Evaluate Numerical Expressions

Evaluating a numerical expression means finding one final answer from a combination of numbers and operations.

For example, Mac is purchasing equipment for a laboratory. He buys three beakers for $40 each and two flasks for $10 each. He also receives a $20 discount.

The total bill is represented by 40 times 3 plus 10 times 2 minus 20. Ignoring the order of operations and working from left to right gives 240, which is incorrect.

To evaluate it accurately, we use the order of operations. Operations in parentheses come first, followed by exponents. Multiplication and division are performed from left to right, followed by addition and subtraction from left to right.

This expression has no parentheses or exponents, so we begin with multiplication. 40 times 3, which equals 120, and 10 times 2, which equals 20.

Adding 120 and 20 to get 140 dollars. Subtracting the 20-dollar discount gives a final bill of 120 dollars.

Following the order of operations helps numerical expressions with different operations produce a consistent result.