Problem 393 - Prealgebra

Question

Divide. Then check by multiplying. $$924 \div 7$$

Step-by-Step Solution

Answer

The quotient is 132. Verified by multiplication: 132 × 7 = 924.

Step 1 - Set Up the Division

Write down the number 924 and the divisor 7, setting it up for long division.

Step 2 - Divide the First Digit

Determine how many times 7 goes into the first digit of 924, which is 9. Since 7 goes into 9 once (1), write 1 above the 9.

Step 3 - Subtract and Bring Down Next Digit

Subtract 7 from 9, which leaves 2. Then bring down the next digit, 2, making the number 22.

Step 4 - Divide the New Number

Determine how many times 7 goes into 22. It goes 3 times (7×3=21). Write 3 above the 2 on top.

Step 5 - Subtract and Bring Down the Last Digit

Subtract 21 from 22, leaving 1. Then bring down the final digit, 4, making 14.

Step 6 - Divide the Final Number

Determine how many times 7 goes into 14. It goes 2 times (7×2=14). Write 2 above the 4 on top.

Step 7 - Subtract to Finish

Subtract 14 from 14, leaving a remainder of 0. The quotient is 132.

Step 8 - Verify by Multiplying

Multiply the quotient (132) by the divisor (7) to check the result: 132 × 7 = 924. Since the product matches the original number, the division is correct.

Key Concepts

Division Steps

To understand long division, it’s essential to break down the process into manageable steps. Each step must be tackled one at a time.
Begin by setting up the division problem. For instance, with 924 ÷ 7:

• First, write down 924 and the divisor 7. This sets up your long division problem.
• Next, focus on the first digit of 924, which is 9. Since 7 fits into 9 once, you write 1 above the 9.
• Then, subtract 7 from 9, leaving you with 2.

The next steps follow a similar pattern but now include the other digits of 924:

• Bring down the next digit from 924, which is 2, making the number 22.
• Determine how many times 7 fits into 22. It fits 3 times, because 7 × 3 = 21, so you write 3 above the 2.
• Subtract 21 from 22, which gives you 1, and then bring down the 4, making 14.
• Finally, determine how many times 7 goes into 14. It fits exactly 2 times (7 × 2 = 14), so you write 2 above the 4.
• The subtraction leaves a remainder of 0, finishing the division.

Following these steps, you get a quotient of 132.

Multiplication to Check Division

After completing a division problem, it’s very important to check your work by using multiplication.
This step verifies that your division was accurate.
Here’s how it works using the example of 924 ÷ 7:

• Take the quotient you obtained from your division, which is 132.
• Multiply this quotient by the divisor, which is 7.
• Perform the multiplication: 132 × 7. You can do this step by step:

• First, multiply 132 by 7.
• 132 × 7 = 924.

Since the product (924) matches the original number you started with, your division is correct.
This method is a great way to cross-check your work and ensures your confidence in the result.

Remainder

In long division, the remainder is what is left after division. It’s the part of the dividend that isn't evenly divisible by the divisor.
In our example of 924 ÷ 7, the steps led us to a quotient of 132 with a remainder of 0.
If there is a remainder when you subtract the last digit, it means the division does not divide the number completely.
Here’s what to do with the remainder:

• Write it down at the end of your division problem.
• Make sure to state that the division is not exact if there is a remainder.
• For example, if the final subtraction left you with 2, then you have a remainder of 2.

Understanding remainders will help you in problems where the numbers don’t divide evenly.
Always check if you have any leftover number after your last subtraction to identify a remainder.
This helps in ensuring the completeness and correctness of your long division.