Order of operations

When a math problem has more than one operation, you need a plan so everyone gets the same answer. That plan is called the order of operations. First solve anything inside parentheses or brackets. Next handle any exponents. Then do all multiplication and division, working from left to right. Last, do all addition and subtraction, also from left to right. Calculators are built to follow this same order automatically, which is why typing 7 + 3 × 4 gives you 19 instead of 40. Practicing this order helps you solve longer expressions step by step without getting confused about what to do first.

Long math expressions are not hard if you tackle them one step at a time in the right order. First, solve anything inside parentheses or brackets, starting with the innermost group and working outward. Second, handle any exponents (that includes square roots too). Third, do all the multiplication and division in the problem, moving from left to right. Fourth, finish with addition and subtraction, again moving from left to right. Following these four steps in order means you will always land on the same correct answer, no matter how long or tricky the expression looks.

Math expressions can use parentheses ( ), brackets [ ], and braces { } to show what should happen first. These symbols group parts of a problem together. For example, the expression 3.5 + (2 × 4.2) tells you to start with 3.5, then add the product of 2 and 4.2. When you write your own expression for a word problem, ask yourself which operation happens first, whether the situation is about groups, parts, or totals, and whether your answer makes sense for the story. Grouping symbols are like a map that tells you exactly which path to take through the problem.

Sometimes a math expression has groups inside other groups, like parentheses inside brackets inside braces. When that happens, always start with the innermost group and work your way out. For example, in {3 + [2 × (4 + 1)]}, first solve the parentheses: 4 + 1 = 5. Next, solve the brackets: 2 × 5 = 10. Finally, solve the braces: 3 + 10 = 13. Working from the inside out, one layer at a time, keeps you from getting lost in a long expression.