Mental Math Tricks

Calculators are everywhere, so why practice mental math? Because mental math trains number sense — the feel for how big numbers are, how they split, and how they round. Estimating a bill, checking a receipt, racing a quiz clock: that is where it shows up.

Add from the left

Written addition starts at the ones place; mental addition goes the other way — start from the big end, saying the running total as you go. To add $47 + 38$ : first the tens, $47 + 30 = 77$ ; then the ones, $77 + 8 = 85$ .

An even friendlier variant is round and compensate: see 38 as 40, so $47 + 40 = 87$ ; you added 2 too many, so give it back — $87 - 2 = 85$ . Rounding tames the numbers, compensating returns the change.

Shortcuts for times 5 and times 9

Times 5 = times 10, then halve: for $48 \times 5$ , first $48 \times 10 = 480$ , then $480 \div 2 = 240$ ;
Times 9 = times 10, minus itself: $34 \times 9 = 340 - 34 = 306$ .

Neither trick is magic: $5 = 10 \div 2$ and $9 = 10 - 1$ .

The times 11 trick

For a two-digit number times 11: pull the digits apart, add them in the middle.

$34 \times 11$ : head 3, tail 4, middle $3 + 4 = 7$ → 374;
With carrying: $67 \times 11$ , head 6, tail 7, middle $6 + 7 = 13$ — write 3 in the middle, carry 1 to the head, so the head becomes $6 + 1 = 7$ → 737.

Check it honestly

The long way: $67 \times 10 = 670$ , then add the number itself, $670 + 67 = 737$ . The shortcut did not lie — times 11 is really "times 10 plus itself", and the trick just lines that up into a tidy shape.

Break big numbers apart

Do not wrestle big numbers — split them into easy chunks:

$6 \times 45 = 6 \times 40 + 6 \times 5 = 240 + 30 = 270$ ;
$98 + 37 = 100 + 37 - 2 = 135$ .

Friendly targets (100, 10, 5) are the compass for splitting. Estimate first, then compute exactly — the same feel trained in Estimation: estimation answers "roughly how much", splitting answers "exactly how much".

Practice habits

Three minutes a day beats one hour at the weekend;
Say the intermediate steps out loud — the reasoning sticks better;
Estimate first: $48 \times 5$ should land near $50 \times 5 = 250$ , so an answer of 240 earns trust;
Shortcuts are accelerated basics — once $48 \times 10$ and $480 \div 2$ are smooth, the fast moves hold steady. Then level up at the Times Tables Challenge.

InteractiveMental Math Arena

98 + 22 = ?

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Compute first, then be quick

Shortcuts grow out of honest arithmetic. Make sure the basic written and oral methods are solid, then pick one or two shortcuts and use them daily — once they settle in, they become your first reflex.

Quick quiz

1. Adding 47 + 38 in your head by “round and compensate”, what should you compute?
2. What is the mental shortcut for 48 × 5?
3. 67 × 11 = ?