# Pre-Algebra : Addition and Subtraction

## Example Questions

### Example Question #1 : Addition And Subtraction

Simplify the expression.

Explanation:

Re-write the expression to group like terms together.

Simplify.

### Example Question #1 : Addition And Subtraction

What is   simplified?

Explanation:

To simplify a problem like the example above we must combine the like-termed variables.

Like terms are the terms that share the same variable(s) to the same power. In this example the like term is .

To combine like terms the variable  stays the same and you add the numbers in front.

Perform the necessary addition, , to get .

We have the simplified version of the equation, .

### Example Question #3 : Addition And Subtraction

Simplify:

Explanation:

Group like terms, and then add or subtract their values from one another.

Note: subtracting a negative number is the same as adding a positive number.

Add or subtract like terms from left to right.

### Example Question #4 : Addition And Subtraction

Explanation:

According to the rules in Order of Operations, we work through this problem by solving from left to right since there is only addition and subtraction.

Step 1: Subtract 6 from 4:

Step 2:  Everytime you add the same number with an opposite sign, the answer will be 0:

Step 3: Subtract 4 from 0:

Step 4: When you subtract a positive number from a negative number, you are actually adding two negative numbers. One way to remember this is to remember the phrase "leave, change, change." You leave the sign of the first number, then you change the operation from subtraction to addition, then you change the sign of the second number from positive to negative:

### Example Question #1 : Addition And Subtraction

Simplify:

Explanation:

Explanation:

Combine like terms: . Remember you can only combine terms that have the same variables, for example  and , but not  and

### Example Question #1 : Addition And Subtraction

Above is the menu at a coffee shop.

Dale has a coupon that entitles him to a free butter croissant with the purchase of one large drink of any kind. The coupon says "limit one per coupon".

He decides to purchase a small espresso, a small iced coffee, and two butter croissants. Disregarding tax, how much will he pay for them?

Explanation:

The coupon only entitles him to one free croissant with a large drink. Since Phil only orders small drinks, he will not use the coupon, and he will pay for the drinks and both croissants. He will therefore pay:

### Example Question #7 : Addition And Subtraction

Above is the menu at a coffee shop.

Andy has a coupon which he can use to get either a free butter croissant with the purchase of a large drink or one dollar off a butter croissant with the purchase of a small drink. The coupon says "limit one per coupon".

Andy orders one large cappucino, one small cappucino, and two butter croissants. Disregarding tax, how much will he spend?

Explanation:

Andy will get one of the butter croissants for free, since he is also purchasing a large drink. He will pay for one large cappucino, one small cappucino, and one butter croissant; add their prices:

### Example Question #8 : Addition And Subtraction

Above is the menu at a coffee shop.

Julia has a coupon which she can use to get either one dollar off the price of a butter croissant with the purchase of a large drink or fifty cents off the price of a butter croissant with the purchase of a small drink. The coupon says "limit 4".

Julia orders five small cappucinos and five butter croissants. Disregarding tax, how much will she spend?

Explanation:

Julia will be able to save on four of the five butter croissants, since the coupon allows discounts on up to four; since she is only buying small drinks, the four croissants will be fifty cents off each. Therefore, we can add the regular prices of the drinks:

The five small cappucinos:

The five butter croissants:

The total before discount:

Then subtract a total discount of :

### Example Question #2 : Addition And Subtraction

Solve  if

.

Explanation:

Plug the given variables into the equation:

Simplify: