Math Tricks for Students: Simple Tips to Make Math Easier

 Math Tricks for Students: Simple Tips to Make Math Easier

Math is one of those subjects that students either enjoy—or find intimidating. But the truth is that math becomes much easier when you learn a few simple tricks. These tricks don’t replace real understanding, but they help you work faster, check your work, and develop confidence.

In this article, we’ll explore fun, practical math tricks every student can use. Whether you’re solving basic arithmetic, fractions, algebra, or mental math, these tips can help make learning smoother and more enjoyable.

Why Math Tricks Matter

Students often ask, “Why do I need to learn tricks if I have a calculator?” The answer is simple: math tricks sharpen your brain. They help you:

• Solve problems faster
• Reduce careless mistakes
• Better understand number patterns
• Improve your memory
• Gain confidence in math class

Even professionals—engineers, scientists, business analysts—use mental shortcuts all the time. You don’t have to be a “math genius” to master these techniques.

Mental Math Tricks That Make Calculation Easier

Let’s start with simple mental math strategies that anyone can use.

The “9s Trick” for Multiplication

Multiplying by 9 can feel hard—but there’s an easy pattern.

Trick:
For any number 1–9, the digits of the answer for 9 × n always add up to 9.

Example:

• 9 × 3 = 27 → 2 + 7 = 9

• 9 × 6 = 54 → 5 + 4 = 9

Another method is using your fingers:
Hold out both hands. To compute 9 × n, bend down the n-th finger. The number of fingers on the left gives the tens digit, and the fingers on the right give the units digit.

Example:
To find 9 × 4, bend your fourth finger. You see 3 fingers on the left and 6 on the right → 36.

Quickly Square Any Number Ending With 5

Numbers ending in 5 are extremely easy to square.

Formula:
If a number ends in 5 (like 35), then

$$(10a + 5)^2 = a(a+1) \,|\, 25$$

Steps:

1. Take the first digit(s) before 5.

2. Multiply that number by the next higher number.

3. Add “25” to the end.

Example:
35²

• Number before 5 = 3

• Multiply 3 × 4 = 12

• Attach 25 → 1225

Try 65²:

• 6 × 7 = 42

• Attach 25 → 4225

Easy, right?

 Multiplying Big Numbers Close to 100

Use this trick when numbers are near 100, like 97 × 96.

Steps:

1. Subtract each number from 100.
2. Multiply those differences.
3. Subtract one number’s difference from the other number.
4. Combine the results.

Example:
97 × 96

• 100 – 97 = 3

• 100 – 96 = 4

Multiply differences:

• 3 × 4 = 12

Subtract one difference from the other number:

• 97 – 4 = 93

Now put them together:
→ 9312

 Multiplying by 11 (Two-Digit Numbers)

For a two-digit number, say ab, multiplying by 11 is easy.

Trick:
Add the digits and place the sum in the middle:

Example:
42 × 11

• 4 + 2 = 6

• Answer: 462

53 × 11

• 5 + 3 = 8

• Answer: 583

If the sum is a two-digit number, carry over.

Example:
57 × 11

• 5 + 7 = 12

• Write 2 and carry 1

• Result: 627

Fraction Tricks

Fractions scare many students, but they’re manageable with a few techniques.

The Butterfly Method for Comparing Fractions

To compare a/b and c/d, cross-multiply and compare:

$$a \times d \quad \text{vs.} \quad b \times c$$

Whichever product is bigger determines the bigger fraction.

Example:
Compare 3/4 and 2/3.

• 3×3 = 9

• 4×2 = 8

Since 9 > 8, 3/4 is larger.

Turning Ugly Fractions Into “Friendly Fractions”

Sometimes changing the fraction makes a problem easier.

Example:
Instead of computing

$$\frac{49}{98}$$

Notice both numbers divide by 49.

→ 49/98 = 1/2

This technique helps simplify long division and algebra later.

The “Cross-Cancel” Trick in Multiplication

When multiplying fractions, reduce across before multiplying.

Example:

$$\frac{4}{15} \times \frac{5}{8}$$

Cross-cancel:

• 4 and 8 → divide by 4 → 1 and 2

• 5 and 15 → divide by 5 → 1 and 3

Now multiply:

$$\frac{1}{3} \times \frac{1}{2} = \frac{1}{6}$$

Much faster!

Algebra Tricks for Beginners

Algebra becomes easier when you know what to look for. Here are some helpful tools.

