### Key Concepts

- Write an algebraic expression using a pattern.
- Write algebraic expressions.
- Identify parts of an expression.

## Explore It!

The table shows the number of games the Hornets won and the number of games the Lynx won.

What pattern do you see in the data in the table? Explain how the pattern relates to the number of games won.

**Step1: **

The pairs of numbers are: 3 and 5, 6 and 8, 9 and 11.

What those pairs have in common is that when subtracted, they all give 2 as a result.

5-3=2

6-8=2

9-11=2

The pattern seen in the data is then the number of games won by the Lynx is 2 more than the number of games won by the Hornets.

Each pair of numbers has a difference of 2. The pattern seen in the data is the number of games won by the Lynx is 2 more than the number of games won by the Hornets.

B. Look for relationships and write numerical expressions to relate the number of games won by the Lynx to the number of games won by the Hornets.

**Step 1 **

When the Hornets won 3 games, the Lynx won 5, which can be written as

3 + 2 = 5.

When the Hornets won 6 games, the Lynx won 8, which can be written as

6+2 = 8

When the Hornets won 9 games, the Lynx won 11, which can be written as

9+2 = 11.

**Step2:** Result

C. Explain how to complete the table above for the Lynx if the Hornets won *n* games.

**Step 1 **

In the table, we can see that when the Hornets won 3 games, the Lynx won 5, the difference being two.

The Hornets 6, the Lynx 8, the difference again is two.

The Hornets 9, the Lynx 11, the difference again is two.

Thus, the pattern is:

Since the difference is then (n + 2) – n, which then equals 2.

**Step 2**

If the Hornets win *n* games, the Lynx win n+ 2 games.

Lynx win n+ 2 games. N indicates as a variable.

Variable is a symbol, usually, a letter, which represents a number, called the value of the variable.

Variable can be either arbitrary, not fully specified, or unknown.

#### Essential question:

How can you write an algebraic expression?

**EXAMPLE 1 **

Darius bought some comic books. How can you write an algebraic expression to represent the total cost of the comic books? Use a variable to write an algebraic expression.

**Step 1:**

Let n= the number of comic books. Each comic book costs $4

**Step 2:**

An **algebraic expression **is a type of math expression that has at least one variable and at least one operation.

#### Try It!

Olivia’s sister Emma bought *m* mystery books for $6.50 each. Show three ways to write an algebraic expression that represents the total cost of the mystery books?

**Solution:**

The algebraic expressions which represent the total cost of the mystery books Rachel bought are

m x $6.50,

m. $6.50 and

m($6.50).

**Convince me! **

How do you know that the expressions you wrote for the cost of the mystery books are algebraic expressions?

**Solution:**

The expressions above are algebraic expressions because each of them contains a variable – a letter that represents an unknown quantity, in this case, it represents the number of mystery books Rachel bought.

The expressions also contain an operation – multiplication.

m x $6.50, m. $6.50, and m($6.50)

The expressions are algebraic expressions because each of them contains a variable and an operation.

**EXAMPLE 2 **

How can an algebraic expression represent a given situation? An algebraic expression can use variables and operations to represent given situations.

**Solution:**

**Try it! **

Write an algebraic expression that represents “9 minus the quantity y divided by 7.”

Solution:

**Step 1:**

9 **minus** the quantity y is 9 – b

**Step 2:**

“9 minus the quantity y **divided** by 7’’ is (9 – y) ÷ 7.

**Term: **

Each part of an expression that is separated by a plus sign or a minus sign is called a term.

**EXAMPLE 3 **

How many terms does the expression 12r + r/2 – 19 have? Describe the parts of the expression.

**Solution:**

**Step 1:**

12r +r/2 – 19 has three terms.

**terms**

∴ The terms are 12r, r/2 and 19

The **first term** 12r is a product of two factors.

A **coefficient** is a number that is multiplied by a variable.

12 is the coefficient of *r*.

The **third term**, 19, is a **constant** numerical value.

Try it!

How many terms does the expression r=9+5.5 have? Explain.

**Step 1:**

A term is each part of an expression separated by a plus sign or a minus sign.

The expression r ÷ 9+5.5 has two terms.

The first term is the quotient r ÷ 9, and the second term is 5.5.

**Step 2: **

The expression has two terms.

**KEY CONCEPT **

A **variable**, written as a letter, represents a quantity that can change. You can use a variable to write an algebraic expression that has at least one operation.

Translate between words and math

There are keywords that tell you which operations to use for mathematical expressions.

## Practice & Problem Solving – Higher Order Thinking

- Some students equally share 2 baskets of oranges. Each basket has 12 oranges. Write an algebraic expression to represent this situation. Then explain how you chose which variable and operations to use?

Solution:

**Step 1: **

There are two baskets of oranges, and each has 18 oranges, so, we will multiply 2 by 18.

Represent the students with *n*. They equally shared two baskets of oranges; thus, we will divide the product 2(18) by *n*.

The following expression represents the given situation

2(18) ÷ n.

36÷ n, where *n* is the number of students.

Practice & Problem Solving

- Use the expression y ÷ 3(8 – 2) +5.9 to complete the table. Identify the parts of the expression that correspond to the descriptions. (Description of Part, Variable, Difference, Product Constant numerical value)

**Step 1 **

The given expression is: .

y÷3(8 – 2) + 5.9

The given expression has the following parts: y, 3(8 – 2) and 5.9

The first part, y is a variable.

The second part, 3(8 – 2), is a product of the numbers 3 and (8 – 2).

This second factor of the product is a difference of 8 and 2.

The third part, 5.9, is a constant numerical value.

### Let’s check your knowledge:

- How can you write an algebraic expression?

- Identify the variable and the operation in the algebraic expression 6x6x .

- Explain why 15 +½n is an algebraic expression.

- Which part of the expression 2(3+4) is the sum of two terms? Explain.

- Write an algebraic expression for each situation.

- Five less than
*y*

- Six times the quantity two
*x*plus three*y*

- Use the expression w/4 + 12.5 – 7z.

- How many terms does the expression have? Explain.

- Which term has a coefficient? Explain.

- Which term is a constant numerical value?

**Answers: **

- We can write an algebraic expression using variables and constants using some operations.

- The variable is
*x*. The operation is division.

- 15 +½n is an algebraic expression because it has two terms, and the second term has variable
*n*.

- In the numerical expression 2(3+4), the adding part is (3+4). Because there is operation of addition between them.

- i. y – 5

ii. 6x+3y

- i. Three terms, they are w/ 4 ,12.5 and -7z

ii. w/4 = 1/4 x w, the coefficient is 1/4 and -7z= -7 x z, the coefficient is -7

## Exercise:

**Match the following:**

A. The sum of 12 and*x*a. 15 – b

B. 15 decreased by*b*b. 1 0x

C. The product of 10 and*x*c. a÷23

D.*a*divided by 23 d. 3y

E. Thrice the number*y*e. x + 12**Answer the following:**

a. Write the terms in the following expression 7 – 2?

b. There are*x*trees with*y*apples each. Then how many apples are with*x*trees?

c. What is an algebraic expression? What are terms it includes?**Answer the following with the help of the expression:**

5 +4y+30

What are the terms in the expression?

What is the coefficient of

What is the constant term in the expression?

How many terms are there in the expression?