1. Test basic sums and subtractions to estimate the cost of spending
Make a note of your purchases before arriving at the checkout. Add up the price of the products and keep the count in mind. When you receive your receipt, compare your calculations with the real price.
For example, if you bought € 3.99 cereal and € 9.49 detergent, the total cost is € 13.48
Step 2. Use multiplications to calculate the cost of gasoline
Wait until you are in reserve, then multiply the cost of gas by the size of your car's tank. For example, if you have a 50 liter tank and gasoline costs € 1.5 per liter, you can multiply € 50x1.5 = € 75. You can also cover the cost of gasoline on the pump as you watch the liters go up and make a calculation in your head to calculate the total expense.
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You can use multiplications to calculate the total cost when purchasing multiple identical items.
For example, if you bought 4 chocolates at € 2 each, you spent 4x2 = € 8
Step 3. Use balances and discounts to practice percentages
Round off the cost of the product to the nearest euro, then calculate the discount percentage. For example, for a 7% discount on an item that costs € 9.65, you can round the price to € 10. 7% of 10 is 0.7 so 70 cents, roughly how much you will save.
- Seven percent of 9.65 is actually 0.67.
- If you buy € 5 meat, with a 25% discount, you save € 1.25.
Step 4. Use splits in mind to split an account
To calculate your share of an account, divide the total by the number of people who have to pay. For example, if the bill is € 125.36 for a dinner for four, each has to pay € 31.34.
- To break down the equation and make it simpler, start with euros and then consider cents.
- Round 125 to 100 to make it easier to divide by 4, 100/4 = 25, then divide 25/4 to get the amount you are missing. Add 6 to 25 to get the total of 31.
