Maths Private Lessons by Sir Emma

INTEGERS cont.....

So when you are being asked to simplify an expression you just consider these things and solve your expression. Example

1. 6-11
Ans: you read from your right and consider the positive and negative tips . The 6 is a positive 6 hence you have 6 mangoes and -11 is a negative number meaning you are owing 11 .
So if I have 6 mangoes and I owe 11 mangoes , what happens ? I pay 6 out of the 11 I owe because that’s what I HAVE , so finally I am still owing 5 mangoes . Therefore your answer is -5 because you are still owing .

2. Let’s look at another example
-6 + 8 - 5 - 3 + 4
Ans : Let’s look at the numbers you have , they are -6, +8, -5 , -3 , +4 . ( Don’t forget every negative number means you are owing or losing or paying and every positive number means you are having or gaining ).
Now let’s analyze , I am owing say 6 cedis (-6) , I gain 8 cedis (+8) , so I pay the 6 cedis (-6) I was owing right . Now I have 2 cedis ( +2 ) . Then I owe another 5 cedis (-5) so I pay with the 2 I have (+2) hence am owing 3 now (-3) then I go ahead to owe 3 (-3) again, it means now am owing a total 6 (-6) . Then I gain 4 (+4) . Remember you were owing 6 before gaining 4 so you will pay with 4 you are gaining. Finally you are still owing 2 . Therefore your answer is -2

Another type of question that confuses students are when 2 negatives are use either apart or together.

For example
1. 3- (-5)
2. -3 - 5
You just have to still stick to the tips . But one thing you to note is when two negatives meet like used in question 1 it becomes a plus (+) . So straightforward that question is simple 3 + 5 which is simply 8 .

But in question 2 , you just have remember that the sign in front of a number is for the number so the two numbers we have there are -3 and -5 .

Let’s analyze: -3 means you are owing 3 and -5 also means you are owing 5 , Hence in total you are owing 8 isn’t it . Therefore your final answer is -8 .

Answer these on your own.

Simply the following
1. 0- (-18)
2. -8 - (-13)
3. -4 + (-3) + 3
4. 39 - (-13)
5. -37 - 37

Life is a math equation. In order to gain the most, you have to know how to convert negatives into positives. –Anonymous

THANK YOU

Sir Emma.

INTEGERS
One problem I have noticed as a teacher of this subject is the difficulty people have when adding or subtracting integers . So today our lesson for the day is INTEGERS

Before we start the lesson I think it is right we know what integers are .

What are integers ?
Integers are simply positive and negative whole numbers .

Now let’s go straight to

ADDITION AND SUBTRACTION OF INTEGERS

I will try my best to explain this in my own words . No use of mathematical jargons whatsoever.

NOTE : In integers numbers without any sign ( +, -) are positive numbers and numbers that have the minus sign (-) before them are negative numbers. And numbers with the plus (+) sign before them are positive numbers.

2. Note that any sign in front of a number is for that number.. For example: if I write an expression like 3 - 5 , the two numbers I have are NOT 3 and 5 but rather 3 and -5 ..
Those are some of the petty mistakes we do , we have to get them right from the on set .

Now in my own words I will explain negative numbers to you as you assuming you are owing or losing or paying that value . So -5 is like you are owing 5 say mangoes , - 100 is like say you are owing 100 cedis or paying 100 cedis and will explain positive numbers as say you are gaining or having that value. So example 87 is like you having 87 goats , 158 is like you gaining 158 cedis .

Hope it’s clear . Read through once again if it wasn’t .

Good afternoon. We will have another session today . Hope we are staying safe and keeping to the measures ..

Let’s start

DIVISIBILITY BY 8
A number is divisible by 8 when the last 3 digits of the number is a multiple of 8. ( 008, 016,024,032,040,...) For example 33488, 12088, 23032, 11408 are all divisible by 8 exactly since their last 3 digits are multiples of 8.

DIVISIBILITY BY 9
A number is divisible by 9 when the sum of the digits of the number into a single digit is 9. For example 31212 is divisible by 9 exactly since the sum of the digits ( 3+1+2+1+2=9 )Let’s try a bigger number 845721 - ( 8+4+5+7+2+1 ) is 27 . So let’s sum the digits to a single digit ie 2+7 = 9 . Hence , 845721 is divisible by 9 exactly.

DIVISIBILITY BY 10
This is practically the simplest of all 😊. Any number that ends with zero (0) is divisible by 10 exactly. For example 2360, 56800, 5467230,27782940.1000040 etc .

