We talked fractional equations and word problems with fractional equations.

Any equation involving any fraction, either x (unknown)  in enumerator or denominator, is called a fractional equation, or also called rational equation.

We studied fractional equations with x in enumerators, and we studied equations with x in denominators. When x is in denominators, one important step is to check the answer to make sure that it does not make any denominator zero and throw away any answer that does.

For word problems, it is important to come up with the right equation with the given information.

Homework is as follows:

Page 9: 49 a c d e g i k m n o, 52 a, 53, 54, 55, 56

We covered the following material today:

• Scientific Notation or Standard Form
• Special Algebraic Rules for Calculations
• Expanding Products

To represent a number, scientists use the form of A * 10^n where 1 <= A < 10, n is an integer. This is called scientific notation or standard form. The key point is, A must be smalled than 10 and not smaller than 1.

We talked about how to convert from a decimal form to the standard form, and vice versa. We talked about how to perform addition, subtraction, multiplication, and division with two numbers in standard form.

For special algebraic rules, we established the following three rules:

• (a + b)^2 = a^2 + 2ab + b^2
• (a – b)^2 = a^2 -2ab + b^2
• (a^2 – b^2) = (a + b)*(a – b)

For expanding products, the key point we went over is the distributive law, using which one should be able to expanding products in any form.

For homework, it is on the Workbook:

• Page 4: 11b, 11d, 11f, 12d, 12f, 12h, 15a, 15b, 15c, 15d
• Page 5: 18a, 18b
• Page 6: 1b, 1d, 2c, 2d, 3d, 3f
• Page 7: 4a, 4c, 4e, 5c, 5e, 5f

We covered the classroom first. With 25 students in the class, we need everyone’s cooperation to have a good learning environment for everyone.

We covered the material about Exponents. The following are the important rules and definitions to memorize:

• a^m * a^n = a^(m+n)
• a^m / a^n  = a^(m-n)
• (a^n)^m = a^(nm)
• a^m * b^m = (ab)^m
• a^m / b^m = (a/b)^m
• a^0 = 1, a<> 0 (a to the power of zero is 1, as long as a is not zero)
• a^(-n) = 1 / a^n, a <> 0

With the above rules and defintions, we can simply expressions. We did several in-class exercises and the homework will be mostly about simplying expressions.

We also talked about exponents with variables, whose operation is no different, except that we use variables, like x, y, a, b, c, etc., to represent the things in the operation. Same rules and definitions apply.

For homework, it is on the workbook:

• Page 1, 1a, 1c, 1e, 1g, 2l, 2n, 2p, 2r
• Page 2, 4a, 4b, 4c, 6a, 6b, 7a, 7b, 7c
• Page 3, 8g, 8i, 9a, 9c