Evaluate Mathematical Expression Using Order of Operations

Let's evaluate the given mathematical expression step-by-step. The expression is:

\(5 \times 4 + (3 + 4)^2 \div 7 \times 4\)

To correctly evaluate this expression, we need to follow the order of operations. A common acronym for remembering the order of operations is BODMAS or PEMDAS.

• Brackets (or Parentheses)
• Orders (or Exponents)
• Division and Multiplication (from left to right)
• Addition and Subtraction (from left to right)

Now, let's apply these rules to the expression:

Step 1: Evaluate operations inside Brackets (Parentheses)

The expression inside the brackets is \(3 + 4\).

\((3 + 4) = 7\)

Substitute this back into the expression:

\(5 \times 4 + (7)^2 \div 7 \times 4\)

Step 2: Evaluate Orders (Exponents)

The term with an exponent is \(7^2\).

\(7^2 = 7 \times 7 = 49\)

Substitute this back into the expression:

\(5 \times 4 + 49 \div 7 \times 4\)

Step 3: Evaluate Division and Multiplication from left to right

We have multiplication (\(5 \times 4\)), division (\(49 \div 7\)), and multiplication (\(7 \times 4\), result of previous step). We perform these operations from left to right.

First, \(5 \times 4\):

\(5 \times 4 = 20\)

The expression becomes:

\(20 + 49 \div 7 \times 4\)

Next, \(49 \div 7\):

\(49 \div 7 = 7\)

The expression becomes:

\(20 + 7 \times 4\)

Finally, \(7 \times 4\):

\(7 \times 4 = 28\)

The expression becomes:

\(20 + 28\)

Step 4: Evaluate Addition and Subtraction from left to right

We only have addition left:

\(20 + 28 = 48\)

So, the final value of the expression is 48.

Revision Table for Order of Operations

Additional Information on Mathematical Operations

Understanding the correct order of operations is crucial in mathematics to ensure consistent and accurate results. If operations are performed in a different order, the result can be significantly different.

For example, in the expression \(5 \times 4 + 49 \div 7 \times 4\), if we did the addition first after \(5 \times 4\):

\(20 + 49 \div 7 \times 4\)

Incorrect step (addition first): \(20 + 49 = 69\)

Then \(69 \div 7 \times 4\), which does not give a simple integer and is clearly different from the correct path.

Division and multiplication have the same priority. When they appear in the same expression, you perform them from left to right as they appear. The same rule applies to addition and subtraction.