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# Signs of Sums

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.

• Signs of Sum
• Properties of Signs of Sum
• Solved Examples
• FAQs

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## 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.

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## Solved Examples

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

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

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

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.

## 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

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