1.1 Integers and Rational Numbers

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$Lesson 2a – Assessment - Scottsdale Community College - Math Blog$

www.ck12.org Chapter 1. Arithmetic ReviewAn equation is a number sentence that can be solved. It has an equal sign where one side of the equals sign isequal to the other side of the equals sign.Example3 + 4 = 7This is an equation. It has an equals sign and can be solved.What is an expression then?An expression is a number sentence without an equals sign. It can be simplified and/or evaluated.Example4 + 3 × 5Now this expression can be confusing because it has both addition and multiplication in it.Do we need to add or multiply first?To figure this out, we are going to learn something called the Order of Operations.The Order of Operation is a way of evaluating expressions. It lets you know what order to complete eachoperation in.Order of OperationsP - parenthesesE - exponentsMD - multiplication or division in order from left to rightAS - addition or subtraction in order from left to rightTake a few minutes to write these down in a notebook.Now that you know the order of operations, let’s go back to our example.Example4 + 3 × 523
1.4. Order of Operations www.ck12.orgHere we have an expression with addition and multiplication.We can look at the order of operations and see that multiplication comes before addition. We need to complete thatoperation first.4 + 3 × 54 + 15= 19When we evaluate this expression using order of operations, our answer is 20.What would have happened if we had NOT followed the order of operations?Example4 + 3 × 5We probably would have solved the problem in order from left to right.4 + 3 × 57 × 5= 35This would have given us an incorrect answer. It is important to always follow the order of operations.Here are few for you to try on your own.1. 8 − 1 × 4 + 3 =2. 2 × 6 + 8 ÷ 2 =3. 5 + 9 × 3 − 6 + 2 =II. Evaluating Numerical Expressions Using Powers and Grouping SymbolsWe can also use the order of operations when we have exponent powers and grouping symbols like parentheses.Let’s review where exponents and parentheses fall in the order of operations.Order of OperationsP - parenthesesE - exponentsMD - multiplication or division in order from left to rightAS - addition or subtraction in order from left to rightWow! You can see that according to the order of operations parentheses comes first. We always do the work inparentheses first. Then we evaluate exponents.Let’s see how this works with a new example.Example2 + (3 − 1) × 224
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1.1 Integers and Rational Numbers

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