Review of Algebra

Fractions

A fraction is a numerical value that can be described as one value $a$ divided by another value $b$ such that $a$ and $b$ are both integer and $b \neq 0$ .

$\frac{a}{b} a n d b \neq 0 \frac{N u m e r a t o r}{D e n o m i n a t o r}$

The denominator indicate the number of parts being split. The numerator shows how many parts are counted. For instance, a fraction $\frac{5}{8}$ shows that the whole was split into 8 parts, and 5 parts are counted for.

A mixed number is a number that combined a whole number and a fraction. Foe example, $5 \frac{2}{3}$ .

A proper fraction is a number such that the numerator is less than the denominator. For example, $\frac{3}{7}$

An improper fraction is a number such that the numerator is greater than the denominator. For example, $\frac{9}{5}$

Decimals

A decimal is a fraction written in a special form. A decimal is a number that consists of a whole and a fractional part. Decimals are the numbers, which consist of two parts namely, a whole number part and a fractional part separated by a decimal point. The word “Decimal” really means “based on 10” (From Latin decima: a tenth part). Thus, a decimal is a number expressed using a system of counting based on the number ten: Three-fifths expressed as a decimal is 0.6.

$\frac{3}{5} = \frac{6}{10} = 0.6$

To change from a fraction to a decimal value, just simply make a long division the numerator value to the denominator value.

To change the decimal value to fraction, just moves the decimal points to the right to make it a whoe number and divide by a numerator 10 to the power of number of digits moves to the right. For example, $0.25 = \frac{25}{100} = \frac{1}{4}$ , after simplification.

Percents

Percentages are expressed as the number of parts in every 100 such that it is a fraction with denominator value of 100. In other words, a percentage is a number or ratio as a fraction of 100. It is normally written with a symbol “%”.

To change a fraction or decimal to a percent, simply multiply the number with 100%. For example, $0.235 \times 100 % = 23.5$

Linear Equation

A linear equation in one unknown is an equation in which the only exponent on the unknown is 1.
The general form of a basic linear equation is $a x + b = c$
Solving linear equations is an important and fundamental skill in algebra.
The goal is to write the equation in the form variable = constant.
The solution to an equation is the set of all values that check in the equation.

Examples

$5 y - 8 = 3 y + 12$

Answer
$\begin{aligned} 5 y - 3 y & = 12 + 8 \\ 2 y & = 20 \\ y & = \frac{20}{2} \\ y & = 10 \end{aligned}$

$1.2 x + 4.3 = 2.1 - x$

Answer
$\begin{aligned} 1.2 x + x & = 2.1 - 4.3 \\ 2.2 x & = - 2.2 \\ x & = \frac{- 2.2}{2.2} \\ x & = - 1 \end{aligned}$