The “Opposite Operation” Rule

To isolate a variable, always do the opposite of what is happening.

If you see:

• addition → subtract
• subtraction → add
• multiplication → divide
• division → multiply
• exponent → take the root

Example:
Solve:

$$3x + 5 = 20$$

Subtract 5: 3x = 15
Divide by 3: x = 5

This rule works in nearly every beginning algebra problem.

Recognizing Common Factor Patterns

Some expressions repeat so often that learning the patterns saves time.

(a + b)² = a² + 2ab + b²

Example:
(2x + 3)²
→ 4x² + 12x + 9

(a – b)² = a² – 2ab + b²

Example:
(5y – 1)²
→ 25y² – 10y + 1

(a + b)(a – b) = a² – b²

Example:
(6 + x)(6 – x)
→ 36 – x²

These shortcuts appear everywhere in algebra.

Solving Proportions Easily

If

$$\frac{a}{b} = \frac{c}{d}$$

Then
ad = bc.

Example:

$$\frac{7}{x} = \frac{14}{20}$$

Cross-multiply:
7 × 20 = 14x
140 = 14x
x = 10

No need to memorize complicated steps.

Geometry Tricks

Geometry is full of patterns and shortcuts too.

The “Triangle Sum” Trick

The angles in every triangle always add to 180°.

If you know two angles, subtract from 180 to find the third.

Example:
Angles are 45° and 85°:
Remaining = 180 – (45 + 85) = 50°

The Pythagorean Triples

If a right triangle has side lengths that follow certain patterns, you can skip calculations.

Common triples:

• 3, 4, 5

• 6, 8, 10

• 5, 12, 13

If two sides match one of these sets, you know the third instantly.

Example:
A right triangle has legs 12 and 5 → hypotenuse = 13.

Area Shortcut for Triangles

The formula

$$\text{Area} = \frac{1}{2}bh$$

is common, but here’s a trick:

If the base is doubled and the height is halved, the area stays the same.

Example:
Triangle with base 10 and height 6 → area = 30
Triangle with base 20 and height 3 → area = 30

Helps with quick simplification.

 Study Strategies for Better Math Performance

Math tricks are helpful, but learning habits matter more. Here are strategies students can use daily.

Practice Small Amounts Daily: Short 10-minute sessions beat long cram sessions. Your brain remembers more when learning is spaced out.

Solve Problems Without a Calculator: Try solving easy problems mentally. This sharpens your intuition and helps you become confident.

Check Your Work the Smart Way

Instead of simply redoing the problem, use fast checks:

• Estimate the answer
• Use the opposite operation
• Plug your answer back into the equation

Example:
If x = 3 is your answer in 2x + 4 = 10:
Plug in: 2(3)+4=10 → correct.

Convert Word Problems Into Drawings: Many students struggle with word problems. Drawing a picture makes the problem clearer.

If a school bus holds 40 students and three buses arrive, draw three rectangles and put 40 in each. Simple visuals make problems easier to understand.

 Memory Tricks for Math

Some formulas and facts are easier when turned into patterns.

PEMDAS – Operation Order

Remember the order of operations:

Parentheses
Exponents
Multiply
Divide
Add
Subtract

A common mnemonic: Please Excuse My Dear Aunt Sally.

Multiplying by 4 Trick

To multiply by 4, just double the number twice.

Example:
12 × 4
12 → 24 → 48

 “11 Rule” for Two-Digit Patterns

We covered multiplying by 11 earlier, but this also helps memorize patterns:

• 121

• 1331

• 14641

These are rows in Pascal’s Triangle, useful for binomial expansions.

References & Further Reading

Below are reputable, general sources for learning math concepts and strategies:

• “How to Solve It” by George Pólya – Classic book on mathematical thinking.
• “The Joy of x” by Steven Strogatz – Friendly introductions to math ideas.
• Khan Academy (math practice and lessons) – Free structured math learning.
• National Council of Teachers of Mathematics (NCTM) – Research-based math strategies.
• MathIsFun.com – Simple explanations and helpful visuals.

These sources provide additional explanations and practice for the tricks covered here.

Conclusion

Math doesn’t have to be difficult or stressful. With the right tricks, a bit of practice, and a positive attitude, any student can improve their math skills. The key is understanding patterns, using smart shortcuts, and practicing regularly.

Remember: Math is not about being perfect. It’s about learning how to think.