Bridging lesson
Signed Numbers
Mga Bilang na May Senyas
Add, subtract, multiply and divide positive and negative numbers, and follow the order of operations.
About 20 minutes
Why it matters in Grade 11
Arithmetic sequences with negative common differences, formulas such as $a_n=a_1+(n-1)d$, and substitution into functions like $f(x)=x^2-2x$ at negative inputs all break down when signs are handled loosely. Profit and loss, temperatures and account balances are signed quantities.
Needed directly for: Patterns, Sequences and Series (Term 1, Weeks 3–4)
Later topics that build on these: Sequences in Finance, Compound Interest, Annuities and Cash Flows, Business and Consumer Loans.
Lesson
Picture a number line
ExplainNumbers to the left are smaller: $-7<-2<0<3$. Adding a positive moves right; adding a negative moves left. $-7+12$ starts at $-7$ and moves 12 to the right, landing on $5$.
Subtracting is adding the opposite
Explain- $-3-5$ means $-3+(-5)$. Same signs: add the sizes, keep the sign: $-8$.
- $8-(-4)$ means $8+4=12$. Two minus signs in a row become a plus.
- Different signs when adding: subtract the sizes, keep the sign of the larger: $-\frac{3}{4}+\frac{1}{2}=-\frac{1}{4}$.
Multiplying and dividing
ExplainSame signs give a positive result; different signs give a negative result. $(-4)(-6)=24$, $-18\div3=-6$, $\frac{-12}{-4}=3$. This rule is for multiplication and division only; two negatives added stay negative.
| Signs | Result |
|---|---|
| $(+)(+)$ or $(-)(-)$ | positive |
| $(+)(-)$ or $(-)(+)$ | negative |
Order of operations and exponents
ElaborateParentheses, then exponents, then multiplication and division (left to right), then addition and subtraction (left to right). $2+3\times4=14$. $8-2(3-7)=8-2(-4)=8+8=16$. Exponents apply only to what is directly in front of them: $-3^2=-9$ but $(-3)^2=9$.
Worked example: an e-wallet balance
ElaborateA wallet has ₱500. Its owner pays ₱850, receives ₱1,200, then pays ₱600: $500-850+1200-600$. Step by step: $500-850=-350$, $-350+1200=850$, $850-600=250$. The balance dipped below zero and recovered to ₱250.
Common errors to watch for
Evaluate- Thinking $-2<-7$ because $2<7$.
- Making two negatives positive when adding ($-3-5\ne8$).
- Writing $-3^2=9$.
- Working left to right instead of multiplying first ($2+3\times4\ne20$).
- Dropping the sign of a quotient or product.
Check yourself
Three quick items with instant feedback. Answer, then press Check.
Ready? Retake the Signed Numbers placement test (13 items) to confirm the skill.
Retake the test