Pre-Algebra: Chapter 6-2
Estimating Products and Quotients
As we did in class today, when we are dealing with fractions, it is easier to estimate, for example, 3 & 4/7 (3 and 4/7) if you think of whole numbers above the fraction and compare the fraction to 1/2. In our example, is 4/7 closer to 0, 1/2 or 1? The answer is 1/2 so our estimate for 3 & 4/7 would be 3 & 1/2. A COMPATIBLE number is rounded so it is easy to compute with them mentally.
We do the same for decimals by rounding them, so to estimate 67.45 / 7.6, we can think of 67.45 being close to 70 and 7.6 being close to 7. Our estimate would be about 70/7 or an answer of 10.
Algebra: Chapter 9-1
Sets, Intersections and Unions
We DIDN’T DO WELL ON THE CHAPTER 8 TEST, Mr. E is totally bummed ….
We can write sets using roster notation and set-builder notation. Roster notation for the set of numbers greater than 20 is written as: {21, 22, 23, 24, …}. We show at least 4 numbers in the pattern and IF the pattern continues, then we use ellipsis “…” (the 3 dots) to show that the pattern continues.
We can also use the ‘wordy’ set-builder notation by writing {x | x is a whole number and x > 20}. We say this as ” the set of all x such that x is a whole number and x is greater than 20″.
The intersection of 2 sets A and B is written A ∩ B. This means find all values of the sets A and B THAT ARE COMMON TO BOTH.
The union of 2 sets A and B is written A ∪ B. This means find all values THAT ARE IN A OR B OR BOTH. In other words, choose everything!
The empty set is defined as ∅, the zero with a slash through it and the ∈ symbol is defined as “is an element of”. The opposite symbol, the ∈ with a slash through it [it doesn’t come out on the webpage!], stands for “is not an element of”.