Dividing Rational Numbers

Master dividing fractions, decimals, and mixed numbers. Alberta Grade 9 mathematics curriculum.

Lesson 3.5 of Rational Numbers in Grade 9 Math — Alberta curriculum lessons.

What you'll learn in this lesson

• Understanding Division with Rational Numbers. Learn how to divide positive and negative rational numbers using integer rules and reasoning.
• Dividing Fractions and Mixed Numbers. Divide fractions and mixed numbers by flipping the second fraction and multiplying, then simplify your answers.
• Real-World Problems. Apply division of rational numbers to everyday word problems and real-life examples.

Inside the lesson — a free preview

Integer Rules for Dividing

We follow the same rules as the rules for multiplying integers.

Note: When Dividing More Than Two Numbers

📝 Multiple Division. When you have more than two integers, divide two at a time — left to right.

Example:(−24) ÷ 3 ÷ (−2)Start with the first two: (−24) ÷ 3 = −8Then divide by the next: −8 ÷ (−2) = +4✅ Final Answer: +4

Dividing Decimals

Just like multiplication, decimals follow the same sign rules.

But before dividing, you must make the divisor (the number you're dividing by) a whole number.

📋 Steps:.

💡 Tip: Remember

🔑 Key Points.

Fraction Rules for Dividing (Flip and Kiss Method)

When dividing fractions, there's a fun trick you can use to make it easy — it's called the Flip and Kiss Method 💋

It means:

💋 Flip and Kiss Steps.

Rules for Dividing Fractions

• You don't need a common denominator.• Keep the first fraction the same.• Flip the second fraction (reciprocal).• Multiply across (top × top and bottom × bottom).• Simplify to lowest terms if possible.

💡 Tip

🔑 Remember. When dividing fractions, just remember: Flip it, then Kiss it Goodbye! (Flip the second fraction and multiply.)

Understanding Real-World Division Applications

Dividing rational numbers is essential in everyday situations like sharing food equally, calculating portions, determining how many groups you can make, and working with rates and ratios.In division word problems, always:• Identify what needs to be divided and by what• Use the "Flip and Kiss" method for fractions• Convert mixed numbers to improper fractions first• Check if your answer makes sense in context

Problem-Solving Tips

Key Strategies:• Read the problem carefully and identify what you're dividing• Look for keywords like "shared equally," "each," "per," or "divided by"• Remember: "How many groups?" vs "How much in each group?"• Always convert mixed numbers to improper fractions before dividing• Use visual representations when helpful (drawings, diagrams)

Worked example: – Dividing Two Negatives

(−12) ÷ (−3)Step 1: Divide absolute values: 12 ÷ 3 = 4Step 2: Both numbers are negative: answer is positive.✅ Answer: +4

Create a free Studyio account to take the full lesson with voice-over teaching, practice questions and instant feedback.