### All Pre-Algebra Resources

## Example Questions

### Example Question #122 : Operations And Properties

Simplify the expression.

**Possible Answers:**

**Correct answer:**

Re-write the expression to group like terms together.

Simplify.

### Example Question #121 : Operations And Properties

What is simplified?

**Possible Answers:**

**Correct answer:**

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 #1 : Addition And Subtraction

Simplify:

**Possible Answers:**

**Correct answer:**

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 #2 : Addition And Subtraction

**Possible Answers:**

**Correct answer:**

According to the rules in *Order of Operations, w*e 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:**

**Possible Answers:**

**Correct answer:**

**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?

**Possible Answers:**

**Correct answer:**

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 #1 : 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?

**Possible Answers:**

**Correct answer:**

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 #3 : 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?

**Possible Answers:**

**Correct answer:**

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 #1 : Addition And Subtraction

Solve if

.

**Possible Answers:**

**Correct answer:**

Plug the given variables into the equation:

### Example Question #1 : Addition And Subtraction

Simplify:

**Possible Answers:**

**Correct answer:**

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

Certified Tutor