Lesson 76: Division with Three-Digit Answers

New Concept

The decimal point in the answer is placed directly above the decimal point inside the division box.

What’s next

Next, you’ll apply the four-step division process to problems with three-digit answers and remainders, solidifying your procedural fluency.

To perform long division, repeat these four steps in order: Step 1: Divide. Step 2: Multiply. Step 3: Subtract. Step 4: Bring down. This cycle continues until no digits remain to bring down. The final leftover number, if any, is the remainder. This structured process breaks down large division problems into manageable parts.

For $4 \overline{)974}$: Divide 9 by 4 is 2. Multiply $2 \times 4 = 8$. Subtract $9 - 8 = 1$. Bring down 7 to make 17. Repeat: Divide 17 by 4 is 4. Multiply $4 \times 4 = 16$. Subtract $17 - 16 = 1$. Bring down 4 to make 14. Repeat: Divide 14 by 4 is 3. Multiply $3 \times 4 = 12$. Subtract $14 - 12 = 2$. The answer is 243 R 2.
For $6 \overline{)1512}$: Divide 15 by 6 is 2. Multiply $2 \times 6 = 12$. Subtract $15 - 12 = 3$. Bring down 1 to make 31. Repeat: Divide 31 by 6 is 5. Multiply $5 \times 6 = 30$. Subtract $31 - 30 = 1$. Bring down 2 to make 12. Repeat: Divide 12 by 6 is 2. The answer is 252.

Think of long division as a dance with four moves: Divide, Multiply, Subtract, and Bring Down! You just keep repeating this dance routine for each digit in your big number until you run out of partners to bring down. It’s the same rhythm every time, making huge problems easy to solve step-by-step!

When dividing numbers involving money, the process is the same as with whole numbers, with one important rule for the decimal point. The decimal point in the answer is placed directly above the decimal point inside the division box. This ensures that the value of the answer correctly represents dollars and cents without any extra calculation.

The total cost of four identical books is 9.20 dollars. To find the cost of each book, divide: $9.20 \div 4 = 2.30$ dollars.
To split 7.95 dollars among 5 friends, you calculate: $7.95 \div 5 = 1.59$ dollars per person.
If eight movie tickets cost 50.00 dollars, each ticket costs: $50.00 \div 8 = 6.25$ dollars.

When dividing money, the decimal point is super polite—it never cuts in line! It just floats straight up from the number you are dividing into its final spot in the answer. This simple trick keeps your dollars and cents perfectly aligned, so you do not accidentally turn ten dollars into ten cents. Easy peasy!

When an exact answer is not needed, you can estimate by using compatible numbers. To estimate in a division problem, you first choose a number close to the dividend that is easily divisible by the divisor. This method allows for quick mental calculations to find a reasonable approximation instead of performing full long division for a precise answer.

To estimate the number of cars in 7 lines with 500 total cars, use a compatible number for 500. Since 490 is close to 500 and divisible by 7, you can estimate $490 \div 7 = 70$ cars per line.
Estimate the attendance for 3 movie showings with 878 total people. Use 900 as a compatible number for 878. The estimate is $900 \div 3 = 300$ people per showing.

When a division problem looks tricky, don’t panic—estimate! Find a 'friendly' number (a compatible number) close to the original one that your divisor gets along with perfectly. This turns a tough calculation into a quick mental math problem, giving you a 'good enough' answer without all the fuss. It's like finding a shortcut!