Subtracting a Positive Number
Subtracting a positive number is equivalent to adding the corresponding negative number, because both operations move left on the number line. For example, 7 - (+12) is the same as 7 + (-12) = -5. This Grade 8 math skill from Yoshiwara Core Math Chapter 7 helps students build fluency with signed number operations by showing that subtraction and addition of negatives are the same movement. Understanding this equivalence is crucial for simplifying algebraic expressions and solving equations involving signed numbers. It also bridges arithmetic to algebra by showing how subtraction can always be rewritten as addition.
Key Concepts
Property Subtracting a positive number is the same as adding the corresponding negative number. For both operations, we move to the left on the number line.
Examples To solve $7 (+12)$, we change it to an addition problem: $7 + ( 12) = 5$. To solve $ 5 (+6)$, we rewrite it as adding a negative: $ 5 + ( 6) = 11$. The subtraction $15 (+8)$ is the same as the addition $15 + ( 8)$, which equals $7$.
Explanation Think of subtracting a positive number as taking away value. This makes you move left on the number line, which is exactly what happens when you add a negative number. It's two ways of describing the same decrease.
Common Questions
How do you subtract a positive number?
Subtracting a positive number is the same as adding the corresponding negative number. For example, 7 - 12 is the same as 7 + (-12) = -5. Both operations move left on the number line by the same amount.
What is the rule for subtracting positive numbers?
The rule is: subtracting a positive is the same as adding a negative. Replace the subtraction sign and positive sign with addition and a negative sign. For example, -5 - 6 = -5 + (-6) = -11.
Why does subtracting a positive number move you left on the number line?
Moving left on the number line means decreasing in value, which is what both subtraction and adding a negative number accomplish. They are two ways of describing the same movement toward smaller numbers.
When do 8th graders learn about subtracting positive numbers?
Students study subtracting positive numbers in Grade 8 math as part of Chapter 7 of Yoshiwara Core Math, which covers signed numbers and operations with negative quantities.
What is the difference between subtracting a positive and subtracting a negative?
Subtracting a positive (e.g., 5 - 3) decreases the value, equivalent to adding a negative. Subtracting a negative (e.g., 5 - (-3)) increases the value, equivalent to adding a positive, because two negatives make a positive.
How does subtracting positive numbers relate to algebra?
In algebra, the ability to rewrite subtraction as addition of a negative simplifies expression manipulation and equation solving. It is the basis for combining like terms and moving terms across an equals sign.