Introduction: Become the Math Wizard You Never Thought You Could Be
Remember that moment when your teacher called on you to solve a math problem, and your mind went completely blank? We’ve all been there. But what if you could not only answer confidently but do it faster than anyone else in the room? These 10 math tricks will transform you from “math anxious” to “math wizard” with techniques so simple, you’ll wonder why no one taught them to you before.
1. Lightning-Fast Multiplication Shortcuts
The 9’s Finger Trick
Still struggling with the 9 times table? This trick requires nothing but your fingers:
- Hold up both hands with all ten fingers extended
- To multiply 9 by any number (1-10), simply fold down the finger that corresponds to that number
- The digits to the left of the folded finger represent the tens place, while the digits to the right represent the ones place
For example, to calculate 9 × 7:
- Fold down your 7th finger
- You’ll have 6 fingers to the left and 3 to the right
- The answer is 63!
Multiplying by 11 (Two-Digit Numbers)
For any two-digit number, add the digits together and place the result between the original digits.
For example, 11 × 25:
- Separate the digits: 2 and 5
- Add them: 2 + 5 = 7
- Place the sum between the original digits: 275
Note: If the sum exceeds 9, carry the 1 to the left digit.
2. Division Tricks That Save Time
Dividing by 5
To divide any number by 5, multiply it by 2 and then divide by 10 (which just means moving the decimal point).
For example, 85 ÷ 5:
- Multiply by 2: 85 × 2 = 170
- Divide by 10: 170 ÷ 10 = 17
The Halving and Doubling Method
When dividing by an even number, you can halve the dividend and halve the divisor until the division becomes simpler.
For example, 96 ÷ 6:
- Halve both: 48 ÷ 3
- Now it’s easier: 48 ÷ 3 = 16
3. Percentage Calculations Without a Calculator
The 10% Method
To find percentages quickly:
- Find 10% by moving the decimal point one place left
- Use that to calculate other percentages
For example, to find 15% of 80:
- 10% of 80 is 8
- 5% of 80 is half of that: 4
- 15% = 10% + 5% = 8 + 4 = 12
The Percentage Flip Trick
To find what percentage one number is of another, you can use this approach:
For example, what percentage is 7 of 28?
- Divide the smaller by the larger: 7 ÷ 28 = 0.25
- Multiply by 100: 0.25 × 100 = 25%
4. Fraction Simplification Hacks
The GCD Shortcut
Instead of finding the greatest common divisor through trial and error, use this trick:
- Subtract the smaller number from the larger repeatedly until both numbers are equal
- That equal number is your GCD!
For example, simplify 48/60:
- 60 – 48 = 12
- 48 – 12 = 36
- 36 – 12 = 24
- 24 – 12 = 12
- 12 = 12 (We’ve reached equality!)
- Divide both by 12: 48/60 = 4/5
The Butterfly Method for Adding Fractions
When adding fractions with different denominators:
- Multiply the first numerator with the second denominator
- Multiply the second numerator with the first denominator
- Add these products for your new numerator
- Multiply the denominators for your new denominator
For example, 2/3 + 3/5:
- (2 × 5) + (3 × 3) = 10 + 9 = 19
- 3 × 5 = 15
- Result: 19/15
5. Memory Techniques for Math Formulas
The FOIL Method Reimagined
For multiplying binomials like (a + b)(c + d), remember “First, Outer, Inner, Last”:
- First terms: a × c
- Outer terms: a × d
- Inner terms: b × c
- Last terms: b × d
For example, (x + 3)(x + 2):
- F: x × x = x²
- O: x × 2 = 2x
- I: 3 × x = 3x
- L: 3 × 2 = 6
- Result: x² + 2x + 3x + 6 = x² + 5x + 6
The Quadratic Formula Song
Sing the quadratic formula to the tune of “Pop Goes the Weasel”: “x equals negative b, plus or minus the square root, of b-squared minus four a c, all over two a!”
6. Quick Mental Math for Everyday Problems
The Left-to-Right Addition Technique
Instead of adding numbers from right to left, try left to right:
For example, 358 + 273:
- Hundreds: 300 + 200 = 500
- Tens: 50 + 70 = 120
- Ones: 8 + 3 = 11
- Total: 500 + 120 + 11 = 631
Squaring Numbers Ending in 5
To square any number ending in 5:
- Multiply the first digit by itself + 1
- Put 25 at the end
For example, 35²:
- First digit (3) × (3 + 1) = 3 × 4 = 12
- Put 25 at the end: 1225
- So 35² = 1225
Conclusion: From Math Anxiety to Math Confidence
These math tricks do more than just help you solve problems—they build confidence. The next time your teacher calls on you, you won’t freeze up; you’ll lean into the challenge with these powerful shortcuts in your mental toolbox.
Remember, math isn’t about memorizing procedures—it’s about finding clever ways to solve problems. Keep practicing these tricks until they become second nature, and you’ll soon be the one helping your classmates!
Ready for more math magic? Sign up for our weekly newsletter “Math Made Easy” and get a new trick delivered to your inbox every Friday. Your next A+ math test is just a few clever shortcuts away!
References and Further Reading:
- Benjamin, A. (2006). Secrets of Mental Math. Three Rivers Press.
- McKellar, D. (2008). Math Doesn’t Suck: How to Survive Middle School Math Without Losing Your Mind or Breaking a Nail. Plume.
- Boaler, J. (2022). Mathematical Mindsets. YouCubed at Stanford University.