Negative Numbers - Pre-Algebra

To make as small as possible, let be as small as possible , and subtract the largest value of possible :

The sum of two numbers of unlike sign is the difference of their absolute values, with the sign of the "dominant" number (the positive number here) affixed:

Subtract vertically by aligning the decimal points, making sure you append the 3.2 with a placeholder zero:

This is the correct choice.

The problem indicates that the result is units more negative than , which is .

This is a straightforward problem. Remember that when adding a negative number, you are actually subtracting:

Be sure to remember that the first number is also negative, meaning we are subtracting a number from a negative number:

The answer is -6.25.

Substitute 8 for in the expression and evaluate, paying attention to the order of operations:

Begin by isolating your variable.

Subtract from both sides:

, or

Next, subtract from both sides:

, or

Then, divide both sides by :

Recall that division of a negative by a negative gives you a positive, therefore:

or

To solve this problem, you need to get your variable isolated on one side of the equation:

Taking this step will elminate the on the side with :

Now divide by to solve for :

The important step here is to be able to add the negative numbers. When you add negative numbers, they create lower negative numbers (if you prefer to think about it another way, you can think of adding negative numbers as subtracting one of the negative numbers from the other).

To solve this equation, you need to isolate the variable on one side. We can accomplish this by dividing by on both sides:

Anytime you divide, if the signs are the same (i.e. two positive, or two negative), you'll get a positive result. If the signs are opposites (i.e. one positive, one negative) then you get a negative.

Both of the numbers here are negative, so we will have a positive result:

To solve, you need to isolate the variable. We first subtract then divide by :

When dividing, if the signs of the numbers are the same (i.e. both positive, or both negative), you yield a positive result. If the signs of the numbers are opposites (i.e. one of each), then you yield a negative result.

Therefore:

First, since we are multiplying a negative value with a positive value, we need to realize the product is going to be negative. Next, we can multiply the values.

Since the answer is negative, the answer is .

To determine the answer, it's best to compare the values without doing any math. Since is bigger than and the has the positive sign in front, the answer is positive. Also, with addition, you can rewrite the expression without altering the answer. So, instead we can write . The positive and negative value combined gives us a negative sign and now we have or .

When given multiple operations, remember PEMDAS. Division comes before subtraction. So we divide by first to get an answer of . Now we have an expression of . To determine the answer, it's best to compare the values without doing any math. Since is bigger than and the has the negative sign in front, the answer is negative. So, just subtract with to get . Since the answer should be negative, the final answer is .

When adding with negative values, the sign turns negative. So now we have . Since they have the same sign, we just treat it as an addition problem and add and then insert the negative sign in front. The answer is .

When subtracting with a negative sign, it turns into addition. Now we have . The answer is .

When two negative values are multiplied, the answer becomes positive. Then, we multiply normally. We should get or .

When dividing with two negative values, the answer becomes positive. Then we just divide by , which equals . The answer is or .

Remember PEMDAS. The parentheses comes first. When adding a negative value, the operation is subtraction. We now have . The answer in the parentheses is , but since there is a negative sign outside, we need to add that in so final answer becomes .

Remember PEMDAS. The parentheses comes first so let's work what's inside. When adding a negative sign, the operation becomes negative. So, we have . To determine the answer, it's best to compare the values without doing any math. Since is bigger than and the has the negative sign in front, the answer is negative. So, we subtract normally to get but the actual answer should be . Now, we hae . Two negatives make a positive so the final answer is .

When multiplying with multiple signs involved, count the number of positive and negative signs. There are negative values and positive values. Since there are more negatiive values, the answer should be negative. When we multiply out the expression, we get . But our answer should be negative because there were more negative values than positive vaules, so our answer is .