Pre-Algebra - Negative Numbers

$\small -3.5+-2.75$ is equal to which of the following?

Explanation

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

$\small a+-b = a-b$

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

$\small -3.5+-2.75$

$\small =-3.5-2.75$

$\small =-6.25$

The answer is -6.25.

Solve:

$\frac{-2(2+2)}{-2(-2-2)}$

$\frac{1}{3}$

$-\frac{1}{3}$

Explanation

When solving this problem remember our orders of operation, or PEMDAS.

PEMDAS stands for parentheses, exponents, multiplication/division, and addition/subtraction. When you have a problem with several different operations, you need to solve the problem in this order and you work from left to right for multiplication/division and addition/subtraction.

Evaluate the quantities inside the parentheses first.

$\frac{-2(2+2)}{-2(-2-2)}$

$\frac{-2(4)}{-2(-4)}$

$\frac{-8}{8}=-1$

Explanation

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

Explanation

Since is greater than and is positive, our answer is positive. We treat as a normal subtraction.

is the answer.

Explanation

Two negative signs become a plus sign. Since is greater than and is positive, our answer is positive. We treat as a normal subtraction.

Answer is

Solve:

Explanation

When dealing with negative numbers, let's see which number is greater. is greater than and is positive so the answer is positive. We treat this as a subtraction problem. .

Solve:

$-3\times4$

Explanation

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.

$3\times4=12$

Since the answer is negative, the answer is .

Explanation

When we add a negative number, the sign turns negative. Since we are adding two negative numbers, we treat this as an addition problem and add a minus sign in the end. .

Explanation

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 .