Problem 362 - Prealgebra

Question

Divide. Then check by multiplying. $$\frac{30}{3}$$

Step-by-Step Solution

Answer

10. To check: \(10 \times 3 = 30\).

Step 1 - Understand the division problem

The given problem is to divide 30 by 3. This is written as \(\frac{30}{3}\). Division is the process of determining how many times one number is contained within another.

Step 2 - Perform the division

To divide 30 by 3, determine how many times 3 fits into 30. \(\frac{30}{3} = 10\). The result of the division is 10.

Step 3 - Check the result by multiplying

To verify the result, multiply the quotient (10) by the divisor (3). If the product equals the dividend (30), the division is correct. \(10 \times 3 = 30\). Since the product (30) matches the dividend, the division is correct.

Key Concepts

headline of the respective core concept

Division is a fundamental arithmetic operation that helps to understand how many times one number can be evenly distributed into another. In the given exercise, we need to divide 30 by 3. The equation is written as \(\frac{30}{3}\). Think of division like sharing. If you have 30 items and you want to distribute them among 3 people equally, how many items does each person get? Let's break it down further.

• **Dividend**: The number being divided (30 in this case).
• **Divisor**: The number by which the dividend is divided (here, it's 3).
• **Quotient**: The result of the division (the answer we need to find).

Summarized, \(\frac{30}{3}\) asks how many groups of 3 fit into 30. Performing the calculation, we get that 10 groups of 3 fit into 30, so the quotient is 10.

headline of the respective core concept

Checking your answer in division is essential to ensure that the calculations are correct. In this context, we use multiplication to verify our result from the division.
Let's recall that: \(\frac{30}{3} = 10\). To confirm this, multiply the quotient by the divisor: \(10 \times 3\). If the result equals the original dividend, you have solved the division correctly. Let's perform the multiplication step-by-step:
\(\begin{array}{r} 10 \ \overline{\times 3} = 30 \) The multiplication confirms that \(\frac{30}{3}\) correctly equals 10 as \(10 \times 3 = 30\). Therefore, our initial division is accurate.

headline of the respective core concept

Understanding quotients and divisors is crucial to mastering division problems. Let's dive into these terms:

• **Quotient**: This is the result you get after dividing one number by another. In our example, the quotient is 10.
• **Divisor**: This is the number by which you divide another number. In our case, 3 is the divisor.
• **Dividend**: This is the number that is being divided. Here, 30 is the dividend.

When we say \(\frac{30}{3} = 10\), it tells us that 30 (dividend) divided by 3 (divisor) results in 10 (quotient). Conclusively, knowing these terms helps in identifying the parts of a division problem and interpreting the results correctly.