Division: Step-by-Step Guide
Division means splitting a number into equal groups. The number being split is the dividend, the number of groups (or the size of each group) is the divisor, and the answer is the quotient. Sometimes there is a little left over, called the remainder. In long division, we work through the dividend one digit at a time from left to right.
Math Racer skill guide · Elementary · Grades K-5
How to solve it, step by step
- Set up the problem. Write the dividend (the number being split) inside the long-division bracket. Write the divisor (the number you are dividing by) outside, on the left.\[\require{enclose} \begin{array}{r} \phantom{q} \\ b\,\enclose{longdiv}{a} \end{array}\]
- Divide into the first digits. Look at the first digit of the dividend. If the divisor fits into it, ask how many times it fits. If it does not fit, use the first two digits instead. Write the answer on top.\[q_i = \left\lfloor \frac{\text{current}}{b} \right\rfloor\]
- Multiply, subtract, bring down. Multiply your answer digit by the divisor and write the result underneath. Subtract. Then bring down the next digit and repeat until there are no more digits.\[r_i = \text{current} - q_i \cdot b,\quad \text{next current} = 10 r_i + a_{i+1}\]
- Write the remainder. If there is something left at the end, write it as 'R' and the number, or as a fraction. You can also keep going with decimals by adding a decimal point and zeros.\[a = q \cdot b + r,\quad 0 \le r < b\]
Worked example
Compute: 754 / 6
Step 1: Set up the problem: 6 ) 754.
Step 2: 6 goes into 7 one time. Write 1 on top. Multiply 1 x 6 = 6. Subtract: 7 - 6 = 1.
Step 3: Bring down the 5 to make 15. 6 goes into 15 two times. Write 2 on top. Multiply 2 x 6 = 12. Subtract: 15 - 12 = 3.
Step 4: Bring down the 4 to make 34. 6 goes into 34 five times. Write 5 on top. Multiply 5 x 6 = 30. Subtract: 34 - 30 = 4.
Step 5: There are no more digits to bring down. The answer is 125 with a remainder of 4, written 125 R 4. As a fraction, that is 125 and 4/6, which simplifies to 125 and 2/3.
Check: 125 x 6 = 750, and 750 + 4 = 754. That matches the number we started with.
Tips and common mistakes
- Work from left to right. This is the opposite of addition and subtraction.
- If the divisor does not fit into the first digit, use the first two digits. If it does not fit into a new number later on, write a 0 on top.
- To guess how many times the divisor fits, round both numbers to something easy.
- Check your work: divisor x answer + remainder should equal the number you started with.
- You can never divide by 0.
- For a decimal answer, put a decimal point in the answer and keep bringing down zeros.
- Divisibility tricks help. A number can be split evenly by 2 if it is even, by 5 if it ends in 0 or 5, and by 3 if its digits add up to a multiple of 3.