Algebra

Constant

3, -2, 8.5 are constants.

Variable

x, a, p are variables.

Term

3x, -2a are terms.

Like Terms

Like terms have the same variable(s)

3x and 5x are like terms.

3x and 8y are not like terms.

3ab and 7ab are like terms.

3ab and 8ak are not like terms.

Addition and Subtraction of Algebraic Terms

Only like terms can be added or subtracted.

3a + 2a = 5a

3a – 2a = a

3a – 2b cannot be simplified.

Examples for Addition

3x + 8x = 11x

4xy + 8xy = 12xy

2xy2 + 18xy2 = 20xy2

Examples for Subtraction

3a – 2a = a

8ab – 2ab = 6ab

8xz3 – 2xz3 = 6xz3

More Examples

3y + 2y – y = 4y

3pq + 8pq – 5pq = 6pq

Multiplication and Division of Algebraic Terms

To multiply/divide, the terms need not be like terms.

3 x 2a = 6a

3a x 2a = 6a2

3a x 2b = 6ab

Examples for Multiplication

k x k = k2

3p x 2p2 = 6p3

3pq2 x 8p2q = 24p3q3

Examples for Division

m2 ÷ m = m

4ab2 ÷ 2b = 2ab

4xy2 ÷ 2y = 2xy

More Examples

m3 x 2m2 ÷ m = 2m4

4b2 ÷ 2b x 3b = 6b2

Expansion of Algebraic Expression

3(y + 8x)

When expanding the above expression,  multiply each and every term inside the brackets by 3.

= 3 (y) + 3 (8x)

= 3y + 24x

8(x – y ) + 5x

= 8(x) – 8(y) + 5x

= 13x – 8y

aPPLICATION OF Algebra

John's daily allowance is $ 10, he spends $ x every day and saves the rest. Find his savings for (a) one day  (b) one week

Daily Allowance = $ 10

Daily Expenses = $ x

(a) Savings for one day = $ (10 - x)

(b) Savings for one week= $ 7(10 - x) = $ (70 - 7x)

Muthu is x years old. His father is 3 times older than him. Their total age is 60. Find Muthu's age (a) now (b) 5 years before (c) m years later

Muthu's Age = x

Father's Age = 3(x) = 3x

Total Age = x + 3x = 4x

4x = 60

x = 60/4 = 15

(a) Muthu's age - now = 15 years

(b) Muthu's age - 5 years before = 15 - 5 = 10 years

(c) Muthu's age - m years later = (15 + m) years

Pam buys a dozen Orange for $ k  and sells each orange for 50 cents. Find her total profit when she buys and sells 5 dozen oranges.

Selling price of one Orange = 50 cents

Selling price of 1 dozen (12 Oranges) = 50 cents x 12 = 600 cents = $ 6

Cost price of 1 dozen Oranges = $ k

Profit for 1 dozen Oranges = $ (6 - k)

Profit for 5 dozen Oranges = $ 5(6 - k) = $ (30 - 5k)

Questions

1. A pencil cost x cents and a pen cost $y. Find the cost of 10 pencils and 5 pens.

2. Distance between two Lamp posts is x metre. Find the total number of lamp posts along a road of length 5 km.

3. Find the total of 5 consecutive integers in terms of y, if the smallest integer is y.

4. Find the total of 5 consecutive even integers in terms of k, if the smallest integer is k.

5. Find the total of 5 consecutive odd integers in terms of p,  if the middle integer is p.

6. Find the maximum number of packets of Sugar you can pack from m kg of Sugar, if each packet weighs 200 g.

7. John runs 5 m in x seconds. Find the distance he can run in 1 minute, at the same average speed.