Problem 402 - Prealgebra

Question

Divide. Then check by multiplying. $$3,208 \div 4$$

Step-by-Step Solution

Answer

3208 ÷ 4 = 802. Multiplying 802 by 4 gives 3208.

Step 1: Set up the division

Write the division problem in long division format: \[ 3208 \boxed{4}\]

Step 2: Divide the thousands place

Determine how many times 4 goes into the first digit, 3. Since 4 does not go into 3, consider the first two digits, 32. 4 goes into 32 exactly 8 times. Write 8 above the line, and multiply 8 by 4 to get 32. Subtract 32 from 32 to get 0.

Step 3: Bring down the next digit

Write down the next digit (0), onto the result. You now have 08. Determine how many times 4 goes into 0, which is 0 times. Write 0 above the line.

Step 4: Divide the next digit

Bring down the last digit, which is 8, making it 08. 4 goes into 8 exactly 2 times. Write 2 above the line, and multiply 2 by 4 to get 8. Subtract 8 from 8 to get 0.

Step 5: Write the quotient

The result of the division is written above the line. Thus, \[3208 \boxed{4} = 802\]

Step 6: Verify by multiplication

To verify the division, multiply the quotient by the divisor: \[802 \times 4 = 3208\]Since the result is equal to the dividend, the division is correct.

Key Concepts

Understanding Division

Division is like sharing. It splits things into equal parts. For example, if you have 3208 candies and you need to share them equally among 4 friends, you use division. Setting up the division in a long format makes the process easier. Write down 3208 inside the division box and 4 outside. Start by checking how many times 4 goes into the leading digit (3). Since it's smaller, move to the first two digits (32). This helps to manage bigger numbers in smaller steps, ensuring clarity.

The Role of Multiplication in Division

Multiplication helps to check how many times a number fits into another. In our example, we see that 4 fits into 32 exactly 8 times by multiplying 4 and 8, which gives 32.
This multiplication confirms each step as we go through the long division. For 3208 divided by 4, we multiply 8 by 4 to get 32, then subtract 32 from 32 to continue. Applying this repeatedly ensures we proceed accurately. Each time we multiply and subtract, it shows how the divisor fits into parts of the dividend.

Verifying Division Results

To ensure our division is accurate, we verify by multiplying the quotient by the divisor. If they multiply back to the original number, the division is correct. In our example, using 802 as the quotient and 4 as the divisor:
Multiplying 802 by 4, we get 3208. This matches the original number, verifying the division is accurate. This checking process confirms the result without errors. It's an essential step in math to prove the work is correct.