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 \(b\ne0\).
\[ \frac{a}{b} \ and\ b\ne0 \\ \frac{Numerator}{Denominator} \]
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 \(ax + b = c\)
- 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
- \(5y − 8 = 3y + 12\)
- \(1.2x + 4.3 = 2.1 − x\)