The sum of two numbers with opposite signs
Adding two numbers with opposite signs means finding the difference of their absolute values and keeping the sign of the number with the greater absolute value. For example, (+45) + (-67) = -22 because 67 - 45 = 22 and 67 is larger, so the answer is negative. Similarly, (-34) + (+43) = +9. This rule is taught in Chapter 7 of Saxon Math Course 2 for 7th grade math and is fundamental for working with integers, solving equations, and understanding real-world situations like gains and losses.
Key Concepts
Property The sum of two numbers with opposite signs has an absolute value equal to the difference of their absolute values. Its sign is the same as the sign of the number with the greater absolute value.
Examples $(+45) + ( 67) = 22$.
$( 34) + (+43) = +9$.
Common Questions
How do you add two numbers with opposite signs?
Find the difference of their absolute values, then use the sign of the number with the larger absolute value. For (+45) + (-67): |67| - |45| = 22, and since 67 is larger and negative, the answer is -22.
Why is the sum of two numbers with opposite signs sometimes positive and sometimes negative?
The sign depends on which number has the greater absolute value. If the positive number is larger, the sum is positive. If the negative number is larger, the sum is negative. The magnitude is always the difference of the absolute values.
What is the rule for adding positive and negative numbers?
Same signs: add the absolute values and keep the shared sign. Opposite signs: subtract the smaller absolute value from the larger and take the sign of the number with the greater absolute value. For example, (-34) + (+43) = +9.
How do you add decimals with opposite signs?
The same rule applies. For (+4.3) + (-7.24), find the difference: 7.24 - 4.30 = 2.94. Since 7.24 is larger and negative, the answer is -2.94. Line up decimal points just as you would in regular subtraction.
What is a real-world example of adding numbers with opposite signs?
Think of a bank account. If you deposit 45 dollars (+45) and then spend 67 dollars (-67), your net change is +45 + (-67) = -22 dollars. The negative result means you spent more than you deposited.
When do students learn to add integers with different signs?
Integer addition with opposite signs is typically taught in 7th grade math. Saxon Math Course 2 introduces this in Chapter 7 as part of a broader unit on operations with positive and negative numbers.