**TOPIC 7: ALGEBRA**

An

algebraic expression – is a collection of numbers, variables, operators

and grouping symbols.Variables – are letters used to represent one or

more numbers

algebraic expression – is a collection of numbers, variables, operators

and grouping symbols.Variables – are letters used to represent one or

more numbers

An

inequality – is a mathematical statement containing two expressions

which are not equal. One expression may be less or greater than the

other.The expressions are connected by the inequality symbols<,>,≤

or≥.Where< = less than,> = greater than,≤ = less or equal and ≥ =

greater or equal.

inequality – is a mathematical statement containing two expressions

which are not equal. One expression may be less or greater than the

other.The expressions are connected by the inequality symbols<,>,≤

or≥.Where< = less than,> = greater than,≤ = less or equal and ≥ =

greater or equal.

Linear Inequalities with One Unknown

Solve linear inequalities in one unknown

An

inequality can be solved by collecting like terms on one side.Addition

and subtraction of the terms in the inequality does not change the

direction of the inequality.Multiplication and division of the sides of

the inequality by a positive number does not change the direction of the

inequality.But multiplication and division of the sides of the

inequality by a negative number changes the direction of the inequality

inequality can be solved by collecting like terms on one side.Addition

and subtraction of the terms in the inequality does not change the

direction of the inequality.Multiplication and division of the sides of

the inequality by a positive number does not change the direction of the

inequality.But multiplication and division of the sides of the

inequality by a negative number changes the direction of the inequality

Example 11

Solve the following inequalities

**Solution**

Linear Inequalities from Practical Situations

Form linear inequalities from practical situations

To represent an inequality on a number line, the following are important to be considered:

- The endpoint which is not included is marked with an empty circle
- The endpoint which is included is marked with a solid circle

Example 12

Compound statement – is a statement made up of two or more inequalities

Example 13

Solve the following compound inequalities and represent the answer on the number line

**Solution**

**TOPIC 8: NUMBERS**

A Rational Number

Define a rational number

A

**Rational Number**is a real number that can be written as a simple fraction (i.e. as a**ratio**). Most numbers we use in everyday life are Rational Numbers.Number | As a Fraction | Rational? |
---|---|---|

5 | 5/1 | Yes |

1.75 | 7/4 | Yes |

.001 | 1/1000 | Yes |

-0.1 | -1/10 | Yes |

0.111… | 1/9 | Yes |

√2(square root of 2) | ? | NO ! |

The square root of 2 cannot be written as a simple fraction! And there are many more such numbers, and because they are

**not rational**they are calledIrrational.
The Basic Operations on Rational Numbers

Perform the basic operations on rational numbers

**Addition of Rational Numbers:**

To

add two or morerational numbers, the denominator of all the rational

numbers should be the same. If the denominators of all rational numbers

are same, then you can simply add all the numerators and the denominator

value will the same. If all the denominator values are not the same,

then you have to make the denominator value as same, by multiplying the

numerator and denominator value by a common factor.

add two or morerational numbers, the denominator of all the rational

numbers should be the same. If the denominators of all rational numbers

are same, then you can simply add all the numerators and the denominator

value will the same. If all the denominator values are not the same,

then you have to make the denominator value as same, by multiplying the

numerator and denominator value by a common factor.

Example 1

1⁄3+4⁄3=5⁄3

1⁄3 +1⁄5=5⁄15 +3⁄15 =8⁄15

**Subtraction of Rational Numbers:**

To

subtract two or more rational numbers, the denominator of all the

rational numbers should be the same. If the denominators of all rational

numbers are same, then you can simply subtract the numerators and the

denominator value will the same. If all the denominator values are not

the same, then you have to make the denominator value as same by

multiplying the numerator and denominator value by a common factor.

subtract two or more rational numbers, the denominator of all the

rational numbers should be the same. If the denominators of all rational

numbers are same, then you can simply subtract the numerators and the

denominator value will the same. If all the denominator values are not

the same, then you have to make the denominator value as same by

multiplying the numerator and denominator value by a common factor.

Example 2

4⁄3 -2⁄3 =2⁄3

1⁄3-1⁄5=5⁄15-3⁄15=2⁄15

**Multiplication of Rational Numbers:**

Multiplication

of rational numbers is very easy. You should simply multiply all the

numerators and it will be the resulting numerator and multiply all the

denominators and it will be the resulting denominator.

of rational numbers is very easy. You should simply multiply all the

numerators and it will be the resulting numerator and multiply all the

denominators and it will be the resulting denominator.

Example 3

4⁄3×2⁄3=8⁄9

**Division of Rational Numbers:**

Division

of rational numbers requires multiplication of rational numbers. If you

are dividing two rational numbers, then take the reciprocal of the

second rational number and multiply it with the first rational number.

of rational numbers requires multiplication of rational numbers. If you

are dividing two rational numbers, then take the reciprocal of the

second rational number and multiply it with the first rational number.

Example 4

4⁄3÷2⁄5=4⁄3×5⁄2=20⁄6=10⁄3