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Course information:
This course would be strictly limited to junior secondary school level or people familiar with numerical digit numbers operation i.e basic operation such as addition, subtraction, multiplication using 0,1,2,3,4,5,6,7,8 and 9. You should also keep in mind that this course would only be a revision to those familiar with it or as a reminder or probably introduction to a new way of understanding them better.
👉For those that don't even know how to handle digits, you can please stay with us, soon the school is going to be starting adult education soon then you might as well join them
Course Requirements:
- You must be able to understand English language to some level
- You must be familiar to basic mathematics operations using digit
- A notebook and a pen
- Time and attention
👉It must also be noted that for you to be able to take this course you must be an English literate to some level
Course lecture
+implies plus, addition or sum
-implies subtraction or difference
×implies multiplication
/implies division
Sign Convention:
-×- = + minus times minus equals to plus
+×- = - plus times minus equals to minus
-×+ = - minus times plus equals to plus
+×+ = + plus times plus equals to plus
For example;
-5 × -2 = 10
the minus from 5 and minus from 2 multiplies each other to give plus(+), while the 5 and 2 multiply each other to form 10. Therefore the final answer is +10 which can also be written as 10 because positive sign(+) can be kept invisible beside a digit.
6 × -3 = -18
NB: any number having no sign beside it is actually having an invisible positive(+) sign.
As in the case of 6. You can therefore also make the positive sign visible to your desire. Therefore 6 in the above can also be written as +6.
From the equation above + × - will give minus(-) according to conventional sign. Also 6 × 3 will give 18. That is how -18 is gotten.
Bracket expansion with conventional sign
When expanding brackets signs play vital role. Signs are one of the major factors of operation in maths, when wrongly applied or used, will make an entire solving or calculation wrong. They are very important in mathematics. Whenever you are expanding a bracket the sign must first be taking into consideration.
For example;
-2(3) = -6
As said earlier 3 can be also written as +3. Bracket is a common symbol in maths which can be simplified to its lowest term meaning multiplication. Therefore minus(-) from2 and plus(+) from 6 will multiply to give minus(-). Also 2 times 3 will give 6, and that was how -6 is gotten.
7(-5) = -35
Now you should understand 7 is the same as +7. Plus(+) from 7 times minus(-) from 5 will give minus(-). While 7 times 5 will give 35. That's also how -35 is gotten.
-5(-4) = 20
minus(-) sign from 5 times minus(-) sign from 4 will give positive(+) sign. Also, 5 times 4 give us 20. Our answer should have been +20 but don't forget positive(+) sign can be kept invisible that is why +20 can also be written as 20.
👇Note this
A digit only owns the sign before it as it after it. For example, in -3+5, 3 owns the minus(-) sign before it, while 5 owns the positive(+) sign before it. Please also take note that the positive sign beside 5 cannot be kept invisible, as this will change the context of the question. If the positive(+) sign from 5 is hidden, then the question would become -35 which is totally wrong. Positive sign can be kept hidden under the following conditions;
- If the digit or variable carrying it is starting a question e.g
+5-3+6-8
Since 5 is starting the question, the positive sign before it can be hid. But, it must be noted that the positive(+) sign before 6 cannot be hidden. The above can also be written as
5-3+6-8 - If a bracket begins with a positive(+) sign the sign can also be hidden e.g in 2-5(+3-4+6), the +3 can also be written as 3 because the positive sign begins the bracket. It must be noted that the +6 cannot be hidden because it did not begin the bracket.
Problems with digit with sign having power
There is difference between -4² and (-4)².
-4²= -4×4
= -16
From the above it means 2 owns the power 3 only.
(-4)²= -4×-4
= 16
From the above it is clearly seen that both 4 and the minus sign are sharing the power 2, because they are both in the bracket. Minus(-) × minus(-) gave plus(+) and that is how +16 or 16 is gotten.
Multiplication and multiple
3² and 3×2 are two entirely different things in mathematics. 3² means self multiple of 3 twice e.g
3¹= 3
3²= 3×3
3³= 3×3×3 and so on
3×2 means self addition of 3 twice or self addition of 2 trice e.g
3×2= 3+3
=6
3×2= 2+2+2
= 6
Also, 4³ and 4×3
4³= 4×4×4
= 64
4×3= 4+4+4
= 12
4×3= 3+3+3+3
= 12
Self practice
Simplify the followings
- -5-2+3
- 4-(-3)
- -10 × 3
- -3²+(3)²
- 6 - (+5 - 3)
We hope you will understand them perfectly as all were typed by phone due to unavailability of computer system at present. Necessary corrections would be made towards the next lesson.
👉Important Notification
The above is just a little touch of mathematics introduction. The part 2 is going to be a video lecture so it could be analysed to a well understandable form. This is to keep us busy for today as the main lecture on mathematics introduction will be posted soon. We eat to make sure we correct or necessary errors before we go into the heart of mathematics.
Help us share to your friends as a lot of important lectures and classes are coming soon on @s-e-c, and we would want them to be part of this school.
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