Long Division
Long division transforms abstract numbers into step-by-step problem solving that students can visualize and master. This systematic approach, aligned with CCSS.4.NBT and CCSS.5.NBT standards, builds number sense while teaching the fundamental skill of breaking large problems into manageable parts.
Try it right now
Why it matters
Long division appears everywhere in real-world calculations, from splitting a $168 restaurant bill among 6 friends to determining how many $25 textbooks fit within a $650 budget. Students use this skill when calculating miles per gallon (420 miles ÷ 12 gallons = 35 mpg), determining hourly wages ($336 earned ÷ 8 hours = $42/hour), or figuring out ingredient portions for recipes. Beyond practical applications, long division develops critical thinking and patience as students learn to estimate, check their work, and handle remainders systematically. The algorithm reinforces place value understanding when students work with numbers like 1,248 ÷ 12, requiring them to think about hundreds, tens, and ones positions. This foundation becomes essential for algebra, where polynomial long division mirrors the same logical sequence of steps students master with whole numbers.
How to solve long division
Long division — how to
- See how many times the divisor fits into the first digits of the dividend.
- Multiply, subtract, bring down the next digit.
- Repeat until nothing is left. Express remainder as a decimal.
Example: 728 ÷ 10: 72 r 8 → 72.8.
Worked examples
How many times does 3 fit into 6?
Answer: 2
- Understand what division means → 6 ÷ 3 — Division means sharing equally. Imagine splitting 6 sweets among 3 friends so everyone gets the same amount.
- How many times does 3 fit into 6? → 3 × 2 = 6 — We ask: '3 times what equals 6?' The answer is 2, because 3 × 2 = 6.
- Check: no leftovers → 6 - 6 = 0 — There is nothing left over. 6 divides evenly by 3.
- Write the answer → 6 ÷ 3 = 2 — Each friend gets 2. That is our answer!
- Verify by multiplying back → 2 × 3 = 6 ✓ — Multiply the answer by the divisor: 2 × 3 = 6. Correct!
168 ÷ 6 = _______
Answer: 28
- Understand what division means → 168 ÷ 6 — Division means sharing equally. Imagine splitting 168 sweets among 6 friends so everyone gets the same amount.
- How many times does 6 fit into 168? → 6 × 28 = 168 — We ask: '6 times what equals 168?' The answer is 28, because 6 × 28 = 168.
- Check: no leftovers → 168 - 168 = 0 — There is nothing left over. 168 divides evenly by 6.
- Write the answer → 168 ÷ 6 = 28 — Each friend gets 28. That is our answer!
- Verify by multiplying back → 28 × 6 = 168 ✓ — Multiply the answer by the divisor: 28 × 6 = 168. Correct!
You have $129.00 to buy items that cost $5.00 each. How many can you buy?
Answer: 25.8
- Understand the division → 129 ÷ 5 — We want to share 129 equally among 5 groups. Sometimes it does not divide perfectly, and we get leftovers.
- How many whole times does 5 go into 129? → 5 × 25 = 125 — 5 fits into 129 a total of 25 whole times. That accounts for 125 out of 129.
- Find the remainder (leftovers) → 129 - 125 = 4 — Subtract what we used: 129 - 125 = 4. There are 4 left that could not be shared evenly.
- Turn the remainder into a decimal → 4 ÷ 5 = 0.8 — Divide the leftover 4 by 5 to get the decimal part: 0.8. Think of it as cutting the remaining pieces into smaller equal slices.
- Combine whole part and decimal → 25 + 0.8 = 25.8 — The whole part is 25 and the decimal part is 0.8, giving 25.8.
- Verify by multiplying back → 25.8 × 5 ≈ 129 ✓ — Multiply the answer by the divisor: 25.8 × 5 should be close to 129.
Common mistakes
- ✗Students often misalign digits when writing quotients, placing 23 above the wrong positions in 736 ÷ 4, resulting in answers like 184 instead of the correct 184.
- ✗Many students incorrectly handle remainders by writing 85 ÷ 6 = 14 r 1 as 14.1 instead of converting properly to 14.17 (since 1 ÷ 6 = 0.166...).
- ✗Students frequently skip the subtraction step, continuing to divide without removing what they've already accounted for, leading to inflated quotients like getting 47 instead of 23 for 138 ÷ 6.
- ✗When estimating how many times the divisor fits, students often choose numbers that are too large, writing 8 × 9 = 82 when dividing 456 ÷ 9, instead of recognizing that 8 × 9 = 72.
Practice on your own
Generate unlimited long division worksheets with customizable difficulty levels and automatic answer keys using MathAnvil's free worksheet generator.
Generate free worksheets →