What Is Substitution?
Substitution: Replacing a variable (letter) in an algebraic expression with a specific numerical value and then calculating the result.
In science and mathematics, we use letters like , , , and to represent unknown or changing values. Substitution is the process of swapping those letters for actual numbers so we can work out a final answer.
Think of a variable like a parking space , it holds a spot for a car (a number) that hasn't arrived yet. When the car pulls in, you can see exactly what's there.
Evaluate when
- Write the expression:
- Replace with :
- Multiply first:
- Add:
When you substitute a number into an expression, it is good practice to put the number inside brackets. This helps avoid sign errors, especially with negative numbers.
Substitution with Negative Numbers
Substitution gets a little trickier when the value you're plugging in is negative. The brackets become your best friend here!
Remember the sign rules for multiplication:
- Positive × Positive = Positive , e.g.
- Positive × Negative = Negative , e.g.
- Negative × Negative = Positive , e.g.
Evaluate when
- Write the expression:
- Substitute :
- Work out the power first:
- Now multiply:
- Subtracting a negative means adding:
A very common mistake: is not the same as .
Always keep the negative sign inside the brackets when it belongs to the variable.
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