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Analyn Sanger, an abacus teacher by profession and a mom to twin boys, believes parents can make math more fun and engaging to little learners by incorporating the subject in everyday life.
“Practical application is key, like letting the kids compute the bill in the restaurant and at the shops. When we’re stuck in traffic, I quiz my sons about plate numbers – I name the plate numbers and they have to find the car and tell me its brand and color. I also let them add or subtract [numbers] based on plate numbers” she says.
Teaching children simple math hacks – or clever solutions to tricky problems – is a commendable move and will go a long way as well. Says Sanger, “The best and simplest math hack is to sing the numbers away! From teaching how to write the numbers to singing the multiplication table and formulas. The internet has tons of useful sources.”
Besides learning arithmetic through songs, here are fourteen other useful Math hacks for kids that even adults will be thankful for. Grade schoolers learning their times tables and getting the hang of the four operations (addition, subtraction, multiplication and division) will benefit from these tips, while older kids, high schoolers and adults will be able to relate more to the solutions that involve money, plus multiple and huge numbers. Make sure to practice and apply these as often as possible for optimum results.
Have fun counting and computing!
1. Subtracting from numbers with multiple zeroes (powers of 10)
Technique: Subtract all digits of a number except the rightmost one from 9; subtract the ones digit from 10.
Examples:
1,000 – 786
Subtract 7 from 9 = 2
Subtract 8 from 9 = 1
Subtract 6 from 10 = 4
Answer: 214
10,000 – 6249
Subtract 6 from 9 = 3
Subtract 2 from 9 = 7
Subtract 4 from 9 = 5
Subtract 9 from 10 = 1
Answer: 3751
Click here to watch the demo.
2. Using fingers to multiply
If your child finds it difficult to memorize the entire multiplication table, he can stop at 5 x 5 and just use his fingers to multiply from 6 to 10.
Technique: Assign one factor per hand. Each hand may have raised fingers and closed fingers. To know how many fingers to raise, subtract 5 from each factor. The sum of the raised fingers in both hands is the number of tens. The product of the closed fingers is the number of ones.
Example: 7 x 9
For 7, use your left hand and raise 2 fingers (7 – 5 = 2). There will be 3 closed fingers.
For 9, use the right hand and raise 4 fingers (9 – 5 = 4). There will be 1 closed finger.
Add the raised fingers: 2 + 4 = 6. This means 6 tens or 60.
Multiply the closed fingers: 3 x 1 = 3. This means 3 ones.
60 + 3 = 63.
Click here for more tips on finger multiplication.
3. Multiplying by 5
Technique 1: Multiply by 10 and then divide by 2.
Examples:
68 x 5 can also be 68 x 10 = 680, 680 ÷ 2 = 340
Technique 2: When multiplying 5 with an even number, halve the number and place a zero after it.
Examples:
5 x 48 becomes 48 ÷ 2 = 24. Put a zero after the number to get the answer: 240
5 x 222 becomes 222 ÷ 2 = 111. Put a zero after the number to get 1110
Technique 3: When multiplying 5 with an odd number, subtract 1 from the odd number, halve your answer and then place a 5 after it.
Examples:
5 x 13 becomes (13 – 1) ÷ 2
12 ÷ 2 = 6. Place a 5 after the number to get your answer: 65
5 x 117 becomes (117 -1) ÷ 2
116 ÷ 2 = 58. Put a 5 after the number. Answer is 585
4. Multiplying by 9
Technique: Multiply by 10 and then subtract the original number.
Examples:
72 x 9 becomes 72 x 10 = 720
720 – 72 = 648
351 x 9 becomes 351 x 10 = 3510
3510 – 351 = 3159
When the factor is 99, multiply by 100 and then subtract the original number.
When the factor is 999, multiply by 1000 and then subtract the original number.
Click Next page for more math hacks for kids.
5. Multiplying by 11
Technique 1: Multiply by 10 and then add the original number.
Example:
97 x 11 becomes (97 x 10) + 97
970 + 97 = 1067
Technique 2: Get the first and last digits of a number and imagine a space between the two digits. Add the two numbers and put the result between the two digits. That’s your answer.
Example: 53 x 11 becomes 5, 5+3, 3 or 583
View the demo.
For larger numbers multiplied by 11, do this: leave the first and last digits alone. Sum each and every pair of digits next to each other. When the sum of a pair is greater than 10, add 1 to to the number on the left but retain the other digit.
Example:
3571 x 11 becomes 3, 3+5, 5+7, 7+1, 1 or 39,281
12,648 x 11 becomes 1, 1+2, 2+6, 6+4, 4+8, 8 or 139,128
459,170 x 11 becomes 4, 4+5, 5+9, 9+1, 1+7, 7+0, 0 or 5,050,870
Watch how it’s done here.
6. Multiplying by 25
Technique:
Divide the number by 2 twice and then multiply your answer by 100.
Example:
492 x 25
492 ÷ 2 = 246
246 ÷ 2 = 123
123 x 100 = 12300
Click here for more examples.
