Pre-Algebra : Operations and Properties

Study concepts, example questions & explanations for Pre-Algebra

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Example Questions

Example Question #3 : Addition And Subtraction

Simplify:

Possible Answers:

Correct answer:

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

Possible Answers:

Correct answer:

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 #5 : Addition And Subtraction

Simplify:

Possible Answers:

Correct answer:

Explanation:

Explanation:

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

Example Question #4 : Addition And Subtraction

Menu

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:

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 #5 : Addition And Subtraction

Menu

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:

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 #6 : Addition And Subtraction

Menu

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:

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 #4 : Addition And Subtraction

Solve  if 

.

Possible Answers:

Correct answer:

Explanation:

Plug the given variables into the equation: 

Example Question #7 : 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 #131 : Operations

Perform the indicated mathematical operations: 

Possible Answers:

Correct answer:

Explanation:

In this problem we have two different types of terms. Those with x and without it. These two cannot be combined, but the fractions can. First we find a common denominator by multiplying one fraction by a number over itself that gives common denominators.

Now subtract the fractions:

Since the 5 term does not have an x we cannot combine the two.

Example Question #12 : Addition And Subtraction

Add:  

Possible Answers:

Correct answer:

Explanation:

Add the ones digit.

This is the ones digit of the final answer.

Add the tens digit.

The ones digit is the tens digit of the final answer.

Since there is a tens digit in this number, carry over the tens digit to the next calculation.

Add the hundreds digit with the carry over.

This number will represent the thousands and hundreds digit.

Combine the numbers.

The answer is:  

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