Mental math tricks for adults, how to tell which result is bigger without the full sum

September 26, 2026 · 7 min read · Tyamka team

Mental math tricks for telling which of two results is bigger. Rounding, comparing term by term, the last digit, and where each trick stops working.

A lot of everyday arithmetic is a comparison, not a calculation. Which basket costs more, which route is shorter, which offer leaves you with more. You rarely need the exact number, only the side that wins. The tricks below are for that one question, and you can try each one in the mental math game online on this site, called Bigger Sum in the app. It shows two expressions and you tap the one with the bigger result.

None of this is school arithmetic, with columns and written working. Each trick skips part of the calculation, and each has a point where it stops working, which is marked below. The most useful habit of all is to skip both totals and compare the parts, as in trick 2.

How the game frames the question

Bigger Sum shows two expressions side by side, such as 38 + 47 and 41 + 46. The results are never equal. Each pair has a time limit, a wrong answer or a timeout costs one of your three lives, and a faster right answer earns more points.

The levels change four things at once:

• Operations. Levels 1 and 2 are addition only, levels 3 and 4 add subtraction, levels 5 to 7 add multiplication, and from level 8 there is division too.
• Numbers. Addends grow from 1 to 9 on level 1 up to 1 to 99 on level 15.
• Closeness. On level 1 the two results can be up to 6 apart. On level 15 they are always exactly 1 apart.
• Time. The limit for a pair drops from 6 seconds to 2.6 seconds.

Trick 1. Estimate first, and know when it cannot decide

Outside a game, rounding settles most comparisons of this kind. A basket of 38 and 47 against one of 12 and 19 is roughly 90 against 30, and there is nothing more to do.

Where it stops. Rounding to the nearest ten moves each number by up to 5. With two numbers per side the error can reach 20. When the rounded results land within about 20 of each other, the estimate is a guess.

Bigger Sum starts exactly where estimation stops. Even on level 1 the two results are never more than 6 apart, so rounding is not reliable enough to pick the winner. Use it to see that two results are close, then switch to one of the tricks below.

Trick 2. Compare term by term, not total against total

When both sides are sums, you do not need either sum. Pair each number on the left with a number on the right and add up only the differences.

Take 38 + 47 against 41 + 46.

• 38 against 41, the right is 3 bigger.
• 47 against 46, the left is 1 bigger.
• Overall the right side is ahead by 2.

The results are 85 and 87, but you never needed them. You only handled small differences.

You can pair in any order that makes the differences easy. For 74 + 48 against 58 + 65, pair 74 with 65 and 48 with 58.

• 74 against 65, the left is 9 bigger.
• 48 against 58, the right is 10 bigger.
• The right side wins by 1.

The results are 122 and 123. With subtraction the same idea works, with one sign flipped. For 91 − 37 against 83 − 28, the first side starts 8 higher (91 against 83) but takes away 9 more (37 against 28). It ends 1 lower, 54 against 55.

Where it stops. Term by term needs the same kind of operation on both sides. Once a sum faces a product, you need at least one real value.

Trick 3. Make the number friendly before you add it

Adding 19 is adding 20 and taking 1 back. Subtracting 48 is subtracting 50 and adding 2. For subtraction there is a second move. Shift both numbers by the same amount and the difference does not change, so 97 − 65 is the same as 102 − 70, which is 32.

These moves are useful when one side is a product and the other a sum, and you need the sum's actual value. Take 6 × 7 against 19 + 24. The product is 42 from the times table. The sum is 20 + 24 − 1, which is 43. The sum wins by 1.

Trick 4. Know a few facts about products

Two small facts save time when both sides multiply.

• With the same sum, the closer pair gives the bigger product. 7 × 8 against 9 × 6. Both pairs add up to 15, and 7 and 8 are closer together, so 7 × 8 wins, 56 against 54.
• A number times itself beats its neighbours. 8 × 8 is 64 and 7 × 9 is 63, always one less. The same holds for 6 × 6 against 5 × 7, 36 against 35.

In the game the factors run from 2 up to 12 on the last levels, so the whole times table up to 12 × 12 is fair game. Division is the times table backwards. The game only shows divisions that come out exactly, such as 42 ÷ 6, so the answer is always a factor you already know, here 7.

Trick 5. When the results are close, look at the last digit

This one comes from how the game is built, and it only works on the levels where the results are close. From level 4 on, the two results are never more than 4 apart. On level 15 they are exactly 1 apart.

When two numbers are at most 4 apart, their last digits alone tell you which is bigger. Count forward from one last digit to the other, wrapping from 9 to 0. If you get there in 1 to 4 steps, the second number is the bigger one.

• 74 + 48 ends in 2, 58 + 65 ends in 3. One step forward, so 58 + 65 is bigger. Correct, 122 against 123.
• 3 × 11 ends in 3, 97 − 65 ends in 2. From 2 to 3 is one step, so 3 × 11 is bigger. Correct, 33 against 32.
• One result ends in 8 and the other in 1. From 8, the steps go 9, 0, 1, three steps, so the one ending in 1 wins, as with 58 against 61.

The last digit is often the cheapest part of a calculation. For a sum, add only the units. For a product, multiply only the units, since 17 × 3 ends in 1 because 7 × 3 = 21.

Where it stops. On levels 1 to 3 the results can be 5 or 6 apart, and the last digit can lie. 43 and 48 end in 3 and 8, which is five steps either way, so the digits alone cannot say. On levels 1 to 3, compare term by term instead.

Speed, and when not to hurry

Points in Bigger Sum come in two parts, 10 for a right answer and a speed bonus of up to 10 more. The bonus starts to drop at 0.2 seconds and then loses one point every 400 milliseconds. An answer in under 0.2 seconds gets the full bonus, an answer at 2 seconds gets 5, and from 3.8 seconds there is no bonus, only the 10 base points.

A wrong answer costs a life and gives nothing. A slow right answer still gives at least 10. So on a pair you are unsure of, if the time limit allows, checking once more is better than guessing.

One more detail. On every level exactly half of the pairs have the bigger result on the first side. Always tapping the same side is right half the time and costs a life on the other half, so it ends the run fast.

Which trick for which level

What this is and is not

These are tricks for one narrow task, choosing the bigger of two results quickly. Some are handy at a till too. We do not claim they change anything beyond that. Your score shows how you did on a level that day, and it moves with sleep, practice and the device you play on.

If you want to try them, Bigger Sum is free up to level 5. Two other logic games on the site sit next to it, the maze and the sum puzzle, and every game is on the all games page.