We end today’s lessons here.. I hope you have learnt a thing or two .

Always remember

“The essence of math is not to make simple things complicated, but to make complicated things simple.”�Stan Gudder.

Another day, another opportunity to learn something new .

Let’s continue . Today we will look at divisibility by 8, 9, and 10.

Now let’s continue from where we ended yesterday.

Today we will be talking about Divisibility of 5,6,7.
Let’s start

DIVISIBILITY BY 5
A number is divisible by 5 when its last digit is either 0 or 5 . So any number that ends with 0 or 5 is divisible by 5 exactly. For example: 7635, 890020, 673225, etc

DIVISIBILITY BY 6
A number is divisible by 6 , when the number is divisible by both 2 and 3 ( refer to divisibility by 2 and 3 ) . So in simple understanding any even number that is divisible by 3 is divisible by 6 . For example 2736 is divisible by 6 exactly since its last digit is an even number (Div. by 2) and the sum of its digit ( 2+7+3+6 = 18) is a multiple of 3 (Div. by 3).

DIVISIBILITY BY 7
When you double the last digit of a given number and subtract it from the number formed by the rest of the digits and the result is a multiple of 7 ( ie 7,14,21,28,35,42 ... ) , then the given number is divisible by 7 exactly. (Repeat till you get a double digit number). For example: 1715 - Let’s double the last digit (5 x 2 = 10 ) then we subtract the results (10) from the number formed by the rest of the digits ie 171 - 10 = 161 . We repeat the steps again for 161 - ( 1 x 2 = 2) then ( 16-2 = 14 ) . Since 14 is a multiple of 7 , the given number 1715 is divisible by 7 exactly.
A bit confusing isn’t it ? Just relax and take it one after the other till it becomes simple 👌🏾

Bare in mind

“Mathematics is not all about numbers ,equations, computations and algorithms. It is about UNDERSTANDING”

William Paul Thurston

Good morning. Let’s continue our lessons on divisibility of numbers. But before we continue let’s have a recap of what we talked about yesterday.

In summary

1. Any number that has its last digit as 2,4,6,8,0 can be divided by 2 exactly.

2. Any number that has the sum of its digits to be a multiple of 3 is divisible by 3 .

3. Any number that has its last 2 digits as a multiple of 4 is divisible by 4.

Bonus fact

Any number divisible by 4 is divisible by 2 but not vice versa . And the reason is simple , 2 is a factor of 4 and not vice versa .

So let’s start with today’s lesson ..

DIVISIBILITY BY 2
Any number that has its last digit as an even number (ie 2,4,6,8,0 ) is divisible by 2 . For example 71352 and 2550 are divisible by 2 exactly because their last digit is an even number ( 2 and 0 ) respectively.

DIVISIBILITY BY 3
A number is divisible by 3 exactly when the sum of the digits of the number is a multiple of 3. For example 12453 is divisible by 3 exactly because the sum of the digits (1+2+4+5+3 = 15) is a multiple of 3 . Same as 561111 , 20022 and many others.

DIVISIBILITY BY 4
A number is divisible by 4 exactly when the last 2 digits of the number is a multiple of 4 (ie 04,08,12,16,20,24 ...). For example: 33148 is divisible by 4 exactly since its last 2 digits is 48 which is a multiple of 4. Same as 11240, 46344 and many others

Over the years of teaching mathematics, I have noticed the difficulty in simplifying fractions into simpler terms .

Today we are going to learn easier ways of simplifying fractions . It is easier to simplify fractions when both the numerator and denominator have a common factor . Now the question is “HOW DO YOU KNOW BOTH THE DENOMINATOR AND NUMERATOR HAVE A COMMON FACTOR ?”

In my next posts , we are going to learn how to easily identify numbers that can be divisible by factors like 2, 3, 4, 5, 6, 7, 8, 9 and 10 .

“The study of mathematics, like the Nile, begins in minuteness but ends in magnificence”�— Charles Caleb Colton

Contact and let’s do business.

Let’s start with some basic facts you probably didn’t know .

1. The sum of two odd numbers is always an even number.

2. Zero is not represented in Roman numerals

3. Four is the only number in the English language that is spelt with the same number of letters as the number itself.

4. 2 is the only prime number that is an even number.

5. Have you noticed the opposite side of a die always adds up to 7

With the continuous spread of the COVID - 19 causing our students to stay at home , I have decided to bring Maths lessons to the door step of the homes of these students via online . Contact me for your private maths lessons for basic level education..

Stay safe and continue to wash your hands regularly.