# Algebraic Expressions

*What is algebra?*

*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?*

*How to write algebraic expressions?*

*Example:*

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

When Greene had $5, Pinky had $12.

When Greene had $57, Pinky had $64.

We use a letter to represent the unknown number.

**is the unknown number here.***x*When Greene had **$ x**, how much had Pinky?

When Greene had **$ x**, Pinky had $7 more than him.

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

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

**to represent the unknown number here.***y*When Greene had **$ y**, Pinky had $(

*y*+ 7).

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

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

When Pinky had $*p*, Greene had $7 less than her.

So, Greene had $(*p* − 7).

Let's put the above in a table.

GreenePinky$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 ofalgebraic expressions.

We say that,

- (
x+ 7) and (7 +x) are algebraic expressions in terms ofx.- (
y+ 7) and (7 +y) are algebraic expressions in terms ofy.- (
p- 7) is an algebraic expression in terms ofp.

*Word Problem 1*

*Word Problem 1*

Section A has more kids than Section B. There are 37 kids in Section A andxkids in Section B.

a) How many kids are there in Section A and Section B together in terms ofx?

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

a) Number of kids in Section A = 37 Number of kids in Section B = xNumber of kids in Sections A and B together = 37 + x

b) Number of kids in Section A = 37 Number of kids in Section B = xThe 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*

*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 inkbags? Write the algebraic expression in terms ofk.

There are 7 marbles in 1 bag.

We write 7 ×a) There are 7 × 3 or 21 marbles in 3 bags.kas 7k.

Also,k× 7 = 7k

b) There are 7 ×kor 7kmarbles inkbags.

*Word Problem 3*

*Word Problem 3*

Sarah hadtrolls 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 oft.

Total number of rolls that Sarah had at first = tNumber 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)

3or 1

3× ( t−2).