MENTALMATH Logs

Take each place value in turn, biggest first, and adjust the running total when a column goes negative. 764 − 328 → hundreds: 700 − 300 = 400 → tens: 60 − 20 = 40, total 440 → units: 4 − 8 = −4, total 436. Check: 764 − 328 = 436. ✓ Where a column would need a "borrow" (units: 4 −...

Quiz: MENTALMATH / Addition & Subtraction | updated: Jul 30, 2026

713 — count up from 487 to 1,200. Use the shopkeeper route: 487 → 500 is 13 500 → 1,200 is 700 Total jump: 13 + 700 = 713 Counting up is often cleaner than borrowing across zeros.

Quiz: MENTALMATH / Addition & Subtraction | updated: Jul 30, 2026

Reduce each number to its digital root, do the same operation on the roots, and compare with the answer's root — a mismatch means an error. The digital root is the digit sum reduced to one digit. To check 47 × 23 = 1081: root(47) = 4+7 = 11 → 2 root(23) = 5 2 × 5 = 10 → 1 root(1...

Quiz: MENTALMATH / Checking & Vedic | updated: Jul 30, 2026

Prepend a zero, then each answer digit = that digit + the digit to its right, carrying as usual. For 633 × 11, write it as 0633 and add each digit to its right neighbour: 3 + (nothing) = 3 3 + 3 = 6 6 + 3 = 9 0 + 6 = 6 → 6963. Check: 633 × 11 = 6963. ✓ It's the same "insert the...

Quiz: MENTALMATH / Checking & Vedic | updated: Jul 30, 2026

Add and subtract the digits alternately; if that result is 0 or a multiple of 11, so is the number — because 10 ≡ −1 (mod 11). Since 10 ≡ −1 (mod 11), consecutive place values flip sign (+1, −1, +1, …), turning the number into an alternating digit sum mod 11: 918,082 → 9 − 1 + 8...

Quiz: MENTALMATH / Divisibility Rules | updated: Jul 30, 2026

Multiply by the round number above (10 or 100) and subtract the original. Because 9 = 10 − 1 and 99 = 100 − 1: 47 × 9 = 470 − 47 = 423. 47 × 99 = 4700 − 47 = 4653. Check: 47 × 9 = 423 ✓, 47 × 99 = 4653 ✓. This generalises: ×n9…9 is "shift and subtract." Far easier than the "fin...

Quiz: MENTALMATH / Multiplication Tricks | updated: Jul 30, 2026

Multiply the shared leading part by one more than itself, then append the product of the units. For t a × t b with a + b = 10: the answer is t·(t+1) followed by a·b (two digits): 84 × 86 → 8×9 = 72, and 4×6 = 24 → 7224. 43 × 47 → 4×5 = 20, and 3×7 = 21 → 2021. Check: 84 × 86 =...

Quiz: MENTALMATH / Multiplication Tricks | updated: Jul 30, 2026

Round each number to something easy, compute, and track whether you rounded up or down so you know which way the true answer leans. 312 + 488 → 300 + 500 = ~800 (actual 800). 47 × 19 → 47 × 20 = 940, but you rounded 19 up by 1 (≈ one 47 too many), so the true value is a bit unde...

Quiz: MENTALMATH / Percentages & Estimation | updated: Jul 30, 2026

Start from 25; add the amount above 50 (or subtract the amount below) for the first part, then tack on the square of that deviation as the last two digits. Write the number as 50 ± d. The result is (25 ± d) followed by d² (two digits): 47² (d = −3) → 25 − 3 = 22, and (−3)² = 09...

Quiz: MENTALMATH / Squaring Shortcuts | updated: Jul 30, 2026

Nudge A by d to the nearest multiple of ten, multiply the rounded-up and rounded-down numbers, then add d². Since A² = (A + d)(A − d) + d², choosing d to round A makes one factor a round number: 37² → d = 3: (40)(34) + 9 = 1360 + 9 = 1369. 48² → d = 2: (50)(46) + 4 = 2300 + 4 =...

Quiz: MENTALMATH / Squaring Shortcuts | updated: Jul 30, 2026