Learn on PengienVision, Mathematics, Grade 7Chapter 4: Generate Equivalent Expressions

Lesson 1: Write and Evaluate Algebraic Expressions

In this Grade 7 enVision Mathematics lesson from Chapter 4, students learn how to write algebraic expressions with variables, constants, and coefficients to represent real-world situations, then evaluate those expressions by substituting given values. The lesson covers translating word problems into expressions such as 20 − (2/5)d and (1/3)m − 32.5, and calculating results using rational numbers including fractions and decimals.

Section 1

Introduction to Algebraic Expressions

Property

An algebraic expression is the same as an arithmetic expression, except that some of the entries are letters representing numbers.

These symbols are called variables and represent an unknown quantity.

To evaluate an algebraic expression, substitute specific values for the variables and perform the arithmetic operations according to the order of operations.

Section 2

The Anatomy of an Algebraic Expression

Property

To work with algebra, you need to speak the language. An expression is made up of separate parts called terms (separated by ++ or −- signs).

  • Coefficient: The number physically attached to the front of a variable (it multiplies the variable). If a variable stands alone like xx, its coefficient is an invisible 11.
  • Constant: A plain number with no variable attached.
  • Like Terms: Terms that have the exact same variable(s) raised to the exact same power. Constants are always like terms with other constants.

Examples

  • Anatomy: In the expression 5x−3y+8−x5x - 3y + 8 - x:
    • There are 4 terms.
    • The coefficients are 55, −3-3, and −1-1 (from the −x-x).
    • The constant is 88.
  • Identifying Like Terms: 4x4x and −9x-9x are like terms. 7x7x and 7y7y are NOT. 3x3x and 3x23x^2 are NOT (the exponents are different). 55 and −12-12 ARE like terms.

Explanation

Think of like terms as specific categories of items. Variables act like unit labels. You can add 3 Apples and 4 Apples to get 7 Apples (3a+4a=7a3a + 4a = 7a). But you cannot mathematically combine 3 Apples and 4 Bananas (3a+4b3a + 4b). They just sit next to each other in the expression.

Lesson overview

Expand to review the lesson summary and core properties.

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Section 1

Introduction to Algebraic Expressions

Property

An algebraic expression is the same as an arithmetic expression, except that some of the entries are letters representing numbers.

These symbols are called variables and represent an unknown quantity.

To evaluate an algebraic expression, substitute specific values for the variables and perform the arithmetic operations according to the order of operations.

Section 2

The Anatomy of an Algebraic Expression

Property

To work with algebra, you need to speak the language. An expression is made up of separate parts called terms (separated by ++ or −- signs).

  • Coefficient: The number physically attached to the front of a variable (it multiplies the variable). If a variable stands alone like xx, its coefficient is an invisible 11.
  • Constant: A plain number with no variable attached.
  • Like Terms: Terms that have the exact same variable(s) raised to the exact same power. Constants are always like terms with other constants.

Examples

  • Anatomy: In the expression 5x−3y+8−x5x - 3y + 8 - x:
    • There are 4 terms.
    • The coefficients are 55, −3-3, and −1-1 (from the −x-x).
    • The constant is 88.
  • Identifying Like Terms: 4x4x and −9x-9x are like terms. 7x7x and 7y7y are NOT. 3x3x and 3x23x^2 are NOT (the exponents are different). 55 and −12-12 ARE like terms.

Explanation

Think of like terms as specific categories of items. Variables act like unit labels. You can add 3 Apples and 4 Apples to get 7 Apples (3a+4a=7a3a + 4a = 7a). But you cannot mathematically combine 3 Apples and 4 Bananas (3a+4b3a + 4b). They just sit next to each other in the expression.