712 + 281 → “700 + 200,” “10 + 80,” and “2 + 1” 700 + 200 = 900, then 10 + 80 = 90, then 2 + 1 = 3 900 + 90 + 3 = 993. Thinking in “hundreds” or “tens” instead of single digits will make it easier to keep track when digits sum to more than ten. For example, for 37 + 45, think “30 + 40 = 70” and “7 + 5 = 12”. Then add 70 + 12 to get 82.
Addition: For 596 + 380, realize that you can add 4 to 596 to round it to 600, then add 600 + 380 to get 980. Undo the rounding by subtracting 4 from 980 to get 976. Subtraction: For 815 - 521, break it up into 800 - 500, 10 - 20, and 5 - 1. To turn the awkward “10 - 20” into “20 - 20”, add 10 to 815 to get 825. Now solve to get 304, then undo the rounding by subtracting 10 to get 294. Multiplication: For 38 x 3, you can add 2 to 38 to make the problem 40 x 3, which is 120. Since the 2 you added got multiplied by three, you need to undo the rounding by subtracting 2 x 3 = 6 at the end to get 120 - 6 = 114.
For example, 7 + 4 + 9 + 13 + 6 + 51 can be reorganized to (7 + 13) + (9 + 51) + (6 + 4) = 20 + 60 + 10 = 90.
For 453 x 4, start with 400 x 4 = 1600, then 50 x 4 = 200, then 3 x 4 = 12. Add them all together to get 1812. If both numbers have more than one digit, you can break it into parts. Each digit has to multiply with each other digit, so it can be tough to keep track of it all. 34 x 12 = (34 x 10) + (34 x 2), which you can break down further into (30 x 10) + (4 x 10) + (30 x 2) + (4 x 2) = 300 + 40 + 60 + 8 = 408.
Let’s look at numbers close to 10, like 13 x 15. Subtract 10 from the second number, then add your answer to the first: 15 - 10 = 5, and 13 + 5 = 18. Multiply your answer by ten: 18 x 10 = 180. Next, subtract ten from both sides and multiply the results: 3 x 5 = 15. Add your two answers together to get the final answer: 180 + 15 = 195. Careful with smaller numbers! For 13 x 8, you start with “8 - 10 = -2”, then “13 + -2 = 11”. If it’s hard to work with negative numbers in your head, try a different method for problems like this. For larger numbers, it will be easier to use a “base number” like 20 or 30 instead of 10. If you try this, make sure you use that number everywhere that 10 is used above. [3] X Research source For example, for 21 x 24, you start by adding 21 + 4 to get 25. Now multiply 25 by 20 (instead of ten) to get 500, and add 1 x 4 = 4 to get 504.
Addition: If all numbers have zeroes at the end, you can ignore the zeroes they have in common and restore them at the end. 850 + 120 → 85 + 12 = 97, then restore the shared zero: 970. Subtraction works the same way: 1000 - 700 → 10 - 7 = 3, then restore the two shared zeroes to get 300. Notice that you can only remove the two zeroes the numbers have in common, and must keep the third zero in 1000. Multiplication: ignore all the zeroes, then restore each one individually. 3000 x 50 → 3 x 5 = 15, then restore all four zeroes to get 150,000. Division: you can remove all shared zeroes and the answer will be the same. 60,000 ÷ 12,000 = 60 ÷ 12 = 5. Don’t add any zeroes back on.
To multiply by 5, instead multiply by 10, then divide by 2. To multiply by 4, instead double the number, then double it again. For 8, 16, 32, or even higher powers of two, just keep doubling. For example, 13 x 8 = 13 x 2 x 2 x 2, so double 13 three times: 13 → 26 → 52 → 104.
What is 72 x 11? Add the two digits together: 7 + 2 = 9. Put the answer in between the original digits: 72 x 11 = 792. If the sum is more than 10, place only the final digit and carry the one: 57 x 11 = 627, because 5 + 7 = 12. The 2 goes in the middle and the 1 gets added to the 5 to make 6.
79% of 10 is the same as 10% of 79. This is true of any two numbers. If you can’t find the answer to a percentage problem, try switching it around. To find 10% of a number, move the decimal one place to the left (10% of 65 is 6. 5). To find 1% of a number, move the decimal two places to the left (1% of 65 is 0. 65). Use these rules for 10% and 1% to help you with more difficult percentages. For example, 5% is ½ of 10%, so 5% of 80 = (10% of 80) x ½ = 8 x ½ = 4. Break percentages into easier parts: 30% of 900 = (10% of 900) x 3 = 90 x 3 = 270.
For problems like 84 x 86, where the tens place is the same and the ones place digits sum to exactly 10, the first digits of the answer are (8 + 1) x 8 = 72 and the last digits are 4 x 6 = 24, for an answer of 7224. That is, for a problem AB x AC, if B + C = 10, the answer starts with A(A+1) and ends with BC. This also works for larger numbers if all digits besides the ones place are identical. [6] X Research source You can rewrite the powers of five (5, 25, 125, 625, . . . ) as powers of 10 divided by an integer (10 / 2, 100 / 4, 1000 / 8, 10000 / 16, . . . ). [7] X Research source So 88 x 125 becomes 88 x 1000 ÷ 8 = 88000 ÷ 8 = 11000.
Memorize the squares from 1 to 20 (or higher, if you’re ambitious). (That is, 1 x 1 = 1; 2 x 2 = 4; 3 x 3 = 9, and so on. ) To multiply two numbers, first find their average (the number exactly between them). For example, the average of 18 and 14 is 16. Square this answer. Once you’ve memorized the squares chart, you’ll know that 16 x 16 is 256. Next, look at the difference between the original numbers and their average: 18 - 16 = 2. (Always use a positive number here. ) Square this number as well: 2 x 2 = 4. To get your final answer, take the first square and subtract the second: 256 - 4 = 252.
Flashcards are great for memorizing multiplication and division tables, or for getting used to tricks for specific kinds of problems. Write the problem on one side and the answer on the other, and quiz yourself daily until you get them all right. Online math quizzes are another way to test your ability. Look for a well-reviewed app or website made by an educational program. Practice in everyday situations. You could add together the total of items you buy as you shop, or multiply the gas cost per volume by your car’s tank size to find the total cost. The more of a habit this becomes, the easier it will be.
