Problem 565 - Prealgebra

Question

Divide. Then check by multiplying. $$52 \div 4$$

Step-by-Step Solution

Answer

13

Step 1: Set up the division problem

Write down the division problem as \[52 \div 4\].

Step 2: Perform the division

Divide 52 by 4 by asking how many times 4 can fit into 52. Since 4 fits into 52 exactly 13 times, \[52 \div 4 = 13\].

Step 3: Verify by multiplying

To verify the result, multiply the quotient by the divisor:\[13 \times 4 = 52\]. Since the multiplication returns to the original number, the division is correct.

Key Concepts

Division Verification

After performing a division, it's crucial to verify the result. Verification helps to ensure that the answer is correct. In our example, we performed the division \(52 \div 4\) and obtained a quotient of 13. To verify this, we can use multiplication.

Here's how to do it:

• Take the quotient, which is 13, and multiply it by the divisor, which is 4.
• \[13 \times 4 = 52\]
• If the product equals the original number (52 in this case), the division is verified as correct.

This method works because of the relationship between multiplication and division. It ensures that the calculations are accurate and no mistakes are made.

Multiplication as Inverse

Multiplication can be considered the inverse operation of division. This means that if you have a quotient and a divisor, you can multiply them to get back to the original number.

In our example:

• Division: \[52 \div 4 = 13\]
• Inverse multiplication: \[13 \times 4 = 52\]

When you reverse a division by using multiplication, you're essentially checking to make sure your result is accurate. This inverse relationship helps to build a stronger understanding of division and multiplication. It's like solving a puzzle in reverse to ensure all the pieces fit together correctly.

Step-by-Step Division

Breaking down a division problem into clear, manageable steps makes it easier to understand and solve. Let's go through the steps one more time for the given problem \[52 \div 4\]:

Step 1: Set up the division problem
Write down the problem as \(52 \div 4\). This helps to clearly see what you are working on.
Step 2: Perform the division
Determine how many times 4 can fit into 52. Since 4 fits into 52 exactly 13 times, the quotient is 13. This means \[52 \div 4 = 13\].
Step 3: Verify by multiplying
To ensure your answer is correct, multiply the quotient by the divisor.

• \[13 \times 4 = 52\]
• If the result matches the original number (52), the solution to your division is correct.

Following these step-by-step procedures makes division simpler and error-free. It helps to build a solid foundation for solving more complex math problems in the future.