The sum of two numbers with the same sign
The rule for adding two numbers with the same sign in Grade 7 is: add their absolute values and keep the shared sign. In Saxon Math, Course 2, Chapter 7, students apply this to both positive and negative integers. (-54) + (-78) = -132 because both are negative — the absolute values add to 132 and the result stays negative. (+20) + (+15) = +35 because both are positive. This rule also applies to mixed numbers and fractions with the same sign, making it a versatile tool for integer arithmetic.
Key Concepts
Property The sum of two numbers with the same sign has an absolute value equal to the sum of their absolute values. Its sign is the same as the sign of the numbers.
Examples $( 54) + ( 78) = 132$.
$(+20) + (+15) = +35$.
Common Questions
What is the rule for adding two numbers with the same sign?
Add their absolute values and give the result the same sign as the original numbers. For example, (-54) + (-78) = -132, and (+20) + (+15) = +35.
Why does adding two negatives give a larger negative?
Because both values represent a deficit or debt. Combining two debts creates a bigger debt. The absolute value increases while the sign stays negative.
How do you add negative fractions or mixed numbers?
Add the absolute values of the numbers as you normally would for fractions, then apply the negative sign to the result. For example, (-2½) + (-3⅓) = -(2½ + 3⅓) = -5⅚.
What happens when you add two positive numbers?
The sum is positive. Add the values normally. For example, (+20) + (+15) = +35. This matches standard addition.
Where is same-sign addition taught in Saxon Math Course 2?
This rule is covered in Chapter 7 of Saxon Math, Course 2, as part of Grade 7 integer and rational number operations.
How does same-sign addition differ from adding numbers with different signs?
Same-sign addition always increases the absolute value and keeps the sign. Different-sign addition subtracts the smaller absolute value from the larger and uses the sign of the larger number.
What real-life situation models adding two negative numbers?
Financial debt: owing $54 and borrowing $78 more gives a total debt of $132, modeled as (-54) + (-78) = -132.