Problem 14 - Elementary Algebra

Question

For exercises 1-80, evaluate. $$ 90 \cdot 3 \div 5 $$

Step-by-Step Solution

Answer

54

Step 1 - Perform Multiplication

First, multiply 90 by 3. This gives us: \[ 90 \times 3 = 270 \]

Step 2 - Perform Division

Next, take the result from Step 1 and divide it by 5. This gives us: \[ 270 \div 5 = 54 \]

Key Concepts

Order of Operations

Understanding the order of operations is crucial in elementary algebra. When we solve problems like this one, we need to follow a specific sequence to get the correct answer.
The order of operations can be remembered using the acronym PEMDAS:

• P: Parentheses
• E: Exponents
• M: Multiplication
• D: Division
• A: Addition
• S: Subtraction

In our exercise, we encounter multiplication and division. According to PEMDAS, we handle multiplication and division from left to right, whatever comes first. So, before dividing, we need to perform the multiplication.

Multiplication

Multiplication is one of the fundamental arithmetic operations, and it's the process of adding a number to itself a certain number of times.
In our exercise, we need to multiply 90 by 3. Mathematically, this means we are adding 90 three times:
\[ 90 \times 3 = 90 + 90 + 90 = 270 \]
Multiplication helps in condensing repetitive addition, making calculations quicker and easier to manage. Always ensure you complete multiplication steps before division, as dictated by the order of operations.

Division

Division is another basic arithmetic operation. It splits a number into equal parts. Once we've completed our multiplication step in the exercise, we then proceed to division.
We need to divide 270 by 5:
\[ 270 \div 5 = 54 \]
Division can be thought of as determining how many times one number is contained within another. Here, 270 divided by 5 equals 54, meaning if you split 270 into 5 equal parts, each part would be 54. By following the order of operations, practicing proper multiplication and division steps, you can accurately solve algebra problems.