Study guides › Level 6 · Master

Multiplying numbers near a round number

Level 6 · Master · for questions like “49 × 51 = ?”

💡 The idea

When two numbers are the same distance either side of a round number, there's a shortcut:

(a − b)(a + b) = a² − b²

🪜 The steps

1. Find the round number in the middle (a) and how far each number is from it (b).
2. Square the round number, then take away b².

✏️ Worked examples

1. 49 × 51: the middle is 50, and each number is 1 away. 50² − 1² = 2,500 − 1 = 2,499.

2. 38 × 42: the middle is 40, and each number is 2 away. 1,600 − 4 = 1,596.

⚠️ Watch out

• Take away b², not b. For 38 × 42 you take away 4, not 2.
• It works only when both numbers are the same distance from the middle.

🎯 Try these

1. 29 × 31
2. 97 × 103
3. 65 × 75

Answers: 1) 899 2) 9,991 3) 4,875 (70² − 5²)

This guide is also in the 10MathQ app: tap “📖 Study guide” after a question.