Opposites. What comes first to your mind if you hear this word? In English, this term refers to words with complete reverse meanings e.g. hot and cold, tall and short, white and black. In Science, opposites are also evident in such ways that matter and forces also come in opposites. For example, proton which are very small particle of matter that has a positive charge of electricity and electron which has the negative charge; biotic factors which include animals and other living organisms are dissimilar in meaning with abiotic factors like earth, sunlight, water, and air. In Social Sciences, concepts like yin and yang, and id and superego are also considered opposites.
In Mathematics, positives and negatives are also present - not just in feeling positive whenever you solved a certain problem or negative every time you are having a hard time understanding the concept of a specific topic. In life, there is also this quote that caught the same idea which is, "Life is as easy as 1, 2, 3, you just have to flip and turn all the NEGATIVES into POSITIVES carefully." Just like this quotation, you just have to take each challenge lightly as you turn the negatives into positive outlook and outcomes. Are you going to allow yourself to live in darkness surrounded by negative vibes?
When talking about Mathematics, positives and negatives are included in integers. Positive and negative numbers are used to represent a certain value. These are any of the whole numbers or its negatives. Integers are numbers which are not expressed as fractions or decimals. Here are some examples of integers.
Integers:
1, 2, 3, 4, 5, - 6, - 7, - 8, - 9, - 10, 0
Non - integers:
1. 5, 12. 4140, 16. 121212, 0.05, 1/4, 3 1/2, 18/20, 112/62
Integers are also used to indicate values in a number line where one unit is a scale of one count. It also includes signs denoting positive ( + ) and negative ( - ) integers / numbers.
Just like any other concepts in Mathematics, operations are also applied in integers. These operations follow certain procedure in performing them. In adding integers, two numbers have the same sign or unlike signs. They are simply combined and the sign of the final answer will depend upon the conditions of the given. Here are some examples:
SIMILAR SIGNS:
1. 4 + 6 = ?
Step 1: Combine the numerical values given: 10
Step 2: Copy the sign of the given numbers: (+) 10
Note: If the numbers is positive, a plus (+) sign may not be written together with the number.
Final Answer: The answer is positive ten (10).
2.15 + 24 = 39 (Follow the same procedure.)
3. - 12 + - 8 = - 20
Final Answer: The answer is - 20. (Same procedure will be observed. The given numbers are
negative so the final answer will also be negative.)
4. - 35 + ( - 12 ) = - 47
5. ( - 18 ) + ( - 3 ) = - 21
That is the procedure in adding integers with similar signs, now, let us proceed in adding integers with dissimilar or opposite signs. In adding integers with unlike signs, subtraction will be observed. The two numbers will be subtracted then the sign of the larger number will be carried out by the final answer. Here are some examples:
UNLIKE SIGNS:
6. - 16 + 2 = ?
Step 1: Subtract the two values. the answer will be 14.
Step 2: Copy the sign of the larger number. The larger number is 16, it is negative so the final
answer will also be negative.
Final Answer: The answer is - 14.
7. 31 + ( - 5 ) = 26 (Follow the same procedures.)
8. - 48 + 15 = - 33
To improve your understanding of integers, I suggest you to play the application "Math Flush". Below are some photos of the game. You can download the app from Google PlayStore through your android phones.
After having the discussion, it is now your time to prove what you've learned today. Solve the following integers.
1. - 8 + 3 6. 48 + ( - 12 )
2. 15 + ( - 4 ) 7. ( - 215 ) + 17
3. 150 + 271 8. 1015 + ( - 2017 )
4. - 66 + 14 9. 555 + 678
5. 24 + ( - 3 ) 10. - 2020 + ( - 1515 )
Congratulations! I am very glad that you learn something from this. Now, for you to have a better or even the best journey in life, remember to always turn your negative outlook to POSITIVE! :)
