Dividing by Two-Digit Divisors

Dividing multi-digit numbers by a two-digit divisor uses the same long division steps you already know: Divide, Multiply, Subtract, and Bring down. The only difference is that you are working with larger numbers!

Estimating the Quotient

Before you start dividing, it helps to estimate the answer. This gives you a target and helps you guess the first digit of your quotient.

Example: Estimate $6{,}345 \div 28$

1. Round the divisor to the nearest ten: $28$ rounds to $30$.
2. Round the dividend to a compatible number (a number easy to divide by 30): $6{,}345$ is close to $6{,}300$.
3. Divide mentally: $6{,}300 \div 30 = 210$.

Your actual answer should be close to $210$.

The Long Division Steps

Let's solve $4{,}536 \div 24$ step-by-step.

1. Divide: Look at the first two digits of the dividend ($45$). How many times does $24$ go into $45$? It goes in $1$ time.
2. Multiply: $1 \times 24 = 24$.
3. Subtract: $45 - 24 = 21$.
4. Bring Down: Bring down the next digit ($3$) to make $213$.
5. Repeat:
   • How many times does $24$ go into $213$? Think: $24$ is close to $25$, and $25 \times 8 = 200$. Let's try $8$.
   • $8 \times 24 = 192$.
   • $213 - 192 = 21$.
   • Bring down the $6$ to make $216$.
6. Repeat Again:
   • How many times does $24$ go into $216$? Let's try $9$.
   • $9 \times 24 = 216$.
   • $216 - 216 = 0$.

Since there is nothing left to bring down and the remainder is $0$, the final answer is $189$.

Checking Your Answer

You can always check your division by using multiplication. Use this formula:

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

Let's check our previous answer ($189$): $189 \times 24 = 4{,}536$ Since there is no remainder, we just multiply. The result matches our original dividend, so the answer is correct!

Example with a Remainder

Let's try $7{,}890 \div 35$:

1. $78 \div 35 = 2$. Multiply $2 \times 35 = 70$. Subtract $78 - 70 = 8$. Bring down the $9$ to make $89$.
2. $89 \div 35 = 2$. Multiply $2 \times 35 = 70$. Subtract $89 - 70 = 19$. Bring down the $0$ to make $190$.
3. $190 \div 35 = 5$. Multiply $5 \times 35 = 175$. Subtract $190 - 175 = 15$.

There are no more numbers to bring down. The quotient is $225$ with a remainder of $15$, written as $225 \text{ R } 15$.

Check the answer: $(225 \times 35) + 15 = 7{,}875 + 15 = 7{,}890$

The math checks out perfectly!