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What are your favorite math tricks for mental calculation?
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I've been teaching math for 15 years and I'm always looking for new mental math techniques for everyday use. One of my favorites is the trick for multiplying by 11: just add the digits of the number and put the sum in the middle. For example, 35 x 11 = 385 (3+5=8, put 8 between 3 and 5).
What are some math tricks for mental calculation that you find most useful in real life situations? I'm particularly interested in quick multiplication shortcuts and division tricks for faster math that people actually use outside the classroom.
The 11 multiplication trick is great! Another one I teach my students is the percentage calculation hacks. For example, to find 15% of a number, find 10% first (just move decimal one place), then add half of that. So 15% of 60 = 6 + 3 = 9.
For quick multiplication shortcuts, I love the doubling and halving method. Like 16 x 25 = 8 x 50 = 400. It works because you're just redistributing the factors.
Division tricks for faster math are super useful. One of my favorites is for dividing by 5: just multiply by 2 and move the decimal. So 47 ÷ 5 = 47 x 2 = 94, move decimal = 9.4.
Also, for square root estimation methods, I use the average method. To estimate √50, find perfect squares around it (49 and 64), average their roots (7+8)/2=7.5, then adjust. Gets you close enough for mental math.
Fraction simplification tricks are essential. When adding fractions with different denominators, instead of finding the LCD immediately, check if one denominator is a multiple of the other. Like 1/3 + 1/6 = 2/6 + 1/6 = 3/6 = 1/2.
Also, decimal to fraction conversion tricks: for repeating decimals like 0.333..., just recognize it as 1/3. For 0.666..., it's 2/3. These mental math techniques for everyday use save so much time.
Times table tricks that actually work: for the 9 times table, use your fingers. Hold up both hands, for 9x3, put down your third finger. You have 2 fingers up before it (20) and 7 after (7) = 27. Works for 9x1 through 9x10.
For prime number identification shortcuts, check divisibility by 2, 3, 5, 7. If it's not divisible by any of those and less than 121, it's prime (except squares of primes like 121).
These are all amazing! As a student, I really need these math tricks for mental calculation. The percentage calculation hacks are especially useful for shopping discounts.
One I use is for 20% off: find 10% and double it. So 20% off $45 = $4.50 x 2 = $9 off, final price $36. Much faster than doing 0.2 x 45 in my head.
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