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On this site you can practice at your own pace and at your own level. But beware: this does require responsibility! Make sure you practice enough, that you are sure that you have mastered the material and above all that you notify your teacher when you run into something.
If you need help with the material or planning, go to your teacher. Remember to always ask questions!
And always read the theory in your textbook!
You can work through this site independently (or when your teacher tells you to). It is important that you watch the video’s, read the extra theory carefully and practice well. Make the exercises from your book! You can find out which exercises you can complete here. Mathematics is something that you learn through practice and repetition!
On the left you can see the sidebar. The items in the sidebar are:
- Planning: before you start, Look at the planner. Planning is important, without a plan you might end up not being able to finish all your work. You can read all about planning right here. The learning objectives per paragraph are also described here. After working through a paragraph, check whether you meet these learning objectives.
- Prior knowledge: Here you can review what you need to know before starting this chapter.
- Paragraphs: these sections are divided into:
- Theory: often contains explanatory videos.
- Extra theory: here the theory is explained again in text and examples. Make sure you read this!
- Mock exam: This is a practice test. There is only 1 version so don't make it too early!
Make sure you work through all the paragraphs and get enough practice
This site was made for tto 1 based on getal & ruimte
Learning objectives
Simplifying 8.1
Addition with letters
When calculating with letters it’s important to know what “like terms” are.
Like terms are terms that have the same letters (and those letters have the same powers)
E.g. 3a and 8a and 333a are like terms. But 12a and 4ab and 9c and 12a2 are not like terms.
When adding with letters you can only add like terms. In equations with letters we usually try and simplify the equation as must as possible.
Calculation with letters is not so different than calculating with numbers. See here:
4+4+4 = 3*4
a+a+a = 3*a (but we don’t write the multiplication sign between the number and the letters) so
a+a+a = 3a
Following this:
3*4 + 3*4 + 4 = 4+4+4 + 4+4+4 + 4 =7*4
3a + 3a + a = a+a+a + a+a+a + a = 7a
And that also means:
3*4 + 3*4 + 4 + 6 = 4+4+4 + 4+4+4 + 4 + 6 = 7*4 + 6 (we can’t write the 6 with the 4’s)
3a + 3a + a + v = a+a+a + a+a+a + a + v = 7a + v (we can’t write the v with de a’s)
E.g.
Simplify 6p + 7c +c2 + 33p
Solution:
6p + 7c + c2 + 33p =
39p + 7c + c2
We can’t simplify it any further. Some students find this difficult because you don’t get a real answer in the form of a number. But without more information this is as far as you can get.
These rules also apply to substraction with letters.
These are the first steps in algebra.
Multiplications with letters
When calculating with letters it’s important to know what “like terms” are.
Like terms are terms that have the same letters (and those letters have the same powers)
E.g. 3a and 8a and 333a are like terms. But 12a and 4ab and 9c and 12a2 are not like terms.
When multiplying with letters you can multiply like terms and not like terms. When multiplying it doesn’t matter if the terms that are multiplied are the same.
When we write down the product of the multiplication (with letters) we first write down the number of the product. Then the letters in alphabetical order. We don’t have to write down the multiplication sign between the number and the different letters.
Calculation with letters is not so different than calculating with numbers. See here:
7*6*3 = 7*6*3
b*q*p = b*p*q (but we don’t write the multiplication sign between the number and the letters) so
b*q*p = bpq
that means:
3*5 * 2*3 * 6 = the same as 6*5*3*6
3*d * 2*n * p = 6*d*n*p
6*d*n*p = 6dnp
E.g.
Simplify \(6p*2a*3g=
\)
Solution:
\(6p*2a*3g=
\)
\(12ap*3g= \)
\(36agp\)
We can’t simplify it any further. Some students find this difficult because you don’t get a real answer in the form of a number. But without more information this is as far as you can get.
Substracting, adding and multiplication with letters
When calculating with letters it’s important to know what “like terms” are.
Like terms are terms that have the same letters (and those letters have the same powers)
E.g. 3a and 8a and 333a are like terms. But 12a and 4ab and 9c and 12a2 are not like terms.
The rules of calculating with letters tell us we can only add like terms and we can multiply all terms. But as with all calculations we make, we should always remember the order of operations!
So, when we have an equation where we both multiply and add terms we should first think about the order of operations and so in which order should we do our calculations. Then when we established the order we should check if we are dealing with addition, in which case we can only add like terms, or multiplication, in which case we can just do that multiplication.
E.g. \(2ab+3a*b+b\)
Solution:
So first we look at the order of operation. This means we first have to multiply. So
\(2ab+3a*4b+b=
\)
\(2ab+12ab+b= \)
\(14 ab+b= \)
And we can’t simplify it any further.
Multiplying out the brackets 8.2
Powers (and how to use them with your calculator) 8.3/8.4
Powers with letters 8.5
Learning objectives
