Problem 17 - College Algebra with Corequisite Support

Question

For the following exercises, simplify the given expression. \(14 \times 3 \div 7-6\)

Step-by-Step Solution

Answer

The simplified expression is 0.

Step 1: Multiply

Start with the first operation, which is multiplication. Multiply the numbers 14 and 3.\[14 \times 3 = 42\]

Step 2: Divide

Next, divide the result from Step 1 by 7.\[42 \div 7 = 6\]

Step 3: Subtract

Finally, subtract 6 from the result of Step 2.\[6 - 6 = 0\]

Key Concepts

Order of Operations

When simplifying mathematical expressions, it's important to perform calculations in the correct order, known as the "Order of Operations." This ensures that everyone interprets the expression consistently and accurately. The standard order to follow is given by the acronym PEMDAS: Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction. It tells us to:

• Solve expressions inside parentheses first.
• Handle exponents, if any.
• Proceed with multiplication and division from left to right.
• Lastly, perform addition and subtraction from left to right.

In our exercise, there are no parentheses or exponents, so we start directly with multiplication and then division before moving to the final subtraction.

Multiplication

Multiplication is often one of the first operations we perform in expressions that contain several operations. In our example, we start by multiplying 14 by 3. Multiplication involves taking a number and adding it to itself a certain number of times, corresponding to the other factor.
For instance, multiplying 14 by 3 can be seen as adding 14 three times (14 + 14 + 14), which equals 42.
This step simplifies the expression and sets up for the next stage of order operations.

Division

After multiplication, we move on to division. Division is essentially splitting a number into equal parts. According to the order of operations, division happens alongside multiplication from left to right.
In our exercise, after multiplying to get 42, we then divide by 7. This means asking how many times 7 fits into 42.

• 42 divided by 7 is 6, because 7 fits into 42 exactly six times.

Completing this step leaves us with a simpler number to work with for any further operations.

Subtraction

Subtraction is the process of removing a number from another. It is often the last operation performed when following the order of operations, after any multiplication or division has been completed.
In this simplified expression, we have 6, and we need to subtract another 6. Subtraction answers the question: "How much is left when one number is taken away from another?"

• When you subtract 6 from 6, nothing is left, resulting in 0.

This completes the simplification of our expression, showing the importance of executing subtraction at the right point in our calculations to achieve the correct result.