Remember, to follow these three steps:
1. Multiply the numbers together.
2. Multiply the variables (letters) together.
3. Multiply the signs together.
Sample Problem:
5(2 – 3)
5 squished up against the parenthesis means multiply 5 by everything in the parenthesis.
so multiply 5 x 2 (the first number inside the parenthesis) and then do 5 x -3 (the second thing inside the parenthesis)
Follow the steps.
1. Multiply the numbers. 5 x 2 = 10
2. Multiply the variables/letters. There are none, so skip this step.
3. Multiply the signs. The 5 has an invisible positive sign. The 2 has an invisible positive sign, so multiply + • + = +
So 5 x 2 = +10
Write +10 down as the first part of your answer.
Next, multiply 5 x -3
Follow the steps:
1. Multiply the numbers 5 x 3 = 15
2. Multiply the variables. There are none, so skip this step.
3. Multiply the signs. 5 has an invisible positive sign. 3 has a negative sign. So multiply + • – = –
So 5 x -3 = -15
Write this down as the next part of your answer.
The answer now looks like this: 10 -15.
Add the +10 and the -15 together.
10 + (- 15) =
Think of “poster number 2″. Add two integers with different signs.
Steps to do this. Take the numbers only (not the signs) and subtract (find the difference of) the numbers.
15-10 = 5
Now look at the two numbers 10 and 15. Choose the biggest number. 15. It wins. Put the sign in front of the biggest number( 15 has a negative sign in front of it), in front of your final answer, 5.
So, 10 + (- 15) = -5
Another Sample Problem:
7(-c + 4)
7 squished up against the parenthesis means multiply 7 by everything in the parenthesis.
so multiply 7 x -c (the first thing inside the parenthesis) and then do 7 x +4 (the second thing inside the parenthesis)
Follow the steps.
1. Multiply the numbers. 7 x invisible 1 in front of the c = 7
2. Multiply the variables/letters. c, so squish c next to the 7 = 7c.
3. Multiply the signs. The 7 has an invisible positive sign. The c has a negative sign,
so multiply + • – = -
So 7 x -c = -7c
Write -7c down as the first part of your answer.
Next, multiply 7 x + 4
Follow the steps:
1. Multiply the numbers 7 x 4 = 28
2. Multiply the variables. There are none, so skip this step.
3. Multiply the signs. 7 has an invisible positive sign. 4 has a visible positive sign. So multiply + • + = +
So 7 x + 4 = + 28
Write this down as the next part of your answer.
The answer now looks like this: – 7c + 28.
This means -7 • mystery number c (must multiply this first) AND THEN add +28.
I do not know what the variable c is yet. It’s a mystery. So I can’t multiply -7 • c until I do know.
c could turn out to be the number 8; then I would multiply -7 • 8= -56. Then I could add 28 to -56 and get my final answer which would be -28.
But c could turn out to be the number -11; then I would multiply -7 • -11 = +77. Then I could add 28 to +77 and get my final answer which would be 105.
As it is, I have no idea what number c will turn out to be. So I just have to be patient and let it be for now, until I do find out.
This means, for now, I have done as much as I can do. And my final answer is -7c + 28
My final answer IS DEFINITELY NOT 21c. I can not add the -7 and the 28 together; because that disobeys the order of operations. I have to be able to multiply -7 and c together first.
Here’s a really good YouTube video that should help you understand distributive property.
