Problem 373 - Prealgebra

Question

Divide. Then check by multiplying. $$43 \div 43$$

Step-by-Step Solution

Answer

43 divided by 43 is 1.

Step 1: Understand the problem

The problem is asking to divide 43 by 43. Division of any number by itself results in 1.

Step 2: Perform the division

Divide 43 by 43. Mathematically, this can be written as: \[ 43 \div 43 = 1 \]

Step 3: Verify by multiplying

To check the result, multiply the quotient (1) by the divisor (43). This should give the dividend (43). \[1 \times 43 = 43 \]

Step 4: Confirm the solution

Since 1 multiplied by 43 gives 43, our division is correct. Therefore, \(43 \div 43 = 1\).

Key Concepts

quotient

The quotient is the result you get when dividing one number by another. In our exercise, we are dividing 43 by 43. The math problem is written as

• 43
• ÷
• 43

Since any number divided by itself equals 1, the quotient here is 1. This means that 43 ÷ 43 = 1 . Dividing can be thought of as distributing a number into equal parts. If you have 43 items and you place them into 43 groups, each group will only get 1 item. Thus, the quotient is 1.

divisor

In a division problem, the divisor is the number you divide by. For this exercise, the divisor is 43. The equation can be represented as

• 43
• ÷
• 43

The divisor is crucial because it tells us how many parts we are creating from the dividend. In this problem, dividing 43 (the dividend) by 43 (the divisor) gives us 1 part for each group. Consider the divisor as the instructor on how to partition the number. It defines the size of each part when the original number is divided. Understanding the role of the divisor helps make sense of the division process.

verify result

Verifying a division problem means confirming that your quotient is correct. After dividing, you multiply the quotient by the divisor and see if you get back to the original number, called the dividend. For our problem, the quotient is 1, and the divisor is 43. Let’s multiply them:

• 1
• ×
• 43

The product should be 43, which is our original number. This process can be written as:

• 1 × 43 = 43

This confirms that our division is correct. If the multiplication gives the original number, then the division result (quotient) is verified as accurate.

multiplication check

A multiplication check is a method used to ensure the accuracy of a division. After finding the quotient in a division problem, you multiply the quotient by the divisor. The product should equal the dividend. If it does, your answer is correct. In our exercise, we divided 43 by 43 to get a quotient of 1. Let's check this division by multiplying:

• Quotient (1)
• ×
• Divisor (43)

This gives us: 1 × 43 = 43 Our multiplication check confirms that the original division (43 ÷ 43) is correct. This practice is very useful in both verifying mathematical solutions and reinforcing the connection between multiplication and division. It's a simple yet powerful way to double-check your work.