Tables & multiplication · lesson 18 of 22 · free

Number patterns near squares — Tables & Multiplication Mastery

When two numbers are the same distance either side of a round number, the answer is that number squared minus the distance squared. 19 × 21 is one less than 20 × 20.

How it works

Middle square — “(a − d) × (a + d) = a² − d²”

  1. Find the middle number (20 for 19 × 21) and the distance from it (1).
  2. Square the middle number.
  3. Take away the distance squared.

Use it for: Pairs like 29 × 31, 47 × 53, 97 × 103 — the pattern 3 × 5 = 15 = 4 × 4 − 1 works for every square.

Worked example: 48 × 52 = 2496

  1. Both are 2 away from 50: 48 × 52 = 50² − 2².
  2. 50² = 2500 and 2² = 4.
  3. Take away: 2500 − 4 = 2496.

Check: 48 × 52 = 48 × 50 + 48 × 2 = 2400 + 96 = 2496 ✓

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🖨️ Multiplication Near Squares Worksheet

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