Long Division Hack

Aim

Help students quickly create key multiples of a two-digit number (e.g., 17) to make long division faster and more manageable.

What You Need

• Pen and paper
• The divisor you are working with (e.g., 17)

How to Play / Steps

1. Start with 1× the divisor.
   • Example: 17 × 1 = 17
2. Double it for 2×.
   • 17 × 2 = 34
3. Double again for 4×.
   • 34 × 2 = 68
4. Calculate 10×.
   • 17 × 10 = 170
   • Easy to use as a reference point for larger multiples.
5. Calculate 5× by halving 10×.
   • 170 ÷ 2 = 85
6. Use these “partial tables” to quickly subtract multiples of the divisor when performing long division.
   • Example: If dividing 306 ÷ 17, you can see 17 × 10 = 170, 17 × 5 = 85, etc., and use these to work out how many times 17 fits into 306 efficiently.

Benefits

• Speed: Reduces the need to write out the full times table.
• Memory Aid: Students can focus on just a few key multiples.
• Doubling & Halving Practice: Reinforces these mental maths strategies.
• Confidence: Makes long division with unfamiliar divisors less intimidating.

Tip

• Encourage students to write only the multiples they are likely to need in the division problem instead of the entire times table.
• This method works well for two-digit divisors and can be adapted for other numbers using the same doubling/halving approach.