1.1 Integers and Rational Numbers

www.ck12.org Chapter 1. Arithmetic ReviewDid you check Joaquin’s work?Let’s see how you did with your answers. Take your notebook and check your work with these correct answers.Let’s begin with problem number 1.We start by adding 4 + 1 which is 5. Then we multiply 7 × 5 and 7 × 2. Since multiplication comes next in our orderof operations. Finally we subtract 35 − 14 = 21.Joaquin’s work is correct.Problem Number 2We start by evaluating the exponents. 3 squared is 9 and 4 squared is 16. Next we multiply 3 × 2 = 6. Finally wecan complete the addition and subtraction in order from left to right. Our final answer is 22.Joaquin’s work is correct.Problem Number 3We start with the multiplication and multiply 3 × 2 which is 6. Then we complete the parentheses 7 − 1 = 6. Nowwe can complete the addition and subtraction in order from left to right. The answer correct is 13.Uh Oh, Joaquin’s answer is incorrect. How did Joaquin get 19 as an answer?Well, if you look, Joaquin did not follow the order of operations. He just did the operations in order from left toright. If you don’t multiply 3 × 2 first, then you get 19 as an answer instead of 16.Problem Number 4Let’s complete the work in parentheses first, 8 × 2 = 16 and 5 × 2 = 10. Next we evaluate the exponent, 3 squared is9. Now we can complete the addition and subtraction in order from left to right. The answer is 17.Joaquin’s work is correct.Problem Number 5First, we need to complete the work in parentheses, 6 × 3 = 18. Next, we complete the multiplication 2 × 3 = 6.Now we can evaluate the addition and subtraction in order from left to right. Our answer is 30.Uh Oh, Joaquin got mixed up again. How did he get 66? Let’s look at the problem. Oh, Joaquin subtracted 18 − 2before multiplying. You can’t do that. He needed to multiply 2 × 3 first then he needed to subtract. Because of this,Joaquin’s work is not accurate.How did you do?Remember, a Math Detective can check any answer by following the order of operations.IV. Insert Grouping Symbols to Make a Given Answer TrueSometimes a grouping symbol can help us to make an answer true. By putting a grouping symbol, like parentheses,in the correct spot, we can change an answer.27