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52 Part I: Back to Basics with Basic Math

9. Evaluate 8 – 3 · 4 ÷ 6 + 1.

 Solve It 

10. Find 10 · 5 – (–3) · 8 ÷ –2.

 Solve It 

7. 12 ÷ –3 · –9 ÷ 6 · –7 = ?

 Solve It 

8. Solve –90 ÷ 9 · –8 ÷ –10 ÷ 4 · –15.

 Solve It 

 Making Sense of Mixed-Operator Expressions Things get a little complicated in this section, but you can handle it. A mixed-operator expres-sion contains at least one addition or subtraction sign and at least one multiplication or divi-sion sign. To evaluate mixed-operator expressions, follow a couple of simple steps:

1. Evaluate all multiplication and division from left to right.

Begin evaluating a mixed-operator expression by underlining all the multiplication ordivision in the problem.

2. Evaluate addition and subtraction from left to right.

Q. What’s –15 · 3 ÷ –5 – (–3) · –4?

 A. –3. Start by underlining all the multiplica-tion and division in the problem; thenevaluate all multiplication and divisionfrom left to right:

–15 · 3 ÷ –5 – (–3) · –4

= –45 ÷ –5 – (–3) · –4

= 9 – (–3) · –4

= 9 – 12

Finish up by evaluating the addition andsubtraction from left to right:

= –3

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11. –19 – 7 · 3 + –20 ÷ 4 – 8 = ?

 Solve It 

12. What’s 60 ÷ –10 – (–2) + 11 · 8 ÷ 2?

 Solve It 

Chapter 4: It’s Just an Expression

Handling Powers ResponsiblyYou may have heard that power corrupts, but rest assured that when mathematicians dealwith powers, the order of operations usually keeps them in line. When an expression con-tains one or more powers, evaluate all powers from left to right before moving on to the BigFour operators. Here’s the breakdown:

1. Evaluate all powers from left to right.

In Chapter 2, I show you that raising a number to a power simply means multiplyingthe number by itself that many times. For example, 23 = 2 · 2 · 2 = 8. Remember thatanything raised to the 0 power equals 1.

2. Evaluate all multiplication and division from left to right.

3. Evaluate addition and subtraction from left to right.

If you compare this numbered list with the one in the preceding section, you’ll notice theonly difference is that I’ve now inserted a new rule at the top.

Q. Evaluate 7 – 42 ÷ 24 + 9 · 23.

 A. 78. Evaluate all powers from left to right,starting with 42 = 4 · 4 = 16:

= 7 – 16 ÷ 24 + 9 · 23

Move on to evaluate the remaining twopowers:

= 7 – 16 ÷ 16 + 9 · 8

Next, evaluate all multiplication and divi-sion from left to right:

= 7 – 1 + 9 · 8

= 7 – 1 + 72

Finish up by evaluating the addition and

subtraction from left to right:= 6 + 72

= 78