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.
If you want a fuller catalogue of the shortcuts these examples lean on, the guide to mental math tricks lays each one out. For the youngest learners, mental math for kids keeps the same methods at a gentler pace.
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: $47 + 38$ (left to right)
Add the tens, then the ones.
$40 + 30 = 70$
$7 + 8 = 15$
$70 + 15 = 85$
Final answer: 85
Example 3: $325 + 476$ (split by place value)
$300 + 400 = 700$
$20 + 70 = 90$
$5 + 6 = 11$
$700 + 90 + 11 = 801$
Final answer: 801
Example 4: $198 + 247$ (compensate)
198 is just 2 short of 200.
$200 + 247 = 447$
$447 - 2 = 445$
Final answer: 445
Example 5: $26 + 39 + 14$ (look for pairs)
26 and 14 make a friendly 40.
$26 + 14 = 40$
$40 + 39 = 79$
Final answer: 79
Subtraction Examples
Example 6: $52 - 38$ (count up)
Count from 38 to 52, not down from 52.
$38 \rightarrow 40$ is 2
$40 \rightarrow 52$ is 12
$2 + 12 = 14$
Final answer: 14
Example 7: $100 - 64$ (count up to a round number)
$64 \rightarrow 100$ is just $36$.
Final answer: 36
Example 8: $83 - 29$ (round and adjust)
Subtract 30, then give back 1.
$83 - 30 = 53$
$53 + 1 = 54$
Final answer: 54
Example 9: $500 - 247$ (count up across places)
$247 \rightarrow 250$ is 3
$250 \rightarrow 500$ is 250
$3 + 250 = 253$
Final answer: 253
Example 10: $1000 - 638$ (the all-nines shortcut)
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: $453 \times 7$ (distribute over place value)
$7 \times 400 = 2800$
$7 \times 50 = 350$
$7 \times 3 = 21$
$2800 + 350 + 21 = 3171$
Final answer: 3171
Example 12: $5 \times 63$ (multiply by 10, halve)
$63 \times 10 = 630$
$630 \div 2 = 315$
Final answer: 315
Example 13: $25 \times 16$ (quarters of 100)
25 is a quarter of 100, so $25 \times 16 = \frac{16}{4} \times 100$.
$16 \div 4 = 4$
$4 \times 100 = 400$
Final answer: 400
Example 14: $99 \times 7$ (round and subtract)
$100 \times 7 = 700$
$700 - 7 = 693$
Final answer: 693
Example 15: $12 \times 15$ (break one factor)
$12 \times 15 = 12 \times 10 + 12 \times 5$
$120 + 60 = 180$
Final answer: 180
Example 16: $18 \times 5$ (doubling and halving)
Halve 18, double 5: $9 \times 10$.
$9 \times 10 = 90$
Final answer: 90
Example 17: $34 \times 11$ (the 11 trick, and why)
$34 \times 11 = 34 \times 10 + 34$
$340 + 34 = 374$
Final answer: 374
Division Examples
Example 18: $144 \div 8$ (halve twice, then once more)
Dividing by 8 is halving three times.
$144 \div 2 = 72$, $72 \div 2 = 36$, $36 \div 2 = 18$
Final answer: 18
Example 19: $96 \div 6$ (split the dividend)
$60 \div 6 = 10$
$36 \div 6 = 6$
$10 + 6 = 16$
Final answer: 16
Example 20: $250 \div 5$ (multiply by 2, divide by 10)
Dividing by 5 is the reverse of the $\times 5$ shortcut.
$250 \times 2 = 500$
$500 \div 10 = 50$
Final answer: 50
Example 21: $420 \div 12$ (use a known fact)
$12 \times 35 = 420$, because $12 \times 30 = 360$ and $12 \times 5 = 60$.
Final answer: 35
Fraction Examples
Example 22: $\frac{3}{4}$ of $60$
Find a quarter, then take three of them.
$60 \div 4 = 15$
$15 \times 3 = 45$
Final answer: 45
Example 23: $\frac{2}{3}$ of $90$
$90 \div 3 = 30$
$30 \times 2 = 60$
Final answer: 60
Example 24: $\frac{1}{2} + \frac{1}{4}$ (re-cut to the same size)
You cannot add halves and quarters directly - rewrite the half as two quarters.
$\frac{1}{2} = \frac{2}{4}$
$\frac{2}{4} + \frac{1}{4} = \frac{3}{4}$
Final answer: $\frac{3}{4}$
Example 25: $\frac{5}{6} - \frac{1}{3}$
Rewrite thirds as sixths.
$\frac{1}{3} = \frac{2}{6}$
$\frac{5}{6} - \frac{2}{6} = \frac{3}{6} = \frac{1}{2}$
Final answer: $\frac{1}{2}$
Percentage Examples
Example 26: $10%$ of $250$ (move the decimal)
$250 \rightarrow 25.0$, so $10%$ of $250 = 25$.
Final answer: 25
Example 27: $25%$ of $80$ (quarter)
$80 \div 4 = 20$
Final answer: 20
Example 28: $15%$ of $60$ (build from 10%)
$10%$ of $60 = 6$
$5%$ is half of that $= 3$
$6 + 3 = 9$
Final answer: 9
Example 29: $20%$ tip on $45$
$10%$ of $45 = 4.5$
$4.5 \times 2 = 9$
Final answer: 9
Example 30: $8%$ of $50$ (swap the percentage)
Here is a move that surprised me the first time I taught it: $a%$ of $b$ equals $b%$ of $a$. So $8%$ of $50$ is the same as $50%$ of $8$.
$50%$ of $8 = 4$
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. When you find $\frac{3}{4}$ of 60 by first finding a quarter, you broke a multi-step fraction into two steps a child can hold. 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, the same one a child meets again in algebra as expanding brackets.
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.
A child who memorizes "halve and times ten for $\times 5$" but never sees why will forget it under pressure. A child who understands that $\times 5$ is just $\times 10 \div 2$ can rebuild it any time. The reasoning is the part that lasts.
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 on $11 \times 47$ where the digits carry, and gets a wrong answer they cannot debug.
The correct way:
Learn the trick as $\times 10 + \times 1$. Then the carrying case ($340 + 34$, or for $47$: $470 + 47 = 517$) is obvious instead of magic.
2. Forgetting the adjustment step.
Where it slips in:
The rusher does $83 - 30 = 53$ to solve $83 - 29$ and stops there, forgetting to add back the extra 1.
The correct way:
Whenever you round to make a problem easier, the very next thought is "what did I change, and how do I undo it?" Round-and-adjust is two steps, never one.
3. Right-to-left thinking carried over from paper.
Doing mental addition right to left forces you to remember digits in reverse - which is exactly when numbers slip. Left to right says the largest part of the answer first and holds less in memory.
How Bhanzu Teaches Mental Math
Bhanzu does not lead with the trick. It leads with the structure, so the tricks become things a learner could have figured out themselves.
A Bhanzu trainer teaching $\times 5$ would not say "memorize: halve and times ten." They would ask why $5$ is half of $10$, let the child notice it, and watch the shortcut appear on its own. That order matters. Mental agility built from understanding number structure transfers - to estimation, to algebra, to any problem the child has not seen before - while a memorized procedure only covers the cases it was drilled on. Every learner starts at Level 0 so the trainer builds on what the child genuinely understands, not on what a grade level assumes.
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. Learn that habit and the individual tricks take care of themselves.
To build this with a teacher who starts from understanding, explore Bhanzu's mental maths for kids program or live math tutoring that teaches the reasoning, not the rote.
Want to see the WHY-first method in a live class? Book a free demo.
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