Problem 360 - Prealgebra

Question

Divide. Then check by multiplying. $$14 \div 2$$

Step-by-Step Solution

Answer

14 ÷ 2 = 7; verified by 7 × 2 = 14.

Step 1: Identify the Dividend and the Divisor

The dividend is the number that is being divided, and the divisor is the number by which the dividend is divided. In this case, the dividend is 14 and the divisor is 2.

Step 2: Perform the Division

Divide the dividend by the divisor: Write the division as: 14 ÷ 2. Using basic division, this equals 7.\( 14 \div 2 = 7 \)

Step 3: Verify the Result by Multiplying

To verify that the division is correct, multiply the quotient by the divisor: \(7\ \cdot \ 2 = 14 \). Since the product is equal to the original dividend, the division is verified correctly.

Key Concepts

Basic Division

Division is one of the fundamental arithmetic operations, just like addition, subtraction, and multiplication. The goal of division is to determine how many times one number (the divisor) is contained within another number (the dividend). In our example, we divided 14 by 2. Here, 14 is the dividend, and 2 is the divisor.
Think of it as dividing something into equal parts. If you have 14 apples and you want to divide them among 2 friends, each friend gets 7 apples. This means 14 divided by 2 equals 7. It's that simple.
For the actual division: write the operation as \(14\div2\). Using basic division principles, we find that 14 divided by 2 equals 7, which is our quotient.

Multiplication Verification

After performing division, it's always a good idea to verify the result using multiplication. This helps to ensure the accuracy of the solution.
Verification involves multiplying the quotient (the result of your division) by the divisor. In our example, the quotient was 7, and the divisor was 2. Multiply them together: \(7 \cdot 2 = 14\).
If the product equals the original dividend, then the division solution is correct.
This simple step of checking your work helps to prevent mistakes and solidify your understanding of both division and multiplication. It's like having a safety net that confirms you've gotten the right answer.

Quotient and Divisor

In every division problem, understanding the role of the quotient and divisor is key. The quotient is the result you get when you divide the dividend by the divisor.
For our example, the dividend is 14, and the divisor is 2. When we perform the division, we get the quotient of 7. So, \(14 \div 2 = 7\).
This means our quotient (7) represents the number of times the divisor (2) fits into the dividend (14). These terms are crucial for solving division problems and for ensuring that you understand what each number in the operation represents.