Let's find the total weight on the scale. The weight of each circle is C.
Since there are three circles, their combined weight is 3 * C or 3 C. We also have a standard weight of three. The total weight is the sum 3 C + 3.
Here's another one. This time we have two different shapes with unknown weights. The weight of a circle is C and the weight of a square is S. There are two circles, so their weight is 2 C. And there are three squares, so their weight is 3S. There's also a standard weight of 15. The total weight is the sum of all these parts 2 C + 3 S + 15.
Even without knowing the exact numerical weight of each shape, we can represent the total. This combination of variables like C and S and constant numbers like 15 joined by arithmetic operations is called an expression. It's how we describe a quantity using algebra. Now let's try building an expression from scratch. This scale has three identical triangles and each one has a weight of t. To find the total weight, we add the weights of all three triangles together.
t + t + t. A simpler way to write that is 3 * t or 3t.
Let's build another one. We have one circle with weight c and two triangles each with weight t. The total weight of the two triangles is 2t. To get the total weight on the scale, we add the weight of the circle to the weight of the triangles. The expression is c + 2t.
On this scale, we have a few different items. There's one triangle with weight t. There are also two squares, each with weight s. So, their combined weight is 2 s. Finally, there's a standard weight of 4. To get the total weight, we add all the parts. That gives us t + 2 s + 4.
We've just practiced how to build algebraic expressions using both known values like the standard weights and unknown values represented by variables.
Being able to translate a situation like this into an expression is the first step toward solving more complex equations and problems.
