Long Division

The Steps: Divide, Multiply, Subtract, Bring Down

Remember the order: DMSB — Dad, Mom, Sister, Brother!

Example: $84 \div 4$

$84 \div 4 = 21$

Steps:

1. Divide: How many times does 4 go into 8? → $8 \div 4 = 2$
2. Multiply: $2 \times 4 = 8$
3. Subtract: $8 - 8 = 0$
4. Bring down the 4
5. Repeat: $4 \div 4 = 1$

Final answer: $84 \div 4 = 21$

Check your work: Multiply your answer by the divisor: $21 \times 4 = 84$ ✓

Remainders

Sometimes there's a number left over — that's the remainder.

Example: $17 \div 3$

| Step | Calculation | |------|------------| | How many 3s fit in 17? | $3 \times 5 = 15$ (fits!) | | What's left over? | $17 - 15 = 2$ | | Answer | $17 \div 3 = 5$ R $2$ |

This means: 3 goes into 17 five times with 2 left over.

Larger Numbers

Example: $156 \div 6$

1. $15 \div 6 = 2$ (remainder $3$)
2. Bring down the $6$ → $36$
3. $36 \div 6 = 6$ (no remainder)
4. Answer: $156 \div 6 = 26$

Check: $26 \times 6 = 156$ ✓

Checking Your Answer

You can always verify your division:

$\text{Quotient} \times \text{Divisor} + \text{Remainder} = \text{Dividend}$

• $84 \div 4 = 21$ → Check: $21 \times 4 = 84$ ✓
• $17 \div 3 = 5$ R $2$ → Check: $5 \times 3 + 2 = 17$ ✓

Tips to Remember

• Follow the steps in order: Divide, Multiply, Subtract, Bring Down
• Estimate first: Think about what the answer should be close to
• Always check by multiplying back
• Watch for remainders — they must be smaller than the divisor