Simplifying Numeric Expressions
You will learn:
1. rules for evaluating an expression
2. learn a mnemonic to help remember the order of operations
3. to identify an expression
4. to simplify expressions with exponents
5. to simplify expressions with scientific notation
Vocabulary
1. Exponent - a numeral used to tell how many times a number or variable is used as a
factor, example
2. Expression - a mathematical phrase that can include operations, numerals, and variables
in algebraic terms: 2l + 3x, in numeric terms: 13.4 – 4.7
3. Order of operations - rules for evaluating an expression
4. Scientific Notation - a way of writing a number in terms of an integer power of 10
multiples by a number greater than or equal to 1 and less than 10
Order of Operations:
1. Work first within parenthesis.
2. Calculate all powers from left to right.
3. Do multiplication or division from left to right.
4. Do addition and subtraction from left to right.
Please Excuse My Dear Aunt Sally is a phrase, which will help you to remember the order of
operations.
EXAMPLE 1: What is the value of the following expression?
Step 1: Find the grouping symbols. Multiply 8 x 4.
Rewrite the problem.
Step 2: There are no powers [exponents]. Go to the next step.
Step 3: Multiply or divide from left to right. Multiply 3 x 2.
Rewrite the problem.
Step 4: Add or subtract from left to right. Subtract 32 – 6.
Rewrite the problem.
Add 26 + 7
8x4-3*2+7
8 x 4 = 32
32-3*2+7
3x2=6
32-6+7
32 – 6 = 26
26+7
26 + 7 = 33
Try it A. What is the value of the following expression? "4 • 3 + 6(5 + 2) =
Show all work.
Work all "TRY IT" problems in your notebook.
!
EXAMPLE 2: What is the value of the expression 8 2 " 4 # (4 + 3) =?
Step 1: Find the grouping symbols. Add 4 + 3
4+3=7
Rewrite the problem.
Step 2: Simplify the powers.
!
Rewrite the problem.
Step 3: Multiply or divide from left to right. Multiply 4 x 7.
!
Rewrite the problem.
Subtract 64 - 28
82 " 4 # 7
8 x 8 = 64
64 – 4 x 7
4 x 7 = 28
64 – 28
64 – 28 = 36
Try it B. What is the value of 4 3 " 5 # 4 + 32 "15 =. Show all work.
Try it C: What is the value of ("1.5) 2 + 12 ÷ 3 = . Show all work.
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Simplify expressions with exponents and scientific notation.
EXAMPLE: Simplify !(4.56 "10 2 ) # 35
Step 1: Use the order of operations. Find the grouping symbols.
Multiply 4.56 "10 2 since that is in the parenthesis.
!
Step 2: Simplify the exponent.
Rewrite the problem.
!
Rewrite the problem.
Step 3: Simplify the exponent.
Rewrite the problem.
Step 4: Subtract.
!
(4.56 "10 2 )
10 2 = 10 "10 = 100
4.56 "100 = 456
456 " 35
!
!
!
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Try it D. What is the value of (3.4 "10 4 ) ÷ (15 # 5) = .Show all work.
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35 = 243
456 – 243 =
213
Try E: The chart below lists the diameters of the planets. Order the planets from smallest
to largest. The diameters are expressed in scientific notation. Find the order by simplifying
the expression.
Planet Diameters (km)
Planet Diameter
Planet Diameter
3
4.88 "10
Mercury
Venus
4
1.2756 ! 10
Earth
Mars
4
5.08 ! 10
Uranus
Neptune
5
1.427 ! 10
Jupiter
Saturn
!
!
3
2.3 ! 10
Pluto
Evaluate each expression.
1)
9 + 13 ! 4 2 =
2)
9 + (13 ! 4)2 =
3)
(5.678 ! 10 3 ) " 1800 =
1.2104 "10 4
6.794 ! 10 4
4.86 ! 10 4
1.2 ! 10 5