When you evaluate a numeric expression, you simplify the expression using the order of operations until you are left with one number. Look at the example below.
52 – 15(3 – 2 × 2) ÷ 5
Step 1: Parentheses and Grouping Symbols
There are parentheses in this problem, so we need to take care of the numbers inside the parentheses first. Since we always do multiplication before subtraction, we will start with 2 × 2.
= 52 – 15(3 – 2 × 2) ÷ 5
Since we know that the 2 × 2 = 4, we replace the 2 × 2 with 4 and rewrite everything around it exactly as it was before.
= 52 – 15(3 – 4) ÷ 5
We have just one thing left to do in the parentheses, that is the subtraction.
= 52 – 15(3 – 4) ÷ 5
Again, solve it and rewrite everything around it exactly as it was before.
= 52 – 15(–1) ÷ 5
Step 2: Exponents
Next we take care of the exponent.
= 52 – 15(–1) ÷ 5
Again, solve it and rewrite everything around it exactly as it was before.
= 25 – 15(–1) ÷ 5
Step 3: Multiply/Divide from left to right
Now we have to take care of the multliplication/division in order from left to right. Since the multiplication part is farther left than the division, we will do the multiplication first.
= 25 – 15(–1) ÷ 5
Solve it and rewrite everything around it exactly as it was before.
= 25 – –15 ÷ 5
Now we can do the division.
= 25 – –15 ÷ 5
Solve it and rewrite everything around it exactly as it was before.
= 25 – –3
Step 4: Add/Subtract from left to right
All that is left is the subtraction problem.