## Algebra and Algebraic Expressions

#### 1. What is algebra?

Algebra is the branch of mathematics in which we represent unknown numbers or quantities in terms of

The unknown number is also called a

**letters**or**symbols**.The unknown number is also called a

**variable**.#### 2. How do we write algebraic expressions?

**Example:**At any time, Pinky had $7 more than Greene.

Let's learn how to write this statement as an algebraic expression.

When Greene had $5, Pinky had $12 as shown below.

When Greene had $57, Pinky had $64 as shown below.

When Greene had

When Greene had $

So, Pinky had

**$**, how much had Pinky?*x*When Greene had $

*x*, Pinky had $7 more than him.So, Pinky had

**$(**.*x*+ 7)
We use a letter to represent the unknown number.

**is the unknown number here.***x*
When Greene had

**$**, Pinky had*y***$(**?*y*+ 7)
We can use any letter to represent an unknown number.

We use the letter

We use the letter

**to represent the unknown number here.***y*
When Pinky had

When Pinky had $

So, Greene had

**$**, how much had Greene?*p*When Pinky had $

*p*, Greene had $7 less than her.So, Greene had

**$(**.*p*− 7)
Since Pinky had $7 more than Greene, this means Greene had $7 less than Pinky.

Let's put the above in a table.

(

We say that,

(

*x*+ 7), (7 +*x*), (*y*+ 7), (7 +*y*) and (*p*- 7) are all examples of**algebraic expressions**.We say that,

- (
*x*+ 7) and (7 +*x*) are algebraic expressions in terms of*x*. - (
*y*+ 7) and (7 +*y*) are algebraic expressions in terms of*y*. - (
*p*- 7) is an algebraic expression in terms of*p*.

#### 3. Section A has more kids than Section B. There are 37 kids in Section A and *x* kids in Section B.

a) How many kids are there in Section A and Section B together in terms of *x*?

b) How many more kids are there in Section A than in Section B expressed in terms of *x*?

a) Number of kids in Section A = 37

Number of kids in Section B =

Number of kids in Section A and B together =

Number of kids in Section B =

*x*Number of kids in Section A and B together =

**37 +***x*
b) Number of kids in Section A = 37

Number of kids in Section B =

The difference between the number of kids in Sections A and B = 37 −

There are

Number of kids in Section B =

*x*The difference between the number of kids in Sections A and B = 37 −

*x*There are

**(37 −**more kids in Section A than in Section B.*x*)#### 4. There are 7 marbles in a bag.

a) How many marbles are there in 3 bags?

b) How many marbles are there in *k* bags? Write the algebraic expression in terms of *k*.

There are 7 marbles in 1 bag.

a) There are 7 × 3 or 21 marbles in 3 bags.

a) There are 7 × 3 or 21 marbles in 3 bags.

b) There are 7 ×

*k*or 7*k*marbles in*k*bags.
We write 7 ×

Also,

*k*as 7*k*.Also,

*k*× 7 = 7*k*#### 5. Sarah had *t* rolls of ribbon.

She kept 2 rolls for herself and distributed the rest equally among 3 of her cousins.

How many rolls did each cousin get?

Express the answer in terms of *t*.

Total number of rolls that Sarah had at first =

Number of rolls that Sarah kept for herself = 2

Total number of rolls that Sarah distributed among the cousins = (

*t*Number of rolls that Sarah kept for herself = 2

Total number of rolls that Sarah distributed among the cousins = (

*t*− 2)
Number of cousins = 3

Number of rolls each cousin got = (

Number of rolls each cousin got = (

*t*− 2) ÷ 3 =

t - 2 |

3 |

We write (

or

× (

*t*− 2) ÷ 3 as(t - 2) |

3 |

1 |

3 |

*t*− 2).