Lesson 3: Fractions and Decimals – Basic Operations

👨🏽‍🏫 Introduction

Have you ever shared a pizza, read a recipe, or counted coins? Then you’ve used fractions and decimals! 🍕📏💰

Fractions and decimals are different ways of showing the same idea — a part of a whole. We use them in measurements, prices, distances, and just about everything else!

In this lesson, you’ll learn to:

• Convert between fractions and decimals
• Add, subtract, multiply, and divide them
• Use them in everyday problems like money, time, and length

🧠 Key Concepts

🔁 1. Converting Between Fractions and Decimals

Fraction to Decimal: Divide the numerator (top) by the denominator (bottom).

Decimal to Fraction: Write the decimal over a power of 10 and simplify.

Example:

➕➖ 2. Adding and Subtracting

🟪 Adding and Subtracting Fractions:

To add or subtract fractions, follow these steps:

1. Check the denominators (bottom numbers): If they’re the same, simply add or subtract the numerators.
2. If denominators are different: Find the Least Common Denominator (LCD).
3. Convert each fraction to have the LCD: Adjust numerators accordingly.
4. Add or subtract the numerators: Keep the common denominator.
5. Simplify your answer if needed.

Example: Add

• LCD of 3 and 6 is 6
• Convert:
  , so
  

🟩 Adding and Subtracting Decimals:

This is just like regular addition — but you must line up the decimal points before calculating.

Steps:

1. Line up the numbers by the decimal point
2. Fill in zeros as needed to equalize decimal places
3. Add or subtract from right to left

Example: Subtract

• Add zero: 3.500 − 1.275 =
  

✖️➗ 3. Multiplying and Dividing

🟧 Multiplying Fractions:

To multiply two fractions:

1. Multiply the numerators (top × top)
2. Multiply the denominators (bottom × bottom)
3. Simplify your answer if possible

Example:

🟨 Dividing Fractions:

Dividing fractions is easy when you remember this trick: Keep-Change-Flip (KCF).

1. Keep</ the first fraction
2. Change</ the division sign to multiplication
3. Flip</ the second fraction (reciprocal)

Example:

🟦 Multiplying Decimals:

To multiply decimals:

1. Ignore the decimal points and multiply like whole numbers
2. Count total number of decimal places from both numbers
3. Place the decimal that many places from the right

Example:

🟥 Dividing Decimals:

If dividing by a decimal, you should turn it into a whole number by multiplying both numbers by 10, 100, etc.

Example:

• Multiply both by 10 →
  

✍🏽 Sample Problem Walkthroughs

1. Convert:
   
2. Convert:
   
3. Add:
   
4. Multiply:
   
5. Divide:
   

🧪 Practice Exercises

✏️ A. Add or Subtract:

✏️ B. Multiply or Divide:

✏️ C. Convert:

1. Convert to a fraction
2. Convert to a decimal
3. Which is greater: or ?

✅ Answers with Explanations

• A1:
• A2: 1.75
• A3: Convert both →
• B1:
• B2: 0.15
• B3:
• B4:
• C1:
• C2:
• C3: ✅

📌 Recap

• ✅ Fractions and decimals are two ways of showing parts of a whole
• ✅ You can convert between them using division or simplification
• ✅ Always line up decimal points, or find common denominators when calculating
• ✅ These operations are essential in everyday life — from money to measurements

💭 Reflection Prompt

Think of a time you dealt with money, recipes, or measurement. Did you see decimals or fractions being used? How might you use both forms to solve the same problem in different ways?