📘 FULL LESSON: Subtraction of Integers

JPM Logic Method by Sir Jeff

1️⃣ Concept Overview — Salary vs. Expense Logic

To make subtraction easy and realistic, imagine every integer as:

Salary / Kita (Positive Number) → nagpapataas ng net worth
Expense / Gastos (Negative Number) → nagpapababa ng net worth

This mindset removes confusion and uses real-life logic.

⭐ Core Principle of Subtraction

1. Subtracting a Salary (bawas kita o bawas sweldo)

10 = Salary (+)

4 = Salary (+)

10 − 4 = 6

Salary − Salary = Net Worth Decreases

(Binawasan mo ang kita → bumaba ang net worth mo.)

2. Subtracting or Reducing an Expense (nagtitipid o bawas gastos)

10 = Salary (+)

−4 = Expense (−)

10 − (−4) = 14

Salary − Expense = Net Worth Increases

(Bawas gastos → dagdag net worth.)

Binawasan mo ang gastos,nakatipid → mas tataas ang net worth mo.

Ang natipid mo ay parang equivalent sa salary o dagdag kita.(+).

2️⃣ Additional Rules

Rule 3 — Expense − Salary = Bigger Loss

−9 = Expense (−)

7 = Salary (+)

−9 - 7 = −16

Expense − Salary = Bigger Loss

Expense minus salary = may expense ka na tapos binawasan mo pa ang income(7) mo.eh di wow..Absent kumbaga.Bawas kita.take not 7 is positive pero ibinawas mo un,kaya minus.Hindi yan as negative sign ng 7 kasi ang sign ng 7 is positive kasi salary yan. Kaya lang absent ka kaya pabawas.Kung pumasok ka,eh di plus 7 sana.

Rule 4 — Expense − Expense = Depends Which Expense Is Bigger

−12 = Expense (−)

−4 = Expense (−)

−12 − (−4) = −8

Because subtracting expense = equivalent to adding salary (+4).

Ang ibinabawas dito ay ang pagiging utangera kay minus negative 4.Negative 4 kasi utang. kapag binawasan mo ang pagiging utangera..madadagan ang pera mo.makatipid ka at makakaipon

3️⃣ Method 2 — Flip the Subtrahend → Add

This is the faster algebra method once the student is more confident.

Keep the first number
Flip the sign of the subtrahend
Change to addition
Apply addition rules (like signs add, unlike signs subtract)

Smart Line-by-Line Example

12 − (−5) 12 + 5 17

⭐ Updated Summary

METHOD 1 — Salary–Expense Logic (Best for Beginners)

Subtracting salary → net worth decreases

(Bawas kita → bawas pera.)

Subtracting expense (equivalent to adding salary) → net worth increases

(Bawas gastos = parang nagdagdag ng salary.)

Imbes na pawala na, nanatili pa sa bulsa.

Parang kumita ka (salary).

METHOD 2 — Flip the Subtrahend → Add

Keep the first number
Flip the sign of the subtrahend
Change to addition
Apply addition rules (like signs add, unlike signs subtract)

⭐ Examples (Included in Summary)

1. Like-Sign Subtraction → Net Worth Decreases

15 − 6

15 = Salary (+)

6 = Salary (+)

15 − 6 = 9

Salary − Salary = Net Worth Decreases

2. Subtracting an Expense → Net Worth Increases

−12 − (−4)

−12 = Expense (−)

−4 = Expense (−), but removing this expense increases net worth

−12 − (−4) = −8

Because subtracting expense = equivalent to adding salary (+4)

3. Expense − Salary → Bigger Loss

−9 − 7

−9 = Expense (−)

7 = Salary (+)

−9 − 7 = −16

Expense minus salary = mas malaki ang lugi