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How to Learn Times Tables & Multiplication
by Paul Dohrman
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Overview
The best way to learn multiplication tables is to be drilled orally by a nonjudgmental person who already knows multiplication tables. The reason is that much more material can be covered in a half-hour of being drilled than in working alone. Of course, there are plenty of online drill sites that perform the same function, but allow procrastination. Schoolhouse Rock videos also can help.
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Drilling
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Start with single-digit numbers.
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Repeat the ones that you get wrong. The aim is not to be perfect the first time, but instead to get all of your mistakes out of the way during drills. Repetition is basic to getting through the mistake phase. Keeping the mood light allows one to work through the mistakes before getting so stressed as to quit. This is why a nonjudgmental driller is important.
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Move on to multiples of 10, 11 and 12.
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Learn the table up to 20 if there is time but keep in mind that with each number added, that number minus one is the number of new product's to learn.
Rhymes
Tricks
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Note that 9 times a single-digit integer is 10 times the number, minus the number. This is because 9 = 10-1. For example, 9 --- 7 = 70 - 7 = 63.
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Note that any integer times 10 is just the same number with a zero tacked onto the end.
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Note that 11 times a number is the number added to itself, but shifted over. This is because 11 equals 10 and 1. So 11 times 13 is 130 + 13, or 143.
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Note that 5 times another integer always ends in 5 or 0.
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Note the symmetry in the multiplication table. For example, 8 --- 7 = 7 --- 8. So an n---n multiplication table needs only half of the numbers to be memorized.
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Step 6
Hold your 10 fingers out. Count off the number you're multiplying nine by, from left to right. Lower that finger. To the left the number of fingers will be the 10s digits. To the right will be the ones digits.
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Step 7
Learn the following mnemonic for 7 --- 8: 5 6 7 8 becomes 56 = 7---8.
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Step 8
Learn the remaining parts of the multiplication table through 11. Note that after the above tricks and rhymes are learned, then aside from learning 3s, the only remaining facts to learn up through 11 are 4 --- 4, 4 --- 6, 4 --- 7, 4 --- 8, 6 --- 7, 7 --- 7 and 8 --- 8. That's only seven things to remember.
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Step 9
Learn 3s by just counting by 3s: 3, 6, 9 ... Note also that, like learning 2s, the number 3 is so low that adding is quickly done too. For example, 3 --- 8 = 8 + 8 + 8 = 16 + 8 = 24.
Advanced Tricks
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Square a number less than but near 50 by taking 2,500, subtracting the difference times 50, and adding the square of the difference. For example, 48 is 50 - 2. Square 50 - 2 to get 2,500 - 2 --- 50 + 4.
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Square a number greater than but near 50 by adding the difference times 50, instead of subtracting it. For example, 55 = 50 + 5. Square 50 to get 2,500 + 5 --- 50 + 25 = 2,775. Nobelist Richard Feynman rehashes when he learned this trick from another Nobelist in his bestselling "Surely You're Joking."
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Generalize this to other numbers. 70 squared is 4,900. The square of 73 is 4,900 + 2 --- 3 --- 7 + 3 --- 3 = 4,951.
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Decompose the multiplier. For example, 16 --- 15 = (4 --- 4) --- 15 = 4 --- 60 = 240.
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Calculate two-digit products below 20 as follows. Add the 1s digits. Multiply the 1s digits. Add 100 to the sum of the ones, but with a 0 tacked on. Then add in the product of the ones. So 14 --- 13 is 100, then (3 + 4) with a 0, then 3 --- 4. So it's 170 + 12 or 182.
