18 Questions
What is the result when adding "+4" and "-4"?
0
In adding positive and negative integers, what do numbers with opposite signs produce?
A sum with the opposite sign
In which real-life scenario is adding integers commonly used?
Accounting for debits and credits
If you add "-7" and "-5", what is the result?
-2
What is a likely real-life application for subtracting expenses from income to determine available balance?
Budgeting personal or organizational finances
If you start with $100 in your wallet and spend $30, then find $50 on the street, how much money do you have now?
$120
After buying a book for $15, you receive a refund of $10. What is the net change in your money?
$5 increase
You have 7 marbles, and you gain 3 more. Later, you lose 5 marbles. How many marbles do you have now?
8
Starting with a temperature of 5 degrees Celsius, if it increases by 8 degrees and then decreases by 4 degrees, what is the final temperature?
9 degrees
You have $60 in savings, but you need to pay a bill of $80. A friend then helps you with $20. What is your financial status now?
$40 debt
When adding two integers with like signs, what is the rule to determine the sum?
Add their absolute values
For the expression \(8 + (-5)\), what is the correct result following the integer rules?
-3
Using mental strategies, what would be the result of \(49 + 36\) after applying the rounding technique?
83
For the sum \(57 + (-28)\), how could you break down the addition using the technique mentioned in the text?
50 + 20, 7 + 8
In the word problem provided, if Jane had \(10\) dollars instead of \(6\) dollars, how much money would Jim have?
8 dollars
If Jim had \(15\) dollars more than Jane in the problem, how much money would they have together?
45 dollars
If Jane had \(y+3\) dollars instead of \(y\), and Jim still had \(y + 12\) dollars, what would be the new total amount of money?
\(2y + 15\) dollars
If they decide to add an additional person named Alex, who has \(z - 5\) dollars, to their money pool, what would be the total amount of money?
\(3y + 2z - 5\) dollars
Study Notes
Adding Integers: A Comprehensive Guide
Adding integers is a fundamental mathematical operation that underpins our understanding of numbers, from simple sums to complex calculations. In this article, we'll delve into the rules for adding integers, the nuances of positive and negative numbers, real-life applications, and word problems involving adding integers.
Rules for Adding Integers
When adding integers, the rules are simple:
- For positive and negative numbers with the same absolute value, the result is zero. For example, (-2 + 2 = 0).
- For positive and negative numbers with opposite signs, the result is the difference of their absolute values. For example, (-2 + 3 = 1) ((3 - 2 = 1)).
- For numbers with the same sign, the result is the sum of their absolute values. For example, (3 + 2 = 5), and (-3 + (-2) = -5).
Adding Positive and Negative Integers
Understanding the behavior of positive and negative numbers during addition is essential.
- Numbers with the same sign add together to produce a result with the same sign.
- Numbers with opposite signs add together to produce a result with the opposite sign.
Real-Life Applications
Adding integers is relevant to countless scenarios in everyday life:
- Accounting: Adding debits and credits to determine a bank account balance.
- Sports: Calculating scores at the end of a game or a match.
- Budgeting: Subtracting expenses from income to determine the available balance for individual or organizational budgets.
Word Problems Involving Adding Integers
Word problems can improve our understanding of adding integers in a more relatable context. Here are some example problems:
- In a video game, you have 50 coins but lose 15. How many coins do you have now? ((50 - 15) = 35)
- Your friend has 3 apples, but you take 2 away. How many apples do they have now? ((3 - 2) = 1)
- A bank account has an initial balance of $200, but $80 is deposited, and $120 is withdrawn. What is the final balance? ((200 + 80 - 120) = $100)
Conclusion
Mastering the art of adding integers is a critical skill that has practical applications in our daily lives. Understanding the rules and the behavior of positive and negative numbers during addition will serve as a solid foundation for more complex mathematical concepts. By solving word problems involving adding integers, we can further cement our understanding and gain confidence in our mathematical abilities.
Test your knowledge on adding integers with this comprehensive quiz covering rules, real-life applications, and word problems. Explore the nuances of positive and negative numbers in mathematical operations.
Make Your Own Quizzes and Flashcards
Convert your notes into interactive study material.
Get started for free
