7 Mental Math Tricks: [Updated Guide]

2 Basic Arithmetic Tricks

1. Addition and Subtraction

Rounding Up and Down

This is a powerful technique for making addition and subtraction a breeze in your head.

Here's how it works: you adjust the numbers to something easier to work with, do the math, then fix your answer at the end.

For example, say you're adding 387 + 456. 

1. You can round 387 up to 400 and 456 up to 460.
2. Now you've got 400 + 460 = 860. Easy, right?
3. But we're not done. Subtract what you rounded up: 860 - (13 + 4) = 843.

Bam! That's your answer.

You can pull the same trick with subtraction. Let's say you're doing 152–87. 

1. Round that 87 up to 90.
2. Now you've got 152–90 = 62.
3. Then just add back the 3 you rounded up: 62 + 3 = 65.

This is particularly useful when you're dealing with numbers close to 10s or 100s.

Working from Left to Right

A favorite of the mental math community.

When you're adding or subtracting in your head, work from left to right. It's how our brains naturally process numbers.

Let's say you're adding 346 + 285. Here's what you do:

1. Break it down: (300 + 40 + 6) + (200 + 80 + 5)
2. Add the hundreds: 300 + 200 = 500
3. Add the tens: 40 + 80 = 120
4. Add the ones: 6 + 5 = 11
5. Put it all together: 500 + 120 + 11 = 631

See how smooth that is? You're working with the big numbers first, then filling in the details.

Identifying Patterns and Multiples of 10

This is one where you can really show off.

Learn to spot patterns and work with multiples of 10. It'll make you lightning fast.

For example, say you've got a series of numbers like 7 + 8 + 3 + 2 + 5. 

Most people would add these up one by one. But not you. You'll see that 7 + 3 = 10 and 8 + 2 = 10. So now you've got 10 + 10 + 5 = 25. Done in a flash.

Another useful technique is the "Aim for Ten" method. When you're adding numbers close to 10, adjust one to make 10 and fix the other.

For instance, to calculate 9 + 7, think of it as (10 + 7) - 1 = 16. Similarly, for 8 + 5, think of it as (10 + 5) - 2 = 13.

2. Multiplication and Division

Multiplying by 5, 9, 10, and 11

These tricks are going to make you look like a math wizard.

• For multiplying by 5: Multiply by 10 and then cut it in half. So if you're doing 12 × 5, first do 12 × 10 = 120, then chop that in half. You get 60. Easy as pie.
• For multiplying by 9: Multiply by 10 and then subtract the original number. For example, 7 × 9 can be calculated as (7 × 10) - 7 = 70–7 = 63.
• For multiplying by 10: Everyone knows to just slap a zero on the end. 5 becomes 50, 23 becomes 230. A child could do it.
• For multiplying by 11 with two-digit numbers: Add the two digits and stick the result in the middle. So for 23 × 11, you add 2 + 3 = 5, and your answer is 253.

Using Multiplication Hacks

These will let you simplify complex-looking problems into more manageable ones.

Here's one called the distributive property. It's a fancy name for a simple idea that allows breaking down larger numbers into smaller, easier-to-manage parts.

Let's say you're multiplying 23 by 5. Think of it as (20 + 3) × 5. Now you've got (20 × 5) + (3 × 5) = 100 + 15 = 115. See how we turned a tricky problem into a couple of easy ones?

Here's another trick: doubling and halving. If you're multiplying two numbers, you can double one and halve the other. The answer stays the same.

So 25 × 16 becomes 50 × 8. Much easier to do in your head, right?

Division Shortcuts

One of the most useful division tricks is the divisibility test method.

This lets you know if a number divides evenly into another without actually doing the division. Here's the cheat sheet:

• Divisible by 2: Last digit is even (0, 2, 4, 6, or 8).
• Divisible by 3: Sum of its digits is divisible by 3.
• Divisible by 4: Last two digits are divisible by 4.
• Divisible by 5: Last digit is 0 or 5.
• Divisible by 6: Divisible by both 2 and 3.

Now, for dividing by 10, 100, or 1000, just move the decimal point left. So 5000 ÷ 100 = 50. You just moved the decimal point two places left. Simple as that.