# FORM ONE MATHEMATICS STUDY NOTES TOPIC 7-9.

**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

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.

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

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.

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.

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.

Example 3

4⁄3x2⁄3=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.

Example 4

4⁄3÷2⁄5=4⁄3x5⁄2=20⁄6=10⁄3

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