## SAT SUBJECT TEST MATH LEVEL 1

## TOPICS IN ARITHMETIC

**CHAPTER 2**

**Basic Arithmetic**

**PEMDAS**

When a calculation requires performing more than one operation, those operations must be carried out in the correct order. For decades, students have memorized the sentence “Please Excuse My Dear Aunt Sally,” or just the first letters, PEMDAS, to remember the proper order of operations.

PEMDAS stands for:

• Parentheses: first do whatever appears in parentheses, following PEMDAS within the parentheses if necessary.

• Exponents: next evaluate all terms with exponents.

• Multiplication and Division: next do all multiplications and divisions *in order* *from left to right*—do not multiply first and then divide.

• Addition and Subtraction: finally do all additions and subtractions *in order from* *left to right*—do not add first and then subtract.

**Remember**

Your calculator automatically uses PEMDAS if you enter the numbers properly.

To be sure you get the right answer, when you enter numbers in your calculator, always use parentheses around negative numbers and fractions.

For example:

• 2 3^{2} = 2 9 = 18, whereas

(2 3)^{2 }= 6^{2} = 36

• 12 6 2 = 2 2 = 4, whereas

12 (6 2) = 12 12 = 1

• 3 4 + 5 = 12 + 5 = 17, whereas

3 (4 + 5) = 3 9 = 27

• –5^{2} = –25, whereas

(–5)^{2 }= 25

**Key Fact A19**

**DISTRIBUTIVE LAW**

**For any real numbers a, b, c, and d**

**where**

*d***0:**

• ** a**(

**+**

*b***) =**

*c***+**

*ab*

*ac*• ** a**(

**–**

*b***) =**

*c***–**

*ab*

*ac*•

•

**TIP**

Sometimes when you do a calculation mentally, it is easier to use the distributive law than to use PEMDAS to evaluate what is in the parentheses.

Here are two ways to evaluate 7(100 – 1):

• Use PEMDAS: 7(100 – 1) = 7(99), which is not so easy.

• Use the distributive law: 7(100 – 1) = 7(100) – 7(1) = 700 – 7 = 693.

Similarly, here are two ways to evaluate (777 + 49) 7:

• Use PEMDAS: (777 + 49) 7 = 826 7, which is not so easy.

• Use the distributive law:

Of course, your calculator can multiply 7 99 as quickly as it can multiply 7 100, but you cannot.