How to do long division
Your division as it's written on paper: the answer on top, and under the dividend what each step took away and left.
Here it is with your numbers:
- 13 doesn't go into 1, so start with 14. 14 ÷ 13 gives 1 (1 × 13 is 13); 14 − 13 leaves 1; bring down the 6 to make 16.
- 16 ÷ 13 gives 1 (1 × 13 is 13); 16 − 13 leaves 3; bring down the 1 to make 31.
- 31 ÷ 13 gives 2 (2 × 13 is 26); 31 − 26 leaves 5.
- Nothing is left to bring down, so the answer is 112 remainder 5.
- Check: 112 × 13 + 5 makes 1,461.
It means 13 goes into 1,461 112 times, with 5 left over.
Source OpenStax Prealgebra 2e · 1.5 Divide Whole Numbers ↗OpenStax Prealgebra 2e · 5.2 Decimal Operations ↗
What is a remainder?
A remainder is what is left over when a number doesn't divide evenly. With 28 cookies in bags of 8, you fill 3 bags and have 4 cookies left, so 28 ÷ 8 is 3 R4. To check an answer, multiply it by the divisor and add the remainder: 3 × 8 + 4 is 28.
The same answer can be a mixed number, 3 1/2, or a decimal, 3.5. Some decimals never end: 4 ÷ 3 is 1.333…, written with a line over the 3 that repeats.
Source OpenStax Prealgebra 2e · 5.3 Decimals and Fractions ↗
Long division examples
| Division | Answer |
|---|---|
| 78 ÷ 3 | 26 |
| 7,263 ÷ 9 | 807 |
| 1,439 ÷ 4 | 359 R3 |
| 74,521 ÷ 241 | 309 R52 |
| 3.99 ÷ 24 | 0.17 |
| −25.65 ÷ −0.06 | 427.5 |
In 7,263 ÷ 9, the 6 brought down is too small for 9, so a 0 goes in the answer: 807, not 87.
FAQs
How do you do long division step by step?
Divide, multiply, subtract, bring down, and repeat. Divide the first digits of the dividend by the divisor and write the answer above. Multiply that digit by the divisor, subtract the product, then bring down the next digit and do it again until there are no digits left. Whatever is left at the end is the remainder. To check, multiply the answer by the divisor and add the remainder.
Is long division still being taught?
Yes. The Common Core standards expect grade 6 students to “fluently divide multi-digit numbers using the standard algorithm”, which is long division.
Sources
- OpenStax Prealgebra 2e: 1.5 Divide Whole Numbers
- OpenStax Prealgebra 2e: 5.2 Decimal Operations
- OpenStax Prealgebra 2e: 5.3 Decimals and Fractions
- OpenStax Prealgebra 2e: 5.1 Decimals
- Common Core: Grade 6 The Number System (6.NS.B.2)