Integer Signs and Order of Operations

What you’ll learn

Calculate with negative numbers and apply operation order.

គណនាចំនួនអវិជ្ជមាន និងអនុវត្តលំដាប់ប្រមាណវិធី។

Meaning and use

An integer has no fractional part and may be positive, negative, or zero. Subtracting a negative adds its opposite. Multiplication and division use sign rules. Evaluate brackets and powers first, then multiplication and division from left to right, then addition and subtraction from left to right.

ចំនួនគត់អាចវិជ្ជមាន អវិជ្ជមាន ឬសូន្យ។ ដកចំនួនអវិជ្ជមានស្មើបូកចំនួនផ្ទុយរបស់វា។ ត្រូវគណនាវង់ក្រចក និងស្វ័យគុណមុន រួចគុណចែក និងបូកដកតាមលំដាប់។

Formulas

Subtract a negative

\[a-(-b)=a+b\]

Product signs

\[(-a)(-b)=ab,\qquad (-a)b=-(ab)\]

Symbols and units

Symbol	Meaning	Unit or restriction
a, b	Numbers in the calculation	No physical unit unless the context supplies one
−	Negative sign or subtraction, according to position	Not a unit

Conditions and limits

• Division by zero is undefined.
• Multiplication does not always precede division: equal-priority operations go left to right.
• ប្រយ័ត្នសញ្ញាដកដែលសម្គាល់ចំនួនអវិជ្ជមាន និងសញ្ញាប្រមាណវិធី។

Worked examples

Subtracting a negative

Evaluate \(7-(-3)\).

1. Replace subtracting a negative with addition.
2. Calculate \(7+3=10\).

10

ដក −3 ស្មើបូក 3 ដូច្នេះបាន 10។

An expression with mixed operations

Evaluate \(18\div3\times2-5\).

1. Work left to right: \(18\div3=6\).
2. Then \(6\times2=12\).
3. Subtract: \(12-5=7\).

7

គុណ និងចែកមានអាទិភាពស្មើគ្នា ដូច្នេះធ្វើពីឆ្វេងទៅស្ដាំ។

Common mistakes

Instead of	Use	Why
−4 × −2 = −8	−4 × −2 = 8	The product of two negative numbers is positive.
12 ÷ 3 × 2 = 2	12 ÷ 3 × 2 = 8	Evaluate equal-priority operations from left to right.

Practice

Solve these before revealing the worked solutions. Include units where relevant.

សាកល្បងដោះស្រាយមុនបើកមើលចម្លើយ។ សូមបង្ហាញជំហាន និងឯកតាដែលពាក់ព័ន្ធ។

1. Calculate −6 + 9.
2. Calculate 5 − (−4).
3. Calculate 2 + 3 × 4.

Answers and steps

Show solutions / បង្ហាញដំណោះស្រាយ

1. 3

   Starting at −6, adding 9 moves nine places toward the positive direction.

2. 9

   Subtracting −4 is adding 4: 5 + 4 = 9.

3. 14

   Multiply first: 3 × 4 = 12; then 2 + 12 = 14.

Quick recap

• Subtracting a negative adds its opposite.
• Use operation order, including left-to-right ties.
• Never divide by zero.