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Elementary Math Tricks

by Pamela Martin, studioD

"Since the mathematicians have invaded the theory of relativity, I do not understand it myself anymore," said Albert Einstein, echoing the cry of thousands of math students every day. Math anxiety may range from mild uneasiness to a phobia-level fear about solving math problems, but a few tricks can help relieve some of the concerns.

Addition and Subtraction

For most adults, adding or subtracting is easy, but to an elementary student just learning about math, even the ones table can be scary. When a student learns adding one is the same as counting, or that subtracting one is just counting backward, the student finds it isn't so hard, after all. Knowing that subtracting two numbers next to each other when counting always leaves one makes subtracting even large numbers less intimidating. "One and one less" is a quick way to remember the sums of nine. When adding nine to another single-digit number, you simply write a one in the tens column and one less than the other addend to the ones column. For example, if given the equation 9 + 6 =?, write a one followed by one less than six, to get 15 as the sum. If the number to which you are adding nine is a two-digit number, add one to the tens digit and then one less to the ones: 24 + 9 =? requires three in the tens column and three in the ones column -- one less than the four in the addend.


Multiplying by nines also has a trick to remember the products. Write one less than the number being multiplied in the tens column, followed by the number you would add to that number to total nine. For example, for 9 x 4, you would write a three in the tens column -- one less than the four by which you are multiplying. Then, you fill the ones place with the number you would add to three to total nine -- a six -- giving you a product of 36. Elevens are fun multipliers, as well. For single digit numbers, you only need to copy that number twice -- 2 x 11 = 22. For larger numbers, write the digits down with a space in between, then write their sum in the middle. For the equation, 23 x 11, write two and three with a space between them. Add them together to get the middle digit of five. Multiplying by tens is even simpler, because you just add a zero at the end of the other number: 10 x 23,759 = 237,590.


Sometimes it is helpful to know if one number can evenly divide another, like when you are trying to reduce a fraction to its simplest terms. You can shortcut the task if you know that two can divide any number that ends with a zero, two, four, six or eight. For divisibility by three, add the digits together until you get a single-digit. If three divides that number with no remainder, it will divide the larger number evenly. For example, add the digits of 258 to get 15, then add those to get six. Since six is divisible by three, you know that 258 will also divide evenly. Five and 10 are even easier, since any number that ends in zero can be divided by 10, and any number that ends in five or zero divides evenly by five. If a number is divisible by both two and three, it is also divisible by six.


Mnemonics, or memory codes, help with those other math concepts that might not deal directly with numerals. For example, the rhyme, "Thirty days has September, April, June and November…" helps you keep the number of days in each month straight, while the phrase "Drive my super-cool buggy" reminds you of the steps in a division problem: divide, multiply, subtract, compare, bring down. "King Howie doesn't usually drink chocolate milk" makes the prefixes for the metric system easier to remember, while "Please excuse my dear Aunt Sally" puts the order of operations for solving equations at your mental fingertips.

About the Author

Pamela Martin has been writing since 1979. She has written newsletter articles and curricula-related materials. She also writes about teaching and crafts. Martin was an American Society of Newspaper Editors High School Journalism Fellow. She holds a Bachelor of Arts in Teaching in elementary education from Sam Houston State University and a Master of Arts in curriculum/instruction from the University of Missouri.

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