Addition and Subtraction - Pre-Algebra

Re-write the expression to group like terms together.

Simplify.

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, .

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:

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.

Plug the given variables into the equation:

Explanation:

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

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:

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:

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 :

When adding or subtracting fractions, you must find the common denominator. This is best done by finding the least common multiple of the denominators, in this case 5 and 3. What is the lowest number that is divisible by both 5 and 3? Often, the easiest solution is to multiply the denominators together. This works most often with single digit numbers. Anything larger and you will have to find the least common multiple another way.

The LCM of 5 and 3 is 15 (5 x 3). Now you know that both fractions must have 15 on the bottom. Now, to convert 4/5 to ?/15, you must recognize how many times 5 goes into 15 (3), and multiply the numerator by that number. Therefore:

Do the same with the other side.

Now that the denominators match, all that's left is to add the numerators together.

This solution is already an improper fraction (the numerator is larger than the denominator), therefore you may leave the fraction as is.

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.

Solve the inside of the parentheses. Then remove all the parentheses by distributing the negative signs.

The correct answer is .

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:

Solve term by term.

The correct answer is .

Add the ones digit.

The ones digit is the ones digit of the final answer. Since there is a one in the tens digit, this is the carry over for the next calculation.

Add the tens digit with the carryover.

Combine all the numbers. The answer is .

Subtract the ones digit. Borrow a one from the tens digit.

After borrowing a one from the , the tens digit of will be .

Subtract the tens digit.

The answer is:

Simplify the parentheses.

A positive and a negative sign will result in a negative sign.

When all numbers are negative that are being added, simply add the integers and then place the negative sign in front of the final answer.

Add the ones digits.

Add the tens digits.

Combine the two digits.

The answer is .

The ones digit cannot be subtracted as is. We cannot borrow a one from the tens digit. Borrow a one from the of both the tens and the hundreds digit of .

This is the ones digit of the final answer.

Because a one was borrowed, the tens digit of will be come a , and the hundreds digit will become zero. Subtract the tens digits.

The correct answer is . Adding 82 and 19 will give 101 as the answer.