In this lesson
Sign decision, then magnitude
Every operation on signed rationals is two steps:
- Decide the sign. Same rules as integer arithmetic.
- Compute the magnitude. Unsigned fraction or decimal arithmetic.
Keeping the two steps separate is what prevents mistakes. Type two values, pick an operation, and read the sign decision and the magnitude as separate steps.
Rational number workspace
Pick the operation, then read the answer in two steps: sign decision, then magnitude.
Workspace for two-step arithmetic with signed rationals. Type two values, pick an operation, and read the sign decision and the magnitude as separate steps.Sign decision
Same signs → magnitudes add. The result has that same sign.
Magnitude
Answer
The sign rules are the ones you've already met for integers: same rules, same colour code. The new piece is applying them to fractions and decimals.
Estimate first
Reasonableness is a habit, not a guess. Before doing the magnitude computation, round to friendly values and predict a range.
Estimate first
Round each value to a friendly number, then predict the answer. Reasonableness is a habit, not a guess.
Estimate the answer to negative three point seven plus two point four by rounding each value to a friendly number, predicting the answer, then revealing the exact computation.Expression
-3.7 + 2.4
Round −3.7 to −4 and 2.4 to 2. Predicted: −4 + 2 = −2.
Exact: −1.3. Within range. The estimate confirms the answer's
sign and rough size. If the exact computation gave +1.3 or −6,
the estimate would catch it.
Worksheet
These aren't graded. The recipe is the same every time: decide the sign first, then compute the magnitude.
Practice · Not graded
MA.7.NUM.2Practice the idea
01 / 09
What is (−1/2) + 1/3?
Multiple choice: what is negative one half plus one third?Show common mistakes
Student says
“(−3/4)(−2/5) = −3/10. I forgot the rule.”
What it reveals
Skipped the sign decision and applied the result's sign by habit.
Targeted response
Workspace: let it surface the sign decision first ('same signs → positive') before the magnitude.
Student says
“(−1/2) + 1/3 = −2/5. I added the numerators and denominators.”
What it reveals
Treating fractions as two separate columns to combine, instead of fractions of a common whole.
Targeted response
Common denominator: −3/6 + 2/6 = −1/6. Show with fraction strips that 1/2 and 1/3 don't share units until rewritten.
Student says
“(−2/3) ÷ (4/9) = (−2/3) × (4/9). I forgot to flip.”
What it reveals
Lost the reciprocal step in division.
Targeted response
Keep, change, flip. (−2/3) ÷ (4/9) = (−2/3) × (9/4) = −18/12 = −3/2.
Going further
Order of operations adds a layer on top: when an expression mixes operations, BEDMAS decides which one runs first. The sign decisions in this lesson don't change. They just happen at the right step in the precedence ladder. That's the next lesson in the strand.