Dividing Multi-Digit by One-Digit Numbers

Dividing large numbers by a single digit is like sharing a big pile of items into a few equal groups. In 4th grade, you will learn to divide numbers up to four digits long by a one-digit number. You can solve these problems using Standard Long Division or Partial Quotients.

Standard Long Division

Long division breaks the problem down into smaller, step-by-step division problems from left to right. A helpful way to remember the steps is: Divide, Multiply, Subtract, Bring down.

Let's solve $852 \div 4$:

1. Divide the hundreds: How many times does $4$ go into $8$? Exactly $2$ times. Write $2$ above the $8$.
2. Multiply & Subtract: $2 \times 4 = 8$. Subtract $8 - 8 = 0$.
3. Bring down: Bring down the next digit, which is $5$.
4. Divide the tens: How many times does $4$ go into $5$? It goes in $1$ time. Write $1$ above the $5$.
5. Multiply & Subtract: $1 \times 4 = 4$. Subtract $5 - 4 = 1$.
6. Bring down: Bring down the last digit, $2$, making the new number $12$.
7. Divide the ones: How many times does $4$ go into $12$? Exactly $3$ times. Write $3$ above the $2$.

Since $3 \times 4 = 12$ and $12 - 12 = 0$, there is no remainder. The answer is $213$.

Division with Remainders

Sometimes, a number cannot be divided perfectly into equal groups. The amount left over is called the remainder.

Let's solve $3{,}645 \div 7$:

1. Thousands: $3 \div 7$ doesn't work (since $3$ is smaller than $7$). So, we look at the first two digits: $36$.
2. Hundreds: $36 \div 7 = 5$ (since $5 \times 7 = 35$). Subtract $36 - 35 = 1$. Bring down the $4$ to make $14$.
3. Tens: $14 \div 7 = 2$. Write $2$ on top. Subtract $14 - 14 = 0$. Bring down the $5$.
4. Ones: $5 \div 7 = 0$. Write $0$ on top. Subtract $5 - 0 = 5$.

There are no more numbers to bring down, and $5$ is smaller than $7$. Our final answer is $520$ with a remainder of $5$, often written as $520 \text{ R } 5$.

Using Partial Quotients

Partial quotients is a method where you take out easy "chunks" of the divisor until nothing is left.

Let's look at $852 \div 4$ again:

• Take out a big chunk: I know $4 \times 200 = 800$. Let's subtract $800$ from $852$. $852 - 800 = 52$ (Partial quotient so far: 200)
• Take out another chunk: I know $4 \times 10 = 40$. Let's subtract $40$ from $52$. $52 - 40 = 12$ (Partial quotient so far: 10)
• Take out the last chunk: I know $4 \times 3 = 12$. Subtract $12$ from $12$. $12 - 12 = 0$ (Partial quotient so far: 3)

Finally, add up all your partial quotients: $200 + 10 + 3 = 213$. Both methods give you the same correct answer!