Signs of Sums
Grade 7 Math Worksheets
In the realm of mathematics, understanding the signs of sums is a fundamental skill that Grade 7 students need to develop.
The concept of positive and negative numbers may seem perplexing at first, but by grasping the rules governing their combinations, students can unlock the power of arithmetic operations involving both positive and negative values.
Table of Contents:
- Signs of Sum
- Properties of Signs of Sum
- Solved Examples
Personalized Online Tutoring
Signs of Sums - Grade 7 Math Worksheet PDF
This is a free worksheet with practice problems and answers. You can also work on it online.
Sign up with your email ID to access this free worksheet.
"We really love eTutorWorld!"
"We really love etutorworld!. Anand S and Pooja are excellent math teachers and are quick to respond with requests to tutor on any math topic!" - Kieran Y (via TrustSpot.io)
"My daughter gets distracted easily"
"My daughter gets distracted very easily and Ms. Medini and other teachers were patient with her and redirected her back to the courses.
With the help of Etutorworld, my daughter has been now selected in the Gifted and Talented Program for the school district"
- Nivea Sharma (via TrustSpot.io)
Signs of Sums
Addition of Like Signs: When adding numbers with like signs, whether positive or negative, the resulting sum takes the sign of the numbers being added. Specifically, adding positive numbers yields a positive sum, while adding negative numbers produces a negative sum. This rule follows the notion that adding quantities with the same sign reinforces their magnitude, resulting in a larger value.
Addition of Unlike Signs: Adding numbers with unlike signs involves a different set of rules. When adding a positive number and a negative number, the sign of the sum depends on the magnitudes of the numbers being added. If the positive number has a greater magnitude, the sum will be positive. Conversely, if the negative number has a greater magnitude, the sum will be negative. In this scenario, subtraction can be thought of as addition with the opposite sign.
Zero as a Neutral Element: Zero acts as a neutral element in arithmetic operations. Adding zero to any number does not change its value, whether the number is positive or negative. Therefore, the sum of any number and zero is always the number itself.
Properties of Signs of Sum
Commutative Property: The commutative property of addition applies to the sign of sums. This property states that changing the order of the numbers being added does not affect the sum. In other words, the sum of two numbers is the same regardless of their order. For example, a + b is equal to b + a. This property holds true for both positive and negative numbers.
Zero as a Neutral Element: The sum of any number and zero is always the number itself. Zero acts as a neutral element in addition, meaning that adding zero to any number does not change its value. For instance, a + 0 = a, regardless of whether a is positive or negative.
Closure Property: The closure property of addition states that when we add two real numbers, the sum is also a real number. This property ensures that the result of adding any two numbers, positive or negative, is always a valid number within the real number system.
Inverse Property: Every positive number has an additive inverse, which is a negative number that, when added to the positive number, yields a sum of zero. Similarly, every negative number has an additive inverse that, when added to the negative number, results in a sum of zero. For example, the additive inverse of 5 is -5, and the additive inverse of -3 is 3.
Associative Property: The associative property of addition applies to the sign of sums as well. This property states that when adding three or more numbers, the grouping of the numbers does not affect the sum. For instance, (a + b) + c is equal to a + (b + c). This property holds true for positive and negative numbers.
Distributive Property: The distributive property of addition over subtraction is a useful property when working with positive and negative numbers. This property states that a number multiplied by the sum of two other numbers is equal to the sum of the products of the number multiplied by each of the other numbers. For example, a * (b + c) is equal to (a * b) + (a * c).
“There have been times when we booked them last minute, but the teachers have been extremely well-prepared and the help desk at etutorworld is very prompt.
Our kid is doing much better with a higher score.”
7th Grade Tutoring
eTutorWorld offers Personalized Online Tutoring for Math, Science, English, and Standardised Tests.
Our Tutoring Packs start at just under $21 per hour, and come with a moneyback guarantee.
Schedule a FREE Trial Session, and experience quality tutoring for yourself. (No credit card required.)
Example 1: Bank Account Transactions
Consider a bank account where positive numbers represent deposits and negative numbers represent withdrawals. Suppose you have a balance of $100 and you withdraw $50, followed by a deposit of $30. To determine the new balance, we can use the sign of sums properties.
Starting balance: $100
Withdrawal of $50 (negative): -50
Deposit of $30 (positive): +30
Adding the transactions:
100 + (-50) + 30
According to the properties of the sign of sums:
100 + (-50) + 30 = 100 – 50 + 30 = 80
The new balance in the bank account is $80.
Example 2: Elevation Changes in Hiking
Suppose you are hiking in a mountainous area and encounter changes in elevation. Positive numbers represent ascending heights, and negative numbers represent descending depths. If you hike up 200 meters, then descend 150 meters, and finally climb up another 100 meters, you can calculate the net elevation change using the properties of the sign of sums.
Starting elevation: 0 meters
Climbing up 200 meters (positive): +200
Descending 150 meters (negative): -150
Climbing up 100 meters (positive): +100
Adding the elevation changes:
0 + 200 + (-150) + 100
According to the properties of the sign of sums:
0 + 200 + (-150) + 100 = 150
The net elevation change is a positive 150 meters, indicating an overall ascent.
