Problem 361 - Prealgebra

Question

Divide. Then check by multiplying. $$\frac{27}{3}$$

Step-by-Step Solution

Answer

The quotient is 9.

Step 1: Understand the Division

The given problem asks to divide 27 by 3. This can be written as \ \ \ \( \frac{27}{3} \).

Step 2: Perform the Division

Divide 27 by 3. This can be calculated as: \ \( 27 \div 3 = 9 \).

Step 3: Check by Multiplying

Multiply the result (9) by the divisor (3) to ensure the quotient is correct: \ \( 9 \times 3 = 27 \). This confirms that the division was performed correctly since the product matches the original dividend.

Key Concepts

Basic Arithmetic

Basic arithmetic is the foundation of mathematics. It involves basic operations like addition, subtraction, multiplication, and division. In this exercise, we focus on division, one of the four fundamental arithmetic operations. Division allows us to determine how many times one number (the divisor) is contained within another number (the dividend). For example, \( \frac{27}{3} \) asks us to find how many times 3 fits into 27.
By understanding basic arithmetic, students can build the confidence needed to tackle more complex mathematical concepts in the future.

Multiplication Check

After performing a division, it's always a good idea to check your work with multiplication. This is called the multiplication check. The multiplication check ensures your answer is correct. Here's how it works using the problem \( \frac{27}{3} \):
First, you perform the division to find the quotient:

\( 27 \div\ 3 \=\ 9 \).

Next, you multiply the quotient (9) by the divisor (3) to confirm the result:

\( 9 \times\ 3 \=\ 27 \).

If this product matches the original dividend (27), then the division is correct. This extra step helps prevent errors and reinforces the understanding of the relationship between division and multiplication.

Prealgebra Operations

Prealgebra serves as the bridge between basic arithmetic and more advanced algebra concepts. Prealgebra introduces students to variables, expressions, and equations, and lays the groundwork for solving real-world problems mathematically.
In this exercise, we are dealing with prealgebra operations like division and multiplication. Understanding these operations is crucial for solving equations and simplifying expressions. For instance, knowing that \( 27 \div\ 3 \=\ 9 \) helps students simplify fractions and solve for unknowns in equations.
Grasping these foundations prepares students for algebraic topics, thereby making the transition to higher math smoother and less intimidating.