In algebra, always remember the following:
n means 1 x n
2p means 2 x p
3y2 means 3 x y2 which is same as 3 x y x y
4a2d means 4 x a2 x d
2(2a + 5b) = 2 x 2a + 2 x 5b = 4a + 10b
n means 1 x n
2p means 2 x p
3y2 means 3 x y2 which is same as 3 x y x y
4a2d means 4 x a2 x d
2(2a + 5b) = 2 x 2a + 2 x 5b = 4a + 10b
Simplifying Algebraic Expressions
Example 1
Work out: 3(2a + 4b) - 2(a + 2b)
= (3 x 2a + 3 x 4b) - (2 x a + 2 x 2b)
= 6a + 12b - 2a + 4b
Putting like terms together
= 6a - 2a + 12b + 4b
= 4a + 16b
= 6a + 12b - 2a + 4b
Putting like terms together
= 6a - 2a + 12b + 4b
= 4a + 16b
Forming and Simplifying Algebraic Expressions
Example 2
Albert, Wilson and Charles shared some apples. Albert got 5 more apples than Charles who got twice as much as Wilson. How many apples did they get all together?
From the information above, we gather that:
Wilson has a apples. Hence:
Charles has (2 x a = 2a) apples
Albert = (2a + 5) apples
Hence
= a + 2a + 2a + 5
= 5a + 5
Wilson has a apples. Hence:
Charles has (2 x a = 2a) apples
Albert = (2a + 5) apples
Hence
= a + 2a + 2a + 5
= 5a + 5
Solving Algebraic Expressions
When solving a quadratic equation, you find the value of the unknown in the equation.
Example 3
Find the value of y in 3(y + 2) = 24
We start by opening the brackets:
3(y + 2) is the same as (3 x y) + (3 x 2)
3y + 6 = 24
3y = 24 - 6
3y = 18
Divide both sides by 3:
3y / 3 = 18 / 3
y = 6
3(y + 2) is the same as (3 x y) + (3 x 2)
3y + 6 = 24
3y = 24 - 6
3y = 18
Divide both sides by 3:
3y / 3 = 18 / 3
y = 6
Forming and Solving Algebraic Expressions
Now that you have learnt how to solve algebraic expressions. Let's try solving real-life mathematical problems.In this section, you will come across words such as more than, greater than, less than, younger than, shorter than, twice as much and similar comparative words.
Example 4
Mwilu is 6 years older than Kyalo. If Kyalo is 12 years old, how old is Mwilu.
Let Mwilu's age be b:
Then b = 6 years + Kyalo's age.
b = 6 + 12
b = 18
Mwilu is 18 years age
Then b = 6 years + Kyalo's age.
b = 6 + 12
b = 18
Mwilu is 18 years age
Inequalities
Let us say an unknown number p is between 8 and 14 but is neither 8 or 14. Can you tell which number p is likely to be?p can be 9, 10, 11, 12, 13
From this, we can say that p is greater than 8 and less than 14.
This can be mathematically expressed as p > 8 and p < 14. This are called inequalities.
Simplifying Inequalities
Example 5
Simplify the following inequality: 3p - 2 > 19
3p - 2 > 19
Collecting like terms together:
3p > 19 + 2
3p > 21
Divide both sides by 3:
3p / 3 > 21 / 3
21 / 3 = 7
p > 7
Collecting like terms together:
3p > 19 + 2
3p > 21
Divide both sides by 3:
3p / 3 > 21 / 3
21 / 3 = 7
p > 7