Chapter 10: Terms, expressions, properties and exponents

Chapter 10: Terms, expressions, properties and exponents

Use your reading guide for the first half of this lesson.

Multiple Select

What is used to express mathematical ideas?

• equation

• expression

Multiple Choice

Classify the polynomial:

 $x^2\ +\ y^3$  

• monomial

• binomial

• trinomial

• polynomial

Fill in the Blank

A ______________ has three terms in the expression.

Multiple Select

What are the terms in this expression?

3x² + 2x - 4

• 3x²

• 2x

• 4

• 3x², 2x only

Fill in the Blank

Use the distributive property to solve: 5(3x - 4y)

Multiple Select

The term Greatest Common Factor can be abbreviated as

• GFC

• GCF

Multiple Choice

When factoring:

10x - 20y - 30z the GCF factored out is

• 5

• 10

• 15

• None of the above

Fill in the Blank

Simplify by combining like terms: 3x + 5y - x + 4y

Multiple Select

When there is a negative sign in front of a parenthesis, distribute it through the terms like a -1.

• True

• False

Fill in the Blank

Evaluate the expression:

x + y when x = 3 and y = -7

Introduction to Algebra

• Variables are used as placeholder in place of numbers. The unknown or variable is holding the place which can be solved. Ex. x + 4 = 7. X is the variable.

• An expression is a collection of numbers and letters connected by operation signs.

• The parts that are to be added or subtracted in an expression are called the terms.

• monomials have one term Ex. 3x

• Binomials have two terms Ex. x + 6

• Trinomials have three terms Ex. 3x² + 4x + 7.

Multiple Choice

What type of expression is this?
-2y² + 5y - 9

• Monomial
• Binomial
• Trinomial
• Polynomial

Multiple Choice

How many terms are there?
-2y² + 5y - 9

• 1
• 2
• 3
• 4

Multiple Choice

What type of expression is this?
-9w³ + 6w²

• Monomial
• Binomial
• Trinomial
• Polynomial

Fill in the Blank

The expression x+16 ÷2 is an example of a(n) ___.

Fill in the Blank

A ____ is a symbol, usually a letter, used to represent a number.

Properties of numbers

• Commutative property of addition Ex. 3 + 4 = 4+ 3

• Commutative property of multiplication 3 x 4 = 4 x 3

• Associative property of addition 2 + (4 +1) = (2 + 4) + 1

• Associative property of multiplication 2(4x3)=(2x4)x3

• Distributive property of multiplication over addition 3(3x + 4) = 9x + 12

• 
  

Multiple Choice

 $9\left(-3\right)=-3\left(9\right)$  

• Associative Property of Addition

• Commutative Property of Addition

• Associative Property of Multiplication

• Commutative Property of Multiplication

Multiple Choice

 $\left(8+9\right)+10=8+\left(9+10\right)$  

• Associative Property of Multiplication

• Commutative Property of Multiplication

• Commutative Property of Addition

• Associative Property of Addition

Multiple Choice

3 + 8 = 3 + 8

• Substitution Property

• Transitive Property

• Symmetric Property

• Reflexive Property

Evaluating expressions

• Evaluating expressions is accomplished by substituting the given value in for the variable given.

• 4y + x when y = 3 and x = -2

• 4(3) + (-2)

• 12 + (-2)

• 10

Multiple Choice

(18 - ab) + 4b if a = -2 and b = -5

• 8

• 28

• 48

• -12

Multiple Choice

x² - xy if x = 8 and y = -3

• 88

• 40

• -8

• -24

Multiple Choice

5m + 9n if m = -7 and n = 4

• 71

• 1

• -1

• -71

Combining like terms

• Like terms mean the terms have to match exactly in order to combine. Exactly including exponents on the variables not the coefficients.

• Ex. (3x + 4y²) + (2x + 8y² - 7y)

• Add the matches: 3x + 2x

• 4y² + 8y²

• Notice the 7y has no match but it will be apart of the answer.

• 5x² + 12y² - 7y

Multiple Choice

Simplify by combining like terms:
5a + 2b - 3a + 4

• 8a + 2b + 4
• 2a + 2b + 4
• 8ab
• 4ab + 4

Multiple Choice

Which expression is equivalent to:
d + d + d + 3 + 2

• 3d + 5
• d + 5
• 2d + 7
• 3d + 4

Multiple Choice

Which expression is equivalent to
v + v + v + v + v?

• 5v
• v⁵
• v + 5
• v5

Multiple Choice

Which of these are like terms in the following expression:
3x + 7 - 9x + 24y + 2x²

• 7, 24y
• 3x, 9x
• 3x, -9x
• 3x, -9x, 2x²

Multiple Choice

What is/are the coefficient(s) of
 2x + 9 + 7x?

• 2, 9, 7
• 2, 7
• 2x, 7x
• 9

Integer exponents

• in X^a the x is the base and the a is the exponent or power.

• That means if we had 2⁴ = 2 x 2 x 2 x 2

• Evaluating this give you 16.

