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shapes as variables

Alright. For this quiz I want you to find the value of a triangle minus a circle. Let me give you the value of the circle. A circle has a value of 5. So is the answer -5, 0, 1, 5, something else, or it's impossible to know? This quiz is a bit tricky so take your time and think about the value of each shape.

shapes as variables

Okay, I know the value of a circle is 5. So I can replace this circle with a 5. So triangle minus 5. But here's my problem. I don't know what the triangle is. I don't know the value of it. The triangle could represent any number, so it's impossible for you to know how to evaluate this. It's okay if you didn't get this one right. I just wanted to get you thinking.

use of variables

So let's talk about shapes as variables. Here are the two important points I wanted you to think about. First is that variables can be assigned a value and replaced, just like this circle. I could have had triangle - 5. I take this symbol the circle, or this variable, and replace it with its assigned value, a 5. The other important part is that some variables are unknown. And their value can vary, or change. This happened with my triangle. I could plug in any number for my triangle. For example, the triangle could be 10, so I'd have 10-5, which would equal 5. Or, the triangle could be -31, and I'd have -31-5, or -36. Or the triangle could be could take on any value. This is a powerful concept in algebra. The idea that a variable could take on any number. We'll return to this idea later. For now, just remember that variables can be unknown. And their value can change or vary. You're probably not used to seeing shapes when doing math. You're probably used to seeing x. Mathematicians have usually used x and it actually originates from the Arabic language. It means something unknown.

evaluate expressions

Okay, lets try and easier quiz this time with evaluating expressions, you'll need to remember how to perform operations with fractions. Here's some expressions, notice I have variables in the expressions. Here are the variables and their assigned values. A smile is equal to 3/4, a diamond is equal to 1/12. You can put your answers in these boxes here. Remember, if your answer's a fraction, enter it as a number, the fraction bar, and then a number. The first number's the numerator, the second one's the denominator. Good luck.

evaluate expressions

Alright, for the first one I'm going to put 3/4 where I see a smiley face. Then I have addition, and then I add 1/12 for the diamond. When adding fractions I need to get a common denominator. So I'm going to multiply this first one by 3 / 3. So I'll get 9/12 + 1/12. 9/12 + 1/12 is 10/12. I can reduce this fraction by dividing by 2. And I get 5/6. For this next one, I'm going to replace this smiley face with diamond is 1/12. Again, I need to convert to a common denominator. Well, I know 3/4 is really 9/12 from the problem before. So I've 9/12 - 1/12. And when I subtract 9/12 - 1/12 = 8/12 and the equivalent fraction for 8/12 is 2/3. I divided 8 by 4 and 12 by 4 and I got 2/3. Here I replace the smiley face with 3/4, I add multiplication, and then the diamond is numerator and in the denominator. I divide get 4. When I multiply my fractions across, 1 1 is 1, 4 4 is 16. And for this last one I have 3/4 / 1/12 Remember, dividing by a number is the same thing as multiplying by its reciporical. So I have of 4, since it appears in the numerator and in the denominator. 12 / 4 is 3. And 4 / 4 is 1. 3 3 is 9. 1 1 is 1. So I have 9 / 1 or 9. Nice work on that quiz.

the importance of parentheses

When I value an expressions, it's important that we use parenthesis. I didn't use parenthesis on that last quiz because I only had two variables and one operation between them. But we should always use parenthesis when replacing variables, here's why. Here's an expression of triangles and circles. One thing that we want to be about is what's the operation between symbols and numbers. Well, we assume that there's multiplication between variables or symbols and numbers. We don't often show it in algebra, but we always want to make sure that we include that there. We'll see other examples of this later throughout the course. I'm going to assign the values of the triangles to be -1 and I'm going to assign the values of the circles to be 3. We want to use parentheses when we replace variables because of negative signs. Here's what it would look like. I would have 3 -1 because a triangle is -1 then 3 because a circle is 3 + 4 -1 again for the triangle. And its squared and then times 3 for the circle and on the end I would have minus -1^3. Here the circle is really an exponent so I have 3 -1 3 which is -9. I know -1^2 is -1 -1. -1 -1 is just positive 1. So this number becomes positive 1. So I have -9 then + and then I have 4 1 3 which is 12. Now on this end part here, I have to do -1^3 first. I know powers come first. I've rewritten the statement over here so now -1^3 is really -1 -1 -1. I know three -1's make up -1, the first two would be +1 then I'd make it negative. So I've -9 + 12. Subtracting a negative is really adding a positive. -9 + 12 is 3 + 1 is 4. When I plug in the value of -1 for my triangles and when I plug in the value of 3 for the circles, I get an answer 4.

practice 1

Alright, let's try some practice. What would the value of this expression be if a=-2, b=-1, and c=5? Here, c is an exponent. You can put your answer in this box here.

practice 2

Here's another problem with evaluating expressions. Notice that the y is an exponent here and then you'd have multiplication between the three the x and the y^2 and the z. X is going to be equal to negative two, y is going to be equal to two, and z is going to be equal to negative three. Alright. Good luck with this problem and you can put your answer here.