7. Calculating discounts and percentages
Technique: To quickly figure out the price cut of an item on sale when given a certain percentage, do the following:
5% ~ Divide the list price by 10 and then divide the answer by 2
10% ~ Divide the list price by 10
20% ~ Divide the list price by 5
25% ~ Divide the list price by 4
50% ~ Divide the list price by 2
75% ~ Divide the list price by 4 and then multiply the answer by 3
80% ~ Divide the list price by 5 and then multiply the answer by 4
Watch this video for other math percentage tricks and shortcuts.
8. Dividing by 5
Technique: To divide a big number by 5, multiply it by 2 and then divide by 10. To divide by 10, just move the decimal point of your answer one place to the left.
Example:
175 ÷ 5
175 x 2 = 350
Move the decimal point to the left: 350 becomes 35
View the demo.
Click Next page for more math hacks for kids.
9. Converting fractions to percents without long division
Technique:
To get a quick percentage estimate, write an equivalent fraction with a blank numerator and 100 as the denominator beside your original fraction.
Multiply the denominator of the original fraction with a number that will bring it closest to 100.
Multiply the numerator with the same number.
Then increase or decrease (+, -) the answer depending on the product of the denominator and the number it was multiplied with. + if the product is less than 100 and – is the product is greater than 100.
Example:
15 = ___
33 100
15 x 3 = 45 +
33 x 3 100
Answer is 45+%
Watch the demo.
10. Finding the sum of numbers in a series
For odd numbers
Technique:
Add 1 to the highest number in the series.
Divide the answer by 2.
Multiply the number you get by itself.
Example:
Odd number series: 1+3+5+7+9+11…..+117
117 + 1 = 118
118 ÷ 2 = 59
59 x 59 = 3481
For even numbers
Technique:
Divide the highest number in the series by 2.
Multiply the result you get with the next higher number.
Example:
Even number series: 2+4+6+8+10+12…..+130
130 ÷ 2 = 65
65 x 66 = 4290
Click here for other shortcuts on adding numbers in a series.
11. Squaring a two-digit number
Technique 1 (for numbers less than 30):
Add the ones digit to the number you are squaring. Write down the answer.
Subtract the ones digit from the number you are squaring. Write down the answer.
Multiply the two numbers you got. To this number, add the square of the ones digit.
Example:
19 x 19
19 + 9 = 28
19 – 9 = 10
28 x 10 = 280
280 + (9 x 9)
280 + 81 = 361
Click here for more examples.
Technique 2:
Multiply each digit by itself and place the answers you get side by side.
Multiply the digits of the number being squared.
Double the answer in step 2 and add a zero.
Add this number to the result in step 1.
Example: 53 x 53
5 x 5 = 25 and 3 x 3 = 9 ~ 2509 (place answers side by side)
5 x 3 = 15
15 x 2 = 30; add a zero ~ 300
2509 + 300 = 2809
12. Squaring a two-digit number ending in 5
Technique:
Multiply the first digit by the next higher number.
Place the number 25 beside your answer.
Example:
85 x 85
8 x 9 = 72
Affix 25 to your answer: 7225
Click here to see the demo.
Click Next page for more math hacks for kids.
13. Multiplying numbers close to 100
Technique 1: Change the number to 100, multiply, and then subtract the other factor n times, where n is the difference of the bigger factor and 100.
Example:
99 x 6 becomes (100 x 6) – (6 x 1) = 594.
98 x 3 becomes (100 x 3) – (3 x 2) = 294
Technique 2: When multiplying 2 numbers that are close to 100,
Find the difference of each factor from 100.
Cross subtract (answer will be the same for both factors). The result will be the first digits of your answer.
Multiply the differences you got. Write the answer beside the number you got from cross subtracting.
Example: 93 x 96
(100 – 93) and (100 – 96) = 7 and 4
Cross subtract: 93 – 4 or 96 – 7 = 89
Multiply the differences: 7 x 4 = 28
Write the results side by side and you get the answer: 8928
Watch this video to see how it’s done.
14. Applying money rules
Rule of 72
To know how long it will take for your money to double, divide 72 by the projected interest rate.
Example: Your money is earning 8% per year. 72 ÷ 8 = 9. It will take 9 years to double your investment.
Click here to teach compound interest and the Rule of 72 to children.
Rule of 115
To know how long it will take to triple your money, divide 115 by your target interest rate.
Watch the demo.
Example: Your money is earning 6% per year. 115 ÷ 6 = 19.17. It will take 19.17 years to triple your funds.
Rule of 70
To know how long it will take for inflation to devalue money by 50%, divide 70 by your expected rate of inflation.
Example: If inflation is pegged at 2.5%, divide 70 by 2.5. The answer, 28, means that in 28 years, your money will only be worth half of its current value.
View the demo.
Analyn Sanger is the teaching directress at CMA Mental Arithmetic Capitol Hills Branch located at 88 Capitol Hills Drive, Old Balara, Quezon City. She invites all Math-loving parents and kids to join the 3rd CMA Mental Arithmetic Competition – the biggest mental arithmetic competition in the Philippines – to be held on March 1, 2015 at the SMX Convention Center, Mall of Asia in Pasay. Call 442-3560 or visit CMACapitolHills for more details.
What other useful math hacks for kids do you know and practice? Share it with us.
About the author: Regina Posadas
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