Squaring, Percentage, and Fraction Tricks You'll Use Every Day

Some math tricks are impressive but impractical. These aren't. The shortcuts in this post cover three areas that come up constantly in real life — squaring numbers, calculating percentages, and working with fractions. They're the tricks you'll actually use at the store, at a restaurant, or while helping with homework.

Squaring Tricks

1. Squaring Numbers Ending in 5

Take the digit(s) before the 5, multiply by one more than itself, and append 25.

• 25² → 2 × 3 = 6, append 25 → 625
• 45² → 4 × 5 = 20, append 25 → 2,025
• 85² → 8 × 9 = 72, append 25 → 7,225
• 115² → 11 × 12 = 132, append 25 → 13,225

2. Squaring Numbers Near 50

For numbers close to 50, there's a beautiful pattern.

Rule: For (50 + d), the answer starts with (25 + d) and ends with d².

• 53² → 25 + 3 = 28, 3² = 09 → 2,809
• 57² → 25 + 7 = 32, 7² = 49 → 3,249
• 46² → 25 − 4 = 21, 4² = 16 → 2,116
• 42² → 25 − 8 = 17, 8² = 64 → 1,764

Note: If d² is a 3-digit number, carry into the left part. For 59²: 25 + 9 = 34, 9² = 81 → 3,481. But for 58²: 25 + 8 = 33, 8² = 64 → 3,364 (no carry needed since 64 < 100).

3. Squaring Numbers Near 100

Rule: For (100 − d), the answer starts with (100 − 2d) and ends with d².

• 97² → 100 − 6 = 94, 3² = 09 → 9,409
• 93² → 100 − 14 = 86, 7² = 49 → 8,649
• 104² → 100 + 8 = 108, 4² = 16 → 10,816

4. The Difference of Squares Shortcut

To multiply two numbers that are the same distance from a round number, use the identity (a + b)(a − b) = a² − b².

• 48 × 52 = (50 − 2)(50 + 2) = 2,500 − 4 = 2,496
• 67 × 73 = (70 − 3)(70 + 3) = 4,900 − 9 = 4,891
• 99 × 101 = 10,000 − 1 = 9,999

5. The Anchor Method for Any Square

To square any number, pick the nearest multiple of 10 as your anchor.

Example: 23²

1. Nearest multiple of 10 is 20 (anchor). Distance = 3.
2. Go the same distance on the other side: 23 + 3 = 26.
3. Multiply anchor × far number: 20 × 26 = 520.
4. Add the distance squared: 520 + 3² = 520 + 9 = 529.

Another example: 67² → anchor 70, far = 64, 70 × 64 = 4,480, plus 3² = 9 → 4,489.

Percentage Tricks

6. The Percentage Flip Trick

This might be the most useful math trick of all: X% of Y always equals Y% of X.

• 8% of 25 is the same as 25% of 8 = 2 (much easier!)
• 4% of 75 = 75% of 4 = 3
• 12% of 50 = 50% of 12 = 6
• 6% of 200 = 200% of 6 = 12

This works because X% of Y = (X/100) × Y = (Y/100) × X = Y% of X. Whenever one direction is hard, flip it.

7. The 10% Method

Finding 10% is easy — just move the decimal point left one place. From there, you can build any percentage.

• 10% of 80 = 8
• 5% = half of 10% = 4
• 15% = 10% + 5% = 8 + 4 = 12
• 20% = 10% × 2 = 16
• 25% = divide by 4 = 20
• 30% = 10% × 3 = 24
• 1% = move decimal two places = 0.80, so 3% = 2.40

Restaurant tip? 15% of $64: 10% = $6.40, 5% = $3.20, total = $9.60. Sale price? 30% off $85: 10% = $8.50, 30% = $25.50, sale price = $59.50.

8. The “Is/Of” Method

For percentage word problems, use this template: “is” over “of” equals “percent” over 100.

• “What is 35% of 60?” → x/60 = 35/100 → x = 21
• “12 is what percent of 80?” → 12/80 = x/100 → x = 15%
• “9 is 25% of what?” → 9/x = 25/100 → x = 36

Fraction Tricks

9. The Butterfly Method for Adding Fractions

Draw two diagonal “wings” between the fractions. Cross-multiply for the new numerators, multiply the denominators for the new denominator.

Example: 2/3 + 3/5

The butterfly works for subtraction too — just subtract the wing products instead of adding. It's not the most elegant method, but it's reliable and easy to remember.

10. Cross-Canceling Before Multiplying Fractions

Before multiplying fractions, look diagonally for common factors and cancel them. This keeps the numbers small and often eliminates the need to simplify at the end.

• (4/9) × (3/8) → cancel 4 and 8 (divide by 4): (1/9) × (3/2). Cancel 9 and 3 (divide by 3): (1/3) × (1/2) = 1/6
• (6/7) × (14/15) → cancel 6 and 15 (divide by 3): (2/7) × (14/5). Cancel 7 and 14 (divide by 7): (2/1) × (2/5) = 4/5

11. Keep-Change-Flip for Dividing Fractions

To divide fractions: Keep the first fraction, Change the operation to multiplication, Flip the second fraction.

• (2/3) ÷ (4/5) → (2/3) × (5/4) = 10/12 = 5/6
• (7/8) ÷ (3/4) → (7/8) × (4/3) = 28/24 = 7/6

12. Cross-Multiplication for Comparing Fractions

To compare two fractions without finding a common denominator, cross-multiply. The larger cross-product points to the larger fraction.

• Is 3/7 or 5/11 larger? 3 × 11 = 33 vs. 5 × 7 = 35. 35 > 33, so 5/11 is larger.
• Is 4/9 or 7/15 larger? 4 × 15 = 60 vs. 7 × 9 = 63. 63 > 60, so 7/15 is larger.

The Common Thread

Every trick on this page works by transforming a hard problem into an easy one. Squaring 97? Turn it into (100 − 3). Computing 8% of 25? Flip it to 25% of 8. Adding unlike fractions? Draw the butterfly.

The best math students don't have bigger brains — they have more tools. Each shortcut is another tool in the kit.

This is Part 6 of our “Math Tricks Your Textbook Never Taught You” series. Next up: Math Competition Secrets: Tricks the Top Students Know.