# 30 Mental Math Examples Worked Step By Step

TL;DR

Mental math examples show the actual moves a person makes in their head to solve a problem without paper — and the 30 below are worked step by step across every operation, with the reasoning, not just the trick. They cover addition, subtraction, multiplication, division, fractions, and percentages, each chosen to teach a method you can reuse. Read the method, not only the answer.

## How To Read These Examples

Each of these 30 mental math examples is worked the way you would actually do it in your head - broken into the small moves, with a line on _why_ the move works. The point is not to memorize 30 answers. It is to pick up six or seven reusable methods that turn hard-looking problems into easy ones.

The examples are grouped by operation, easiest first. A few habits to carry through all of them:

- **Work left to right.** Written algorithms go right to left because of carrying. In your head, left to right is easier - you say the big part of the answer first and hold less in memory.
- **Round, then adjust.** Most mental shortcuts are some version of "use a friendly number, then fix the difference." Spotting that pattern once unlocks dozens of problems.
- **Read the method, then cover it.** Look at the worked steps, then redo the example yourself before checking. Passive reading does not build the skill; the redo does.

## Addition Examples

### **Example 1: 63+29**

Round 29 up to 30, add, then take back the 1 you added.

63+30=93  
93−1=92

**Final answer: 92**

### **Example 2: 47+38**

Add the tens, then the ones.

40+30=70  
7+8=15  
70+15=85

**Final answer: 85**

### **Example 3: 325+476**

300+400=700  
20+70=90  
5+6=11  
700+90+11=801

**Final answer: 801**

### **Example 4: 198+247**

198 is just 2 short of 200.

200+247=447  
447−2=445

**Final answer: 445**

### **Example 5: 26+39+14**

26 and 14 make a friendly 40.

26+14=40  
40+39=79

**Final answer: 79**

## Subtraction Examples

### **Example 6: 52−38**

Count from 38 to 52, not down from 52.

38→40 is 2  
40→52 is 12  
2+12=14

**Final answer: 14**

### **Example 7: 100−64**

64→100 is just 36.

**Final answer: 36**

### **Example 8: 83−29**

Subtract 30, then give back 1.

83−30=53  
53+1=54

**Final answer: 54**

### **Example 9: 500−247**

247→250 is 3  
250→500 is 250  
3+250=253

**Final answer: 253**

### **Example 10: 1000−638**

Subtract each digit from 9, then the last from 10.

9−6=3, 9−3=6, 10−8=2

**Final answer: 362**

## Multiplication Examples

### **Example 11: 453×7**

7×400=2800  
7×50=350  
7×3=21  
2800+350+21=3171

**Final answer: 3171**

### **Example 12: 5×63**

63×10=630  
630÷2=315

**Final answer: 315**

### **Example 13: 25×16**

25 is a quarter of 100, so 25×16=4×100.  
16÷4=4  
4×100=400

**Final answer: 400**

### **Example 14: 99×7**

100×7=700  
700−7=693

**Final answer: 693**

### **Example 15: 12×15**

12×15=12×10+12×5  
120+60=180

**Final answer: 180**

### **Example 16: 18×5**

Halve 18, double 5: 9×10.

9×10=90

**Final answer: 90**

### **Example 17: 34×11**

34×11=34×10+34  
340+34=374

**Final answer: 374**

## Division Examples

### **Example 18: 144÷8**

Dividing by 8 is halving three times.

144÷2=72, 72÷2=36, 36÷2=18

**Final answer: 18**

### **Example 19: 96÷6**

60÷6=10  
36÷6=6  
10+6=16

**Final answer: 16**

### **Example 20: 250÷5**

Dividing by 5 is the reverse of the ×5 shortcut.

250×2=500  
500÷10=50

**Final answer: 50**

### **Example 21: 420÷12**

12×35=420.

**Final answer: 35**

## Fraction Examples

### **Example 22: 34\frac{3}{4} of 60**

Find a quarter, then take three of them.

60÷4=15  
15×3=45

**Final answer: 45**

### **Example 23: 23\frac{2}{3} of 90**

90÷3=30  
30×2=60

**Final answer: 60**

### **Example 24: 12+14\frac{1}{2} + \frac{1}{4}**

You cannot add halves and quarters directly - rewrite the half as two quarters.

**Final answer: 34\frac{3}{4}**

### **Example 25: 56−13\frac{5}{6}**

Rewrite thirds as sixths.

**Final answer: 12\frac{1}{2}**

## Percentage Examples

### **Example 26: 10% of 250**

250→25.0, so 10% of 250=25.

**Final answer: 25**

### **Example 27: 25% of 80**

80÷4=20.

**Final answer: 20**

### **Example 28: 15% of 60**

10% of 60=6;
5% is half of that =3.

**Final answer: 9**

### **Example 29: 20% tip on 45**

10% of 45=4.5;  
4.5×2=9.

**Final answer: 9**

### **Example 30: 8% of 50**

Here is a move that surprised me the first time I taught it: a% of b equals b% of a.

**Final answer: 4**

## Why These Methods Work - The Idea Underneath

Every mental math example above is one idea wearing different clothes: change the problem into an easier one, then correct for the change.

That is the whole game. When you turn 63+29 into 63+30−1, you traded a hard addition for an easy one plus a tiny correction. Mental math is not a bag of unrelated tricks - it is the repeated habit of reshaping a number into a friendlier form.

That reframing rests on a few structural facts about how numbers work:

- **Numbers can be split and recombined.** 325 is 300+20+5, and you can add or multiply each piece on its own. This is the distributive property.
- **Operations have partners.** Subtraction undoes addition; division undoes multiplication. Counting up to solve 52−38 uses that partnership directly.
- **Friendly numbers are everywhere.** Tens, hundreds, halves, and quarters are easy to compute with, so the skill is spotting how close a problem sits to one of them.

## Common Mistakes With Mental Math

### **1. Memorizing the trick without the reasoning.**

Where it slips in: A student learns the 11-times shortcut as a rule, then misapplies it.

The correct way: Learn the trick _as_ ×10+×1. Then the carrying case is obvious.

### **2. Forgetting the adjustment step.**

Where it slips in: The rusher does 83−30=53 and stops there, forgetting to add back the extra 1.

The correct way: Whenever you round to make a problem easier, always think about what you changed, and how to undo it.

### **3. Right-to-left thinking carried over from paper.**

Doing mental addition right to left is unnecessarily complex. Work from left to right instead.

## Conclusion

Mental math examples are worth far more when you read the method than when you just check the answer. Every one is the same move in disguise: reshape the number into something friendlier, then correct for the change.