• There are rules when working with exponents performing algebra.

• Zero exponent Rule: Any base raised to the zero power will equal 1.

• Ex. 4⁰ = 1

Integer rules(con't)

• Negative exponents: Any base raised to a negative power, the -n is the reciprocal of the value.

• Ex.   $4^{-2}\ =\ \frac{1}{4^2}\ =\ \frac{1}{16}$  

• Product Rule of exponents:  When two base units are multiplied, the bases have to be the same and the exponents are added.

• Ex:   $3^2\ \times\ 3^4\ =\ 3^{2+4}\ =3^6$  

• Quotient Rule of exponents:  When two base units are divided, the bases need to be the same and subtract the exponents.

• Ex.   $\frac{6^3}{6^2}\ =\ 6^{3-2}\ =\ 6^1$  

Integer Rules (con't)

• Power Rule of exponents: When raising an exponential expression to a power multiply the exponents.

•  $\left(2^3\right)^2\ =\ 2^{3x2}\ =2^6$  

  Ex:

• When there are more terms in the expression, all terms will have the power distributed through each term and evaluated.

• Ex:   $\left(x^2\ y^{-2}\right)^4\ =\ x^{2x4}\ y^{-2x4}\ =\ x^8\ y^{-8}\ to\ make\ it\ positive\ flip\ the\ y\ \frac{x^8}{y^8}$  

Multiple Choice

Using exponents, simplify the following expression:

(6²)³ * 6⁴

_______________

6⁸

• 6

• 6²

• 6¹⁶

• 6¹⁷

Multiple Choice

Which two exponent rules do you need to use to simplify this expression?

• Product Rule and Quotient Rule

• Power Rule and Negative Exponent Rule

• Power Rule and Product Rule

• Zero Rule and Power Rule

Multiple Choice

Rewrite using positive exponents

• 2⁴

• 1/2⁴

• 4²

• 1/4²

Multiple Choice

Simplify the following expression:

-9⁰

• -9

• 0

• -1

• 1

Multiple Choice

Simplify the following expression:

(xyz)⁰ =

• 0

• 1

• xyz

• -1

Multiple Choice

Simplify the following expression:

(xyz)⁰ =

• 0

• 1

• xyz

• -1

Multiple Choice

Simplify the following expression:

(xyz)⁰ =

• 0

• 1

• xyz

• -1

Multiple Choice

Using exponents, simplify the following expression:

z^-3 * z⁶ * z^-3

• 1

• z⁶

• z⁵⁴

• 1/z⁶

Multiple Choice

Using exponents, simplify the following expression:

5⁵ * 5^-3

• 5^-15

• 5⁸

• 5^-8

• 5²

Scientific notation ( M x 10ⁿ)ⁿ

• Move the decimal point in the given number so that there is only one digit to the left of the decimal and as many to the right as needed. Ex. 3 . 4387 x 10ⁿ

• Count how many places you moved the decimal point, if you moved it left the n will be positive, if you moved it right the n will be negative.

• Write it in M x 10

• Ex: 34,000 = 3.4 x 10⁴

• Writing in standard form :

• Ex. 3.5 x 10^-3 = 0.0035

Multiple Choice

How many zeros would be in this number if written in standard form?
6.47 x 10¹¹

• 11
• 9
• 10
• 12

Multiple Choice

Convert to standard notation:
2.4 x 10^-3 

• 2400
• 0.24
• 0.024
• 0.0024

Multiple Choice

Convert to scientific notation:
520,000,000  

• 52 x 10⁷
• 5.2 x 10⁷
• 5.2 x 10⁸
• 0.52 x 10⁹

Multiple Choice

How would you write 5.6 x 10^-3 in standard form?

• 56,000

• 5,600

• 0.00056

• 0.0056

Multiplying and dividing in scientific notation

• Use the calculator to solve these problems.

• If the answer is not in scientific form, move the decimal and add or subtract the places moved to the power of 10.

Multiple Choice

Evaluate. Leave your answer in scientific notation. 
(9.6×10⁸)  ⁄  (3×10⁴)
(hint - it's division...)

• 6.6×10²
• 3.2×10¹²
• 3.2×10⁴
• 6.6×10⁴

Multiple Choice

When dividing numbers in scientific notation, what do you do to the exponents?
For example:
(4×10⁵) ∕ (3×10²)

• Add them
• Subtract them
• Keep them the same
• Divide them

Multiple Choice

Multiply:
(9.4 x 10⁶)(3.2 x 10⁵)

• 30.08 x 10¹¹
• 3.8 x 10¹
• 3.008 x 10¹²
• 2.9375 x 10¹

Multiple Choice

Which of these numbers are NOT in scientific notation?

• 1.2 x 10³
• 5.3 x 10⁹
• 2.0 x 10⁰
• 10 x 10²

This was a long lesson. When you come back after Thanksgiving, we will finish chapter 10. HAVE THE READING GUIDE FOR CHAPTER 10 FINISHED AND WE WILL HAVE THE FIANL READING CHECK. Have a great Holiday!