Problem 76 - Algebra 1: Concepts and Skills

Question

NUMERICAL EXPRESSIONS Evaluate the expression. Then simplify the answer. (Lesson 1.3) $$ 63 \div 3 \cdot 3 $$

Step-by-Step Solution

Answer

The simplified answer to the expression \(63 \div 3 \cdot 3\) is 63.

Step 1: Perform Division

First, perform the division operation \(63 \div 3 = 21 \). The result converts the expression to \(21 \cdot 3\).

Step 2: Perform Multiplication

Next, perform the multiplication operation \(21 \cdot 3 = 63\). This gives us the simplified expression.

Key Concepts

Order of Operations

Understanding the order of operations is crucial for correctly evaluating mathematical expressions, especially when they involve more than one operation, as in the case of the exercise given: evaluating the expression \(63 \div 3 \cdot 3\).

The order of operations is a set of rules to determine which procedure to perform first in a mathematical expression. In the United States, a common acronym used to remember these rules is PEMDAS, which stands for Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).

In the absence of parentheses and exponents, as in the provided expression, we start with multiplication and division, performed from left to right. This is why division was correctly performed before multiplication in the step-by-step solution, yielding the right answer of \(63\).

Simplifying Expressions

Simplifying expressions involves reducing them to their simplest form while keeping their value the same. This might include combining like terms, using properties of equality, or following the order of operations.

In our numerical expression \(63 \div 3 \cdot 3\), simplification doesn't involve combining like terms or using properties of equality, as it's a straightforward calculation. Instead, by applying the correct order of operations, the expression is simplified naturally through evaluation. Simplification here ensures that after the division and multiplication have been performed in the correct sequence, the most reduced form of the expression, which is the final answer of \(63\), is reached.

Arithmetic Operations

Basic arithmetic operations include addition, subtraction, multiplication, and division. These operations are foundational to higher-level math and every student must master them to succeed in a wide array of topics.

In the given expression, two arithmetic operations are displayed: division (\(\div\)) and multiplication (\(\cdot\)). As showcased in the solution, division was completed first, converting \(63 \div 3\) into \(21\), and then multiplication followed to get \(21 \cdot 3 = 63\). The correct application of these arithmetic operations following the order of operations leads to the accurate evaluation and simplification of the expression.