Lesson 2 (part 1) - Vocabulary of Algebraic Expressions

Lesson 2 (part 1) Vocabulary of

Algebraic Expressions

Monday 1/24/22

Terms

parts of an expression separated by addition.

The terms of the expression 3x + 7 + x + 2 are 3x , 7 , x , and 2.

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The terms of the expression 5n - 8 are 5n and -8 because when rewritten as addition, the expression is 5n + -8.

Coefficients

the numerical part of a term that contains a variable

The coefficient of:

3x is 3           -4n is -4           p is 1           -w is -1

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​* p can be written as 1p and -w can be written as -1w.

Constants

a term without a variable.

Constants can be:

5 , -4 , 1/2 , -3/4 , 0.75 , -0.25

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They can be positive, negative, fractions, decimals... but CANNOT be multiplied by a variable.​

Like Terms

terms that contain the same variables raised to the same exponents.

2n and 5n ARE like terms (same variable)

6p and -7p ARE like terms (same variable)

x² and 3x² ARE like terms (same variable raised to the second power)

2x and 4n ARE NOT like terms (different variables)

8w and 9w² ARE NOT like terms (same variable, but raised to different exponents

Multiple Choice

Identify the TERMS of the expression. (Write this expression down, since you will see it for the next few examples)

6x - 2y + x - 5

• 6x , 2y , x , 5

• 6x , -2y , x , -5

• 6 , 2 , 1 , -5

• 6 , -2 , 1 , -5

The terms are 6x , -2y , x , -5

When the expression 6x - 2y + x - 5 is written using addition, it becomes:

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​6x + -2y + x + -5

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Since terms are separate by addition, the terms are 6x , -2y , x , and -5.​

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Multiple Choice

This expression has ONE PAIR of LIKE TERMS. What are they?

6x - 2y + x - 5

• 6x and -5

• -2y and -5

• 6x and x

• x and -5

The like terms are 6x and -x.

Like terms have the same variable raised to the same exponent. These are the only two terms that match that description, since -2y has a y and -5 has no variable.

Multiple Choice

What are the COEFFICIENTS of the expression?

6x - 2y + x - 5

• 6 , -2 , 1 , -5

• -5

• 6 and -2

• 6 , -2 , 1

The coefficients are 6 , -2 , 1

The 6 and -2 are SEEN in front of the terms 6x and -2y. But, the term x can be written as 1x. Therefore, 1 is also a coefficient.

Multiple Choice

What are the CONSTANTS of the expression?

6x - 2y + x - 5

• 6 , -2 , 1 , -5

• -5

• 6 and -2

• 6 , -2 , 1

The only constant is -5

The last remaining term (-5) does not have a variable multiplied to it. Therefore, it is the only constant in this expression.

Answer the next four questions based on the new expression. The answers will be revealed at the end.

Some text here about the topic of discussion

Multiple Choice

Identify the TERMS of the expression.

$$7n-8-\frac{2}{3}n+11$$  

• $$7\ ,\ 8\ ,\ \frac{2}{3}\ ,\ 11$$  

• $$7n\ ,\ 8\ ,\ \frac{2}{3}n\ ,\ 11$$  

• $$7n\ ,\ -8\ ,\ -\frac{2}{3}n\ ,\ 11$$  

• $$7n\ and\ -\frac{2}{3}n$$  

Multiple Select

There are TWO PAIRS of LIKE TERMS. What is ONE of them?

$$7n-8-\frac{2}{3}n+11$$  

• $$-8\ ,\ and-\frac{2}{3}n$$  

• $$7n\ and\ -\frac{2}{3}n$$  

• $$7n\ and\ 11$$  

• $$-8\ and\ 11$$  

Multiple Choice

What are the COEFFICIENTS of the expression?

$$7n-8-\frac{2}{3}n+11$$  

• $$7\ and\ -\frac{2}{3}$$  

• $$-8\ and\ 11$$  

• $$7\ ,\ -8\ ,\ 11$$  

• $$\frac{2}{3}\ and\ 11$$  

Multiple Choice

What are the CONSTANTS of the expression?

$$7n-8-\frac{2}{3}n+11$$  

• $$7\ and\ -\frac{2}{3}$$  

• $$-8\ and\ 11$$  

• $$7\ ,\ -8\ ,\ 11$$  

• $$\frac{2}{3}\ and\ 11$$  

Answers for 7n - 8 - 2/3n + 11

Terms: 7n , -8 , -2/3n , 11

Like Terms: 7n , -2/3n AND -8 , 11

(there were two pairs)

Coefficients: 7 and -2/3

Constants: -8 and 11​