Mathematics » The Language of Algebra » Use the Language of Algebra

# Summary and Key Concepts

## Key Concepts

OperationNotationSay:The result is…
Addition$$a+b$$$$a\phantom{\rule{0.2em}{0ex}}\text{plus}\phantom{\rule{0.2em}{0ex}}b$$the sum of $$a$$ and $$b$$
Multiplication$$a·b,\left(a\right)\left(b\right),\left(a\right)b,a\left(b\right)$$$$a\phantom{\rule{0.2em}{0ex}}\text{times}\phantom{\rule{0.2em}{0ex}}b$$The product of $$a$$ and $$b$$
Subtraction$$a-b$$$$a\phantom{\rule{0.2em}{0ex}}\text{minus}\phantom{\rule{0.2em}{0ex}}b$$the difference of $$a$$ and $$b$$
Division$$a÷b,a/b,\phantom{\rule{0.2em}{0ex}}\frac{a}{b},b\overline{)a}$$$$a$$ divided by $$b$$The quotient of $$a$$ and $$b$$
• Equality Symbol
• $$a=b$$ is read as $$a$$ is equal to $$b$$
• The symbol $$=$$ is called the equal sign.
• Inequality
• $$a<b$$ is read $$a$$ is less than $$b$$
• $$a$$ is to the left of $$b$$ on the number line

• $$a>b$$ is read $$a$$ is greater than $$b$$
• $$a$$ is to the right of $$b$$ on the number line

Algebraic NotationSay
$$a=b$$$$a$$ is equal to $$b$$
$$a\ne b$$$$a$$ is not equal to $$b$$
$$a<b$$$$a$$ is less than $$b$$
$$a>b$$$$a$$ is greater than $$b$$
$$a\le b$$$$a$$ is less than or equal to $$b$$
$$a\ge b$$$$a$$ is greater than or equal to $$b$$
• Exponential Notation
• For any expression $${a}^{n}$$ is a factor multiplied by itself $$n$$ times, if $$n$$ is a positive integer.
• $${a}^{n}$$ means multiply $$n$$ factors of $$a$$

• The expression of $${a}^{n}$$ is read $$a$$ to the $$n\text{th}$$ power.

Order of Operations When simplifying mathematical expressions perform the operations in the following order:

• Parentheses and other Grouping Symbols: Simplify all expressions inside the parentheses or other grouping symbols, working on the innermost parentheses first.
• Exponents: Simplify all expressions with exponents.
• Multiplication and Division: Perform all multiplication and division in order from left to right. These operations have equal priority.
• Addition and Subtraction: Perform all addition and subtraction in order from left to right. These operations have equal priority.

## Glossary

### expressions

An expression is a number, a variable, or a combination of numbers and variables and operation symbols.

### equation

An equation is made up of two expressions connected by an equal sign.

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