Problem 405 - Prealgebra

Question

Divide. Then check by multiplying. $$\frac{91,881}{9}$$

Step-by-Step Solution

Answer

The quotient is 10,209. Verification: 10,209 multiplied by 9 equals 91,881.

Step 1: Divide the Numbers

Start by dividing 91,881 by 9. Perform the division as you would with long division.1. Divide the first digit: 9 goes into 9 once (1).2. Subtract the product 9 from 9, which gives 0. Bring down the next digit (1).3. 9 goes into 1 zero times (0). Bring down the next digit (8) after subtracting 0.4. 9 goes into 18 twice (2). Subtract 18 from 18, which gives 0. Bring down the next digit (8).5. 9 goes into 8 zero times (0). Bring down the next digit (1).6. 9 goes into 81 nine times (9). Subtract 81 from 81, which gives 0.So, the quotient is 10,209.

Step 2: Check by Multiplying

To verify the result, multiply the quotient (10,209) by the divisor (9).\[10,209 \times 9 = 91,881.\]If the product equals the original number, the division was correct.

Step 3: Result Confirmation

The product of 10,209 and 9 equals 91,881, so the division is verified.

Key Concepts

division verification

When you divide a number, it's important to check if your answer is correct. This process is known as division verification. Let's walk through this with our example: dividing 91,881 by 9.

After performing long division, we found the quotient (answer) to be 10,209. But how do we know for sure that it's correct? We use multiplication to verify.

In simple steps:

• Take the quotient 10,209.
• Multiply it by the divisor 9.
• The product should match the original number (91,881).

If the product (result of multiplication) equals the original number, your division result is verified correctly. In our case, multiplying 10,209 by 9 gives 91,881, confirming our division was accurate.

multiplication check

Checking your division by multiplying is simple and effective. This is known as the multiplication check.

Let's use our example again. We divided 91,881 by 9 and got 10,209. To ensure this is correct, we perform the multiplication check.

Here are the steps:

• Multiply the quotient (10,209) by the divisor (9).
• Set up the multiplication like this: \[10,209 \times 9 = 91,881.\]
• Perform the multiplication to get the product. If it matches the original number (91,881), the division was done correctly.

As shown, multiplying 10,209 by 9 gives 91,881, the original number. This confirms the division was correct.

quotient and divisor

Understanding key terms like quotient and divisor is crucial in division.

Quotient:
The quotient is the result of the division. It's the number you get after dividing one number by another. In our example, the quotient of dividing 91,881 by 9 is 10,209.

Divisor:
The divisor is the number you are dividing by. It's the number that 'goes into' the original number. Here, our divisor is 9.

Example Breakdown:

• Start with 91,881 (the original number).
• Divide by 9 (the divisor).
• Get 10,209 as a result (the quotient).

Knowing these terms helps you understand the division process better and apply it correctly to various problems.