# Algebraic Expressions

### What is algebra?

Algebra is the branch of mathematics in which we represent unknown numbers or quantities in terms of letters or symbols. The unknown number is also called a variable.

### How to write algebraic expressions?

Example:

At any time, Pinky had \$7 more than Greene.

We use a letter to represent the unknown number. x is the unknown number here.

So, Pinky had \$(x + 7).

We can use any letter to represent an unknown number. We use the letter y to represent the unknown number here.

Since Pinky had \$7 more than Greene, this means Greene had \$7 less than Pinky.

So, Greene had \$(p − 7).

Let's put the above in a table.

 Greene Pinky \$5 \$12 \$57 \$64 \$x \$(x + 7) or \$(7 + x) \$y \$(y + 7) or \$(7 + y) \$(p − 7) \$p

(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.

### Word Problem 1

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 = x Number of kids in Sections A and B together = 37 + x

 b) Number of kids in Section A = 37 Number of kids in Section B = x The difference between the number of kids in Sections A and B = 37 − x

There are (37 − x) more kids in Section A than in Section B.

### Word Problem 2

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.
We write 7 × k as 7k.
Also, k × 7 = 7k
a) There are 7 × 3 or 21 marbles in 3 bags.
b) There are 7 × k or 7k marbles in k bags.

### Word Problem 3

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 = t Number of rolls that Sarah kept for herself = 2 Total number of rolls distributed among the cousins = (t − 2)

Number of cousins  =  3
Number of rolls each cousin got  =  (t − 2) ÷ 3
=  (t − 2)
3
We write (t−2) ÷ 3 as
 (t−2)   3 or 13 × (t−2).