# Basic Algebra/Introduction to Basic Algebra Ideas/Variables and Expressions

Variable
Term
Operation
Expression
Evaluate
Substitute

## Lesson

A variable is a letter or symbol that takes place of a number in Algebra. Common symbols used are $a$, $x$, $y$, $\theta$ and $\lambda$. The letters x and y are commonly used, but remember that any other symbols would work just as well.

Variables are used in algebra as placeholders for unknown numbers. If you see "3 + x", don't panic! All this means is that we are adding a number who's value we don't yet know.

Some examples of variables in use:

• $3x$ -- three times of $x$.
• $5 - y$ -- five minus $y$
• $2 \div s$ or $\frac {2}{s}$-- 2 divided by $s$

A term is a number or a variable or a cluster of numbers and variables multiplied and or divided separated by addition and subtraction.

Examples of terms:

• $3 + 5$ The terms are 3 and 5.
• $\frac {6}{x}$ The term is $6/x$, 6 over $x$ is one term, because the operation is division.
• $6x + 5$ The terms are 6$x$ and 5, 6$x$ and 5 are separate terms because they are separated by a addition or subtraction.

An operation is a thing you do to numbers, like add, subtract, multiply, or divide. You use signs like +, , *, or / for operations.

An expression is two or more terms, with operations between all terms.

Examples of expressions:

• $3 \div 6$
• $8 \times x$
• $x \times 6 + y$
• $a \times b \times c \times d$

To evaluate an expression, you do the operations to the terms of an expression.

Examples of evaluating expressions:

• $3 + 4$ evaluates to 7.
• $18 \div 3$ evaluates to 6.
• $4 \times 5 - 3$ evaluates to 17.

To evaluate an expression with variables, you substitute (put a thing in the place of an other thing) numbers for the variables.

Examples of substituting: (Substitute 3 for x in these examples.)

• $x + 4$ is $3 + 4$.
• $18 \div x$ is $18 \div 3$.
• $4 \times 5 - x$ is $4 \times 5 - 3$.

## Example Problems

Evaluate $5 \times x$ when $x$ is 2.

Substitute 2 for $x$ to get $5 \times 2$.

Evaluate $5 \times 2$ to get the answer 10.

Evaluate $\frac{x}{3} + y$ when $x$ is 9 and $y$ is 4.

Substitute 9 for $x$ and substitute 4 for $y$ is to get $\frac{9}{3} + 4$.

Evaluate $\frac{9}{3} + 4$ to get the answer 7.

## Practice Problems

Evaluate each expression if $a$ = 1, $b$ = 2, $c$ = 3, and $d$ = 5. remember order of operations

1. $5 \times b=$
2. $9 \times c=$
3. $c-2=$
4. $d-5=$
5. $\frac{b}{2}=$
6. $\frac{36}{c}=$
7. $b \times c + 2=$
8. $b \times c \times d - 5=$

Evaluate each expression if $x$ = 4, $y$ = 2, and $z$ = 3.

1. $x+y=$
2. $2z=$
3. $xz=$
4. $x+y+z=$
5. $xy+z=$
6. $yz-x=$
7. $\frac{6}{y}+z=$
8. $\frac{2x}{2+y}=$

More harder questions:

Evaluate each expression if $x$ = 5, $y$ = 8, and $z$ = 9.

1. $(2+x) \times y=$
2. $\frac {3y-9}{5}=$
3. $\frac {27}{x+4} - (y-5)=$
4. $\frac {z+12}{2x-3} + y=$
5. $(\frac {6x}{2+y} - z)+(x- \frac{z}{3})=$
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