Evaluate variable expressions involving rational numbers
key notes :
| Understanding Variable Expressions |
Definition:
- A variable expression is a mathematical phrase that includes numbers, variables (letters that represent numbers), and operations (addition, subtraction, multiplication, division).
Examples:
| Evaluating Variable Expressions |
Substitution:
- To evaluate a variable expression, substitute the values of the variables into the expression and perform the operations according to the order of operations (PEMDAS/BODMAS).
Order of Operations:
- Parentheses/Brackets: Solve expressions inside parentheses/brackets first.
- Exponents/Orders: Evaluate exponents or orders (powers and roots).
- Multiplication and Division: From left to right.
- Addition and Subtraction: From left to right.
| Steps for Evaluation |
Substitute Values:
- Replace each variable in the expression with its given value.
Simplify Inside Parentheses:
- If the expression contains parentheses, simplify the expression inside them first.
Apply Exponents:
- If the expression contains exponents, apply them next.
Perform Multiplication and Division:
- Perform all multiplication and division from left to right.
Perform Addition and Subtraction:
- Perform all addition and subtraction from left to right.
| Examples |
Simple Variable Expression:
Expression with Multiple Variables:
Expression with Parentheses:
Complex Expression:
| Practice Problems |
Simple Expressions:
Expressions with Multiple Variables:
Expressions with Parentheses:
Complex Expressions:
| Tips for Success |
Careful Substitution:
- Ensure that each variable is correctly substituted with its given value.
Follow Order of Operations:
- Adhere strictly to the order of operations to avoid mistakes.
Simplify Step-by-Step:
- Simplify the expression step-by-step to prevent errors.
Check Your Work:
- After evaluating the expression, double-check each step to ensure accuracy.
Evaluate the expression for t = -0.7.
Write your answer as a decimal or whole number.
-15t =_______
Plug in t = -0.7 and simplify.
| -15t | |
| -15(–0.7) | Plug in t = -0.7 |
| 10.5 | Multiply |
Evaluate the expression for b = 13 and c = 12. Simplify your answer.
b/b-c =
Evaluate.
b/b-c
=13/13 − 12 Plug-in b = 13 and c = 12
=13/1 Simplify the denominator
=13 Divide
Learn with an example
🎯 Evaluate the expression for x = 0.1 and y = 8.8.
Write your answer as a decimal or whole number.
xy =
Plug in x = 0.1 and y = 8.8, then simplify.
xy
0.1(8.8)
0.88
🎯 Evaluate the expression for y = -12 and z = –4.
Simplify your answer.
y/z =
Evaluate.
y/z
= -12/-4 Plug in y = -12 and z = -4
= 3 Divide
🎯 Evaluate the expression for n = -9.
Simplify your answer.
n/3 =
Evaluate.
n/3
= -9/3 Plug in n = -9
= -3 Divide
Let’s Practice!
