Problem 86 - Algebra 1

Question

Evaluate the expression. $$ 12 \cdot 9 \div 6-13.5 $$

Step-by-Step Solution

Answer

The result of evaluating the expression \(12 \cdot 9 \div 6 - 13.5\) is 4.5

Step 1: Perform Multiplication

Find the product of 12 and 9, which equals 108.

Step 2: Perform Division

Divide 108 by 6 to obtain 18.

Step 3: Perform Subtraction

Subtract 13.5 from 18 to get the final result.

Key Concepts

Multiplication

Multiplication is the process of adding a number to itself a certain number of times. When you multiply numbers, you are essentially calculating the total amount of something when grouped into equal sizes. In our example, the expression starts with the calculation of \(12 \cdot 9\). This means you add the number 12 to itself 9 times.

• The first term is 12, which is the multiplicand.
• The second term is 9, which is the multiplier.
• The result of \(12 \cdot 9\) is 108.

So, when performing multiplication, remember to follow the same pattern of repeated addition. The equation translates to 12 added 9 times, yielding a product of 108.

Division

Division is the operation of splitting a number into equal parts. It is the inverse of multiplication and answers how many times a number fits into another. In the expression, we divide 108 by 6, which is performed after completing the multiplication.

• 108 is called the dividend, the number you divide.
• 6 is the divisor, the number you divide by.
• The result, or quotient, is 18.

Understanding division as a reverse multiplication helps. Here, if you think in terms of multiplication: 6 times what number gives you 108? The answer, fitting it exactly 18 times, represents this division result.

Subtraction

Subtraction involves taking one number away from another, reducing the value of the original number. It is essential to follow after other operations. Here, we finally subtract 13.5 from the result of the division, 18.

• The number from which you subtract (18 in this case) is the minuend.
• The number to subtract (13.5) is the subtrahend.
• The result is known as the difference, which is 4.5 for this expression.

When subtracting, line up the numbers correctly, ensuring that decimal points are aligned when dealing with decimals. By decreasing 18 by 13.5, we find the difference as the final solution to our expression.