A numerical expression is a mathematical phrase that contains only numbers and operations. Examples include 5 plus 3, 12 minus 7, and 4 times 6 divided by 2. These expressions do not contain variables like x or y.
The four basic operations are addition, subtraction, multiplication, and division. They are represented by the symbols plus, minus, times, and divided by. For example, 5 plus 3, 10 minus 4, 6 times 2, and 15 divided by 3.
The order of operations is crucial for evaluating expressions correctly. PEMDAS stands for Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction. For example, in the expression 2 plus 3 times 4, we multiply first to get 2 plus 12, which equals 14.
We can translate word problems into numerical expressions. For example, the sum of 8 and 5 becomes 8 plus 5. 12 decreased by 7 becomes 12 minus 7. The product of 6 and 4 becomes 6 times 4.
Parentheses are used to group parts of an expression. They tell us to perform the operations inside them first. For example, in the expression (15 plus 5) divided by 4, we add first. In 3 times (8 minus 2) plus 7, we subtract inside the parentheses first.
Exponents represent repeated multiplication. For example, 2 to the power of 3 means 2 times 2 times 2. In expressions, exponents are evaluated before multiplication and division. For example, 2 squared plus 4 times 5 is 4 plus 20, which equals 24.
Numerical expressions are used in everyday life. For example, to calculate the total cost of a $25 shirt with $2 tax, we write 25 plus 2. To find the area of a rectangle that is 5 meters by 3 meters, we write 5 times 3. To find the average of scores 85, 90, and 75, we write (85 plus 90 plus 75) divided by 3.
Let's evaluate a complex expression step by step. Consider 3 times (8 plus 4) minus 2 squared. First, we evaluate the parentheses: 8 plus 4 equals 12. Next, we evaluate the exponent: 2 squared equals 4. Then we multiply: 3 times 12 equals 36. Finally, we subtract: 36 minus 4 equals 32.