Example 3: Temperature Changes
Consider a weather report showing temperature changes throughout the day. Positive numbers represent temperature increases, and negative numbers represent temperature decreases. If the temperature rises by 5 degrees Celsius, then drops by 3 degrees Celsius, and later increases by 2 degrees Celsius, you can calculate the net temperature change using the properties of the sign of sums.
Starting temperature: 20 degrees Celsius
Temperature increase of 5 degrees Celsius (positive): +5
Temperature decrease of 3 degrees Celsius (negative): -3
Temperature increase of 2 degrees Celsius (positive): +2
Adding the temperature changes:
20 + 5 + (-3) + 2
According to the properties of the sign of sums:
20 + 5 + (-3) + 2 = 24
The net temperature change is a positive 24 degrees Celsius, indicating an overall temperature increase.
Do You Stack Up Against the Best?
If you have 30 minutes, try our free diagnostics test and assess your skills.
Signs of Sums FAQS
Why is it important to understand the properties of the sign of sums?
Understanding the properties of the sign of sums is important because it allows us to accurately perform arithmetic operations involving positive and negative numbers. These properties provide guidelines and rules for adding, subtracting, and interpreting the results of these operations. They help us make sense of real-world scenarios and mathematical problems that involve quantities with different signs.
How do the properties of the sign of sums apply to real-life situations?
The properties of the sign of sums have real-life applications in various contexts. For example, in financial transactions, positive and negative numbers represent deposits and withdrawals, respectively. By applying the properties, we can determine the net balance in a bank account. Similarly, in elevations changes during hiking or temperature fluctuations, the properties help us calculate the net changes and interpret the overall outcome.
Can the properties of the sign of sums be used with numbers other than positive and negative integers?
Yes, the properties of the sign of sums can be extended to other number systems and mathematical operations. These properties apply to rational numbers, including fractions and decimals, as well as to algebraic expressions. They provide a foundation for understanding the behavior of numbers and operations in a broader mathematical context.
How can I apply the properties of the sign of sums to problem-solving?
The properties of the sign of sums provide guidelines for performing arithmetic operations and interpreting the results. When faced with a problem involving positive and negative quantities, identify the appropriate operation (addition, subtraction, etc.) and apply the properties accordingly. By following these rules, you can accurately solve problems and analyze real-life situations involving positive and negative numbers.
Are there any common mistakes to avoid when applying the properties of the sign of sums?
One common mistake is to overlook the importance of parentheses when dealing with multiple operations. Ensure that you correctly group numbers and operations according to their hierarchy and apply the properties in the correct order. It is also important to remember the specific rules for addition, subtraction, and multiplication when dealing with positive and negative numbers. Practice and attention to detail can help avoid common mistakes and enhance proficiency in applying the properties.
Gloria Mathew writes on math topics for K-12. A trained writer and communicator, she makes math accessible and understandable to students at all levels. Her ability to explain complex math concepts with easy to understand examples helps students master math. LinkedIn
Affordable Tutoring Now Starts at Just $21
eTutorWorld offers affordable one-on-one live tutoring over the web for Grades K-12. We are also a leading provider of Test Prep help for Standardized Tests (SCAT, CogAT, MAP, SSAT, SAT, ACT, ISEE, and AP).
What makes eTutorWorld stand apart are: flexibility in lesson scheduling, quality of hand-picked tutors, assignment of tutors based on academic counseling and diagnostic tests of each student, and our 100% money-back guarantee.
Whether you have never tried personalized online tutoring before or are looking for better tutors and flexibility at an affordable price point, schedule a FREE TRIAL Session with us today.
*There is no purchase obligation or credit card requirement
- Elements and Compounds
- Solar Energy
- Electricity and Magnetism
- Law of conservation of energy
- Periodic table
- Properties of Matter
- Energy Resources
- Weather and Climate
- Immune, Circulatory and Digestive Systems
- Organs in Multi-cellular Organism
- Sedimentary, Igneous, and Metamorphic Rocks
- Structure of the Earth
- Law of Conservation of Mass
- Physical and Chemical Changes
- Scientific Method
- Human Digestive System
- Environmental Science
- Renewable and Non-renewable energy Resources
- Characteristics of Living Organisms
- Life Science
- Earth and Space Science
- Solar Eclipse
- Heat Technology
- Newton’s Laws of Motions
- Physical Science
- Tools, Measurement and SI Units
- Earth Atmosphere
- Interactions of Living things
- The Earth Ecosystem
- Organelles in Plant and Animal cells
- Layers of the Earth
- Cycles in Nature
- Linear equations word problems
- Properties of Parallel Line
- Finding slope from an equation
- Identifying Quadrilaterals
- Percent Change
- Properties of addition and multiplication
- Pythagorean Theorem
- Solving two step inequalities
- Fractions to Decimals (New)
- Whole Number Exponents with Integer Bases (New)
- Adding and Subtracting Fractions (New)
- Integer Addition and Subtraction (New)
- Dividing Mixed Numbers (New)
- Basics of Coordinate Geometry (New)