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Use order of operations with whole numbers

Whole-number expressions are interpreted by attending first to grouping symbols, then evaluating whole-number exponents, multiplication and division from left to right, and addition and subtraction from left to right, so that each expression has a consistent value rather than being calculated strictly in the order written. This understanding includes nested grouping and distinguishing an operation from the number it acts on; it does not extend to negative or fractional numbers, algebraic variables, or advanced exponent rules.

Detailed Explanation: Use order of operations with whole numbers

First, follow the order of operations:

  1. Grouping symbols: Work inside parentheses, brackets, or braces. If they are nested, start with the innermost group.
  2. Exponents: Evaluate whole-number powers.
  3. Multiplication and division: Work from left to right.
  4. Addition and subtraction: Work from left to right.

Example:

18+{24÷[2(3+1)]}×22−518+\left\{24\div\left[2(3+1)\right]\right\}\times 2^2-5

Step 1: Evaluate the innermost grouping.

3+1=43+1=4

Now the expression is

18+{24÷[2(4)]}×22−518+\left\{24\div[2(4)]\right\}\times 2^2-5

Step 2: Finish the grouping.

The expression 2(4)2(4) means 2×42\times4.

2×4=82\times4=8

Now we have

18+{24÷8}×22−518+\{24\div8\}\times2^2-5

Step 3: Evaluate the exponent.

The exponent 22 tells us to multiply 22 by itself:

22=2×2=42^2=2\times2=4

Now we have

18+{24÷8}×4−518+\{24\div8\}\times4-5

Step 4: Do division and multiplication from left to right.

24÷8=324\div8=3

Then multiply:

3×4=123\times4=12

Now the expression is

18+12−518+12-5

Step 5: Do addition and subtraction from left to right.

18+12=3018+12=30 30−5=2530-5=25

Therefore,

25\boxed{25}

Do not calculate strictly from left to right. Always finish grouping and exponents first, then handle multiplication and division, and finally handle addition and subtraction.

Learn by doing: Use order of operations with whole numbers

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    Order of Operations - Add, Subtract, Mutiply, Divide, with Exponents

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