Substitution


 * TASK: Describe substitution in your own words. Refer back to your flashcards if you need a reminder.**

When we substitute one thing for another, we are replacing one thing with something else that has the same value. For example, many people substitute applesauce for oil or butter if they want to reduce the amount of fat in their cakes when baking because it has the same sweetness and texture (when cooked) as oil or butter, but less fat. They can substitute them because they have the same taste and function, they're just different products.

The same thing goes for math. Most often we see substitution as substituting numbers in for variables. We can substitute any number in for a variable as long as the number and the variable are equal. In order to do this, we simply replace the variable with the number that it's equal to.


 * Example:** Simplify: 3x + 4 when x = -- 2

Since x = --2, we can replace the x with --2 in the expression. We get: 3(-2) + 4 Which simplifies to: -- 6 + 4 = -- 2

Sometimes we will be asked to substitute numbers in for more than one variable.

Evaluate when a = 7 and b = 4.
 * Example:**

In order to simplify this expression, wherever we see an "a," we need to replace it with a 7 and wherever we see a "b" we need to replace it with a 4. We get:



The 7 is in parentheses to indicate multiplication because the 3 and the "a" were being multiplied in the original problem.

We can then simplify the above expression using order of operations (as we learned in the previous lesson) as follows:



//**Reminder:** Be careful with the signs when you're asked to substitute negative numbers!//

**TASK: Evaluate each expression below for c = -- 2 and d = 5**