The Ultimate List of Math Hacks, Tricks, and Tips

Regardless of the age, grade or degree, mathematics could be challenging at times no matter if you’re learning arithmetic, geometry, fractions, algebra or children learning times tables. However, the important thing is the subject has its hacks and tricks to hijack, helpful in tackling tough problems and managing time in the assessment.

Mathematics’ tricks are techniques, most of them are methods of quick calculations through which complex mathematical problems are solved easily and mathematical skills are improved. Most of the hacks are devised for the basic operations of addition, subtraction, multiplication, division percentage, fractions etc.

Arithmetic Operations

Through the principles of ‘tens and unit places’, it becomes relatively easy to perform calculations rather than using finger count or calculator.

1. Two-digit Addition

• The two-digit addition of numbers becomes easy and quick to perform such as:
• Say, 33 + 23
• Split the second number into tens and units, such that: 23= 20 + 3
• Finish the addition of ten’s, such that: 33 + 20 = 53
• Then add the rest with unit place digit, such that: 53 + 3 = 56.

2. Subtraction

• Consider two numbers say, 1000 and 546
• Subtract 1 from each number, we get: 999 and 545
• Then subtract, the both numbers, we get: 454
• And, 1000 – 546 = 454

3. Multiplication

• We have numbers say, 20 and 12
• Splitting 20, we get 4 x 5
• Multiply 5 with 12, we get 60
• Multiply 60 x 4, we get: 240.

4. Multiply 2 and 4

When a number is multiple of 2 and 4, then the last digit of the output value will always be an even number.

• 19 x 4 = 76
• 19 x 6 = 114

5. Division

The numbers which are ‘evenly divided by certain numbers’:

• Divisible by 2: The even numbers ending at 0, 2, 4, 6 or 8.
• Divisible by 3: If the sum of the digits is divisible by 3.
• Divisible by 4: If the last two digits of the number are divisible by 4.
• Divisible by 5: If the last digit of the number is 0 or 5.
• Divisible by 6: If a number is divisible by 2 or 3.
• Divisible by 8: If the last three digits are divisible by 8.
• Divisible by 9: If the sum of the digits is divisible by 9.
• Divisible by 10: If the last digit of a number is 0.

6. Finding Percentage

• Let’s say: we need to find 5% of the number 255.
• Move the decimal point over one place, say 255 becomes 25.5.
• Divide the number 25.5 by 2, we get:12.75
• 75 is the solution.

7. Squares Ending at 5

• Consider the number 125 to find its square.
• Start writing the last two-digit number that is 25.
• Take the first number i.e., 12 and the one that follows i.e., 13.
• Multiple 12 x 13, to get 156.
• Use it as prefix with 25 i.e., 15625.
• 125² = 15625

8. Memorizing Table of 9

• Let’s focus on the pattern of the complete table of 9.
• 09, 18, 27, 36, 45, 54, 63, 72, 81, 90
• The numbers at ten’s place are increasing by 1, whereas those at unit’s place are decreasing by 1.

9. Distance Formula

In order to calculate the total time for a trip, a simple hack is the distance formula which is usually remember by all: Distance = Rate x Time or Time = Distance/ Rate, if one intends to calculate the total time. For instance, for 5 miles of distance, at the rate of 2 miles per hour, the time would be calculated as: 5/2 = 2.5 hours.

10. Fraction into Percentages

Everyone has the understanding about percentages and how to measure them, but most of the time it is not understand that what fraction of a pie makes a certain percentage? Mostly, easy fractions are known to all such that 1/2 makes 50%, 1/4 makes 25%. Let us memorize a few hard approximate values to use them arbitrarily when questioned.

• 1/6^th makes 16% of the pie.
• 1/7^th makes 14% of the pie.
• 1/8^th makes 12-12.5% of the pie.
• 1/9^th makes 11% of the pie
• 1/11^th makes 9% of the pie.
• 1/12^th makes 8% of the pie.

11. Butterfly Method

This method is used for the quick addition or subtraction of fractions.

12. Mnemonics

In Mathematics, mnemonics are taught to the students which help in memorizing the formulas better, for their quick and effective calculations.

• “Some People Have Curly Brown Hair Through Proper Brushing”.

This mnemonic is useful in learning the formulas of trigonometric rations where every first letter starts with:

• Sin θ = Perpendicular/ Hypotenuse
• Cos θ = Base/ Hypotenuse
• Tan θ = Perpendicular/Base

• “King Henry Died Drinking Chocolate Milk”

This mnemonic is useful in learning the metric systems with the order of values where every first letter starts with:

• Kilo, Hecto, Deca, Deci, Centi, Milli.

• “Please Excuse My Dear Aunt Sally”

The mnemonic is used for the order of arithmetic operations to be solved first, where every first letter starts with:

• Parenthesis, Exponents, Multiply, Divide, Addition, then Subtraction.