### Key Concepts

- Add expressions by using properties
- Add expressions with more than one variable
- Add more complex expressions

**4.6 Add expressions**

## How to add expressions?

In addition to algebraic expressions, while adding algebraic expressions, we collect the like terms and add them.

The sum of several like terms is the like term whose coefficient is the sum of the coefficients of these like terms.

**Example:**

Add: x + y + 3 and 3x + 2y + 5

**Solution:**

Horizontal Method:

(x + y + 3) + (3x + 2y + 5)

= x + y + 3 + 3x + 2y + 5

Arrange the like terms together, then add.

Thus, the required addition

= (x + 3x)+( y + 2y) + (3 + 5)

= 4x + 3y + 8

**4.6.1 Add expressions by using properties **

**Properties:**

Associative property of multiplication

(a x b) x c = a x (b x c)

Associative property of addition

(a + b) + c = a + (b + c)

**Example1:**

Sophia and Ollie each deposit $120 to open a joint account. They each make monthly deposits, as shown. What expression represents the amount in the account after *m* months?

**Solution:**

Use the bar diagram to represent the situation and write an expression for the cost of each club.

Add the expressions to find the amount in the account.

(120+150m) +(120+135m)

= (120+120) +(150m+135m)

=240+285m

The expression 240+285m can be used to determine the amount in the account after *m* months.

**Example 2:**

Add 5 + 6i and 7 − 3i

**Solution:**

(5 + 6i) + (7 − 3i) = 5 + 6i + 7 − 3i

= 5 + 7 + 6i − 3i

= 12 + 3i

**4.6.2 Add expressions with more than one variable**

“In a fruit bowl, there are ‘4a’ apples and ‘5’ bananas. In a paper bag, there are 8 apples and 9b bananas. What is the total number of pieces of fruit?”

**Solution:**

(4a+5) +(8+9b)

= 4a+9b+(5+8)

= 4a+9b+13

The expression 4a+9b+13 represents the total number of pieces of fruits.

**Example2:**

Add expressions 12x +15y and (-6x) +14y.

**Solution:**

(12x+15y) +(-6x +14y)

= (12x+(-6x) +(15y +14y)

=6x +29y

**4.6.3 Add more complex expressions**

**Example 1:**

Add the expression (8.7 c – 25.50) + (-4.3p + 18.70)

**Solution:**

(8.7 c – 25.50) + (-4.3p + 18.70)

8.7c-4.3p+(-25.50 +18.70)

=8.7c – 4.3 p + (-6.8)

= 8.7c – 4.3 p -6.8

**Example2:**

( 1/2 a – 4 – 5b) + ( 1/4 a – 2b +4)

**Solution:**

( 1/2 – 5 – 5b) + ( 1/4 a – 2b +4)

( 1/2 a + 1/4 a ) +(-5b+( –2b)) +(-5+4)

=3/4 a-7b -1

## Exercise:

1.Find the sum.

(6b+7) + (4x – 2) + (3c+8)

2. Combine like terms.

(-3y- 5) + (3m+6y) + (4+5m)

3. Charmin is going to plant *b* plants in one garden and 4b+6 plants in another garden. How many plants is Charmin growing altogether?

4. Find the sum.

(-4.5t – 3s +4.6) +(-7.2-0.2s +4.2t)

5. Fill in the boxes to add the expressions.

(4a+5) +(9a+4)

= ( 4a+____ ) +(5 + ____)

= ___ + 9

6. Fill in the boxes to add the expression.

(6t+3) +(7t-4)

= (6t +____ ) +(3 + ____)

= ___ -1

7. After $𝑥of discount, Olivia paid $189 for her new sewing machine. Write the expression for the original price of the sewing machine.

8. Add 4 + 7i and 2 + 3i.

9. Combine like terms (6a + 8b – 7c) and (2b + c – 4a)

10. Find sum (-13.2b – 36.65) +(3.46d-117.6 -2.5d)

### Concept Map

### What have we learned:

- Understand how to add the expressions.
- Understand how to add expressions by using properties
- Add expressions with more than one variable
- Add more complex expressions

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