Hello Math Explorer! Get ready for an exciting adventure.
Each topic has fun activities and games to help you learn. Complete all sections to learn well!
Math Adventure Complete! 🎉
Understanding Fractions with Shapes
A fraction represents equal parts of a whole. The numerator (top number) tells how many parts we have. The denominator (bottom number) tells how many equal parts the whole is divided into.
For example: If a shape is divided into 4 equal parts and 3 are shaded, the fraction is 3/4.
Let's practice with fractions! 🍕
Click on the pizza slice to show the fraction!
Now select the correct fraction that matches what you shaded!
Like & Unlike Fractions
Shade the blocks to match the fractions, then decide if they are like or unlike!
How to Play
1. Click on the blocks to shade them and match the target fraction.
2. When both fractions are correctly shaded, choose if they are "Like Fractions" or "Unlike Fractions".
3. Like fractions have the same denominator (bottom number). Unlike fractions have different denominators.
0/0
0/0
Are these fractions like or unlike?
Create your own fraction!
Choose a color and click on squares to shade them:
Adding and Subtracting Fractions
To add or subtract fractions, they must have the same denominator. Here's how:
- Find a common denominator (LCM of denominators)
- Convert each fraction to have that denominator
- Add or subtract the numerators
- Simplify if possible
Example: 1/2 + 1/4 = 2/4 + 1/4 = 3/4
Fraction Operations Practice
Solution Steps:
Step 1: Find the Least Common Multiple (LCM) of the denominators
LCM of 2 and 4 is:
Comparing and Ordering Fractions
To compare fractions, you can:
- Find a common denominator and compare numerators
- Use cross multiplication
- Visualize with fraction models
Remember: The larger the denominator, the smaller each piece becomes!
Visualize fractions with pizzas! Each pizza is divided into slices. The shaded slices represent the fraction. Compare the two pizzas
Pizza 1
Pizza 2
Solution
Pizza 1 has 1/2 shaded.
Pizza 2 has 1/3 shaded.
Therefore: 1/2 > 1/3
Comparing Fractions Practice
Compare these fractