Interpreting Notation
When a string of numbers is separated by plus and minus signs, the most effective strategy is to treat the entire expression as a sum of signed numbers, converting each minus sign into adding a negative. For example, -4 - 7 + 5 becomes (-4) + (-7) + (+5) = -6. This Grade 8 math skill from Yoshiwara Core Math Chapter 7 removes ambiguity in reading and evaluating multi-term expressions with signed numbers. Rewriting expressions this way also allows you to add terms in any order using the commutative property, making complex arithmetic more flexible and reliable.
Key Concepts
Property When we see a string of numbers separated by plus or minus signs, we’ll treat it as a sum of signed numbers.
Examples The expression $ 4 7 + 5$ can be treated as the sum $ 4 + ( 7) + 5$. This simplifies to $ 11 + 5$, which is $ 6$. We can simplify $8 10 + 3 5$ by adding the signed numbers: $(+8) + ( 10) + (+3) + ( 5) = 4$. The expression $12 5 10$ is the sum of $12$, $ 5$, and $ 10$. Adding them gives $12 + ( 5) + ( 10) = 3$.
Explanation An expression like $8 10 + 3$ is easier to solve if you read it as a sum of signed numbers: $(+8) + ( 10) + (+3)$. This way, you can add them in any order and avoid confusion with subtraction.
Common Questions
How do you interpret expressions with plus and minus signs?
Treat each term as a signed number. A subtraction sign in front of a number makes that number negative. Then rewrite the whole expression as an addition of signed numbers. For example, 8 - 10 + 3 - 5 = (+8) + (-10) + (+3) + (-5) = -4.
Why is it helpful to rewrite subtraction as addition of negatives?
Rewriting subtraction as addition allows you to use the commutative and associative properties, adding terms in any convenient order. It also makes it easier to identify like terms in algebra and avoid sign errors.
What is the rule for a chain of additions and subtractions?
Work from left to right, or rewrite the entire expression as signed number additions. Every subtraction sign means the next term is negative. For example, 12 - 5 - 10 = (+12) + (-5) + (-10) = -3.
When do 8th graders learn about interpreting mixed plus and minus signs?
Students study signed number notation in Grade 8 math as part of Chapter 7 of Yoshiwara Core Math, which introduces signed numbers and their operations.
Can you reorder terms when you have mixed plus and minus signs?
Yes, once you rewrite the expression as a sum of signed numbers, you can add them in any order. For example, 3 - 8 + 5 = (+3) + (-8) + (+5). You could add +3 and +5 first to get 8, then 8 + (-8) = 0.
How does this relate to algebra?
In algebra, correctly interpreting signs is essential for combining like terms. The expression 3x - 5 + 2x is read as 3x + (-5) + 2x = 5x - 5. Misreading a sign leads to wrong answers throughout algebra.