Grade 7 Algebraic Expressions and Operations

Concept: An algebraic expression is a combination of variables, constants, and mathematical operations (+, -, x, /).

Variables: These are symbols (usually letters like x, y, a, b) that represent unknown values. Their value can change.

Example: In 3x + 5, 'x' is the variable.

Constants: These are numbers that have a fixed value.

Example: In 3x + 5, '5' is the constant.

Terms: These are parts of an expression separated by addition (+) or subtraction (-) signs. A term can be a variable, a constant, or a product/quotient of variables and constants.

Example: In 3x + 5, '3x' is one term and '5' is another term.

Example: In 2y² - 7y + 1, the terms are '2y²', '-7y', and '1'.

Coefficient: The numerical factor of a term that contains a variable.

Example: In the term '3x', the coefficient is 3.

Example: In the term '-7y', the coefficient is -7.

Example: In the term 'y²', the coefficient is 1 (since y² is 1 * y²).

Like Terms: Terms that have the same variables raised to the same powers. Only the coefficients can be different.

Example: 5x and -2x are like terms (same variable 'x' raised to power 1).

Example: 3y² and 1/2 y² are like terms (same variable 'y' raised to power 2).

Example: 7ab and -4ab are like terms (same variables 'a' and 'b' raised to power 1 each).

Unlike Terms: Terms that have different variables or the same variables raised to different powers.

Example: 5x and 5y are unlike terms (different variables).

Example: 3y and 3y² are unlike terms (same variable but different powers).

Example: 7ab and 7a are unlike terms (different variables).

Important: Only like terms can be added or subtracted.

Step 1: Write the expressions to be added.

(3x + 5) + (2x - 4)

Step 2: Remove the parentheses. Since we are adding, the signs of the terms inside the second parenthesis remain the same.

3x + 5 + 2x - 4

Step 3: Group the like terms together.

(3x + 2x) + (5 - 4)

Step 4: Add or subtract the coefficients of the like terms.

• For the 'x' terms: 3 + 2 = 5. So, 3x + 2x = 5x.
• For the constant terms: 5 - 4 = 1.

Result: Combine the results from Step 4.

The sum is 5x + 1.

So, (3x + 5) + (2x - 4) = 5x + 1.

Step 1: Write the subtraction problem carefully. "Subtract (2a - 3) from (5a + 7)" means (5a + 7) - (2a - 3).

(5a + 7) - (2a - 3)

Step 2: Remove the parentheses. When subtracting an expression, change the sign of each term inside the second parenthesis.

5a + 7 - 2a + 3

Step 3: Group the like terms together.

(5a - 2a) + (7 + 3)

Step 4: Add or subtract the coefficients of the like terms.

• For the 'a' terms: 5 - 2 = 3. So, 5a - 2a = 3a.
• For the constant terms: 7 + 3 = 10.

Result: Combine the results from Step 4.

The difference is 3a + 10.

So, (5a + 7) - (2a - 3) = 3a + 10.

Step 1: Identify the terms in the expression: 4y, 7, -2y, 3z, -5.

Step 2: Group the like terms together.

(4y - 2y) + (3z) + (7 - 5)

Step 3: Combine the coefficients of the like terms.

• For the 'y' terms: 4 - 2 = 2. So, 4y - 2y = 2y.
• For the 'z' terms: There is only one '3z' term.
• For the constant terms: 7 - 5 = 2.

Result: Write the simplified expression by combining the results.

The simplified expression is 2y + 3z + 2.

So, 4y + 7 - 2y + 3z - 5 = 2y + 3z + 2.