1. Work left to right

School teaches right-to-left, but mentally it's easier to add the big parts first.

47 + 38 → 40 + 30 = 70, then 7 + 8 = 15 → 85

2. Round and compensate

Round one number to something easy, then correct at the end.

47 + 38 → 47 + 40 = 87, took 2 extra, so 87 − 2 = 85

3. Make a ten (bridging)

Move part of one number to complete a round number.

9 + 6 → take 1 from the 6 to make 10, then 10 + 5 = 15

68 + 27 → take 2 from 27: 70 + 25 = 95

1. Count up instead of down

Subtraction is just the distance between two numbers — walk from the small one up to the big one.

83 − 47 → from 47 to 50 is 3, from 50 to 83 is 33 → 3 + 33 = 36

2. Round and compensate

Subtract a round number, then give back the difference.

83 − 47 → 83 − 50 = 33, subtracted 3 too many, so 33 + 3 = 36

3. Work left to right

When no borrowing is needed, subtract tens then ones.

86 − 32 → 80 − 30 = 50, then 6 − 2 = 4 → 54

1. Break the number apart (distributive law)

Split one factor into tens and ones, multiply each, add them up. This is the workhorse of mental multiplication.

7 × 46 → 7 × 40 = 280, 7 × 6 = 42 → 280 + 42 = 322

2. Multiply by 5: ×10 then halve

48 × 5 → 48 × 10 = 480 → 480 ÷ 2 = 240

3. Multiply by 9: ×10 then subtract

9 × 37 → 370 − 37 = 333

4. Multiply by 11 (two-digit numbers)

Write the digits apart and put their sum in the middle (carry if needed).

11 × 52 → 5 _ 2 with 5 + 2 = 7 in the middle → 572

11 × 78 → 7 _ 8 with 15 in the middle → 7+1, 5, 8 → 858

5. Double one, halve the other

If one factor is even, you can trade until the problem becomes easy.

16 × 25 → 8 × 50 = 400 → 400

6. Squares ending in 5

Multiply the leading digit(s) by one more than itself and stick "25" on the end.

35² → 3 × 4 = 12 → 1225

1. Think of it as a multiplication question

Division is just asking "what times the divisor gives the dividend?" Strong times tables make division automatic.

84 ÷ 7 → 7 × ? = 84 → 7 × 12 = 84 → 12

2. Divide by 4 or 8: halve repeatedly

96 ÷ 4 → half of 96 is 48, half again → 24

3. Divide by 5: double, then ÷10

245 ÷ 5 → 245 × 2 = 490 → 490 ÷ 10 = 49

4. Break the dividend apart

Split the number into friendly chunks that the divisor goes into cleanly.

96 ÷ 6 → (60 + 36) ÷ 6 → 10 + 6 = 16

312 ÷ 4 → (280 + 32) ÷ 4 → 70 + 8 = 78

Solving problems you only hear trains working memory — the core skill of mental math.

• Visualize the numbers as you hear them — picture them written on a whiteboard.
• Start computing immediately. Process "forty-seven plus…" before the second number even arrives.
• Repeat without shame. Press R as many times as you need; holding numbers in your head improves quickly.
• Say intermediate results to yourself ("seventy… eighty-five") to anchor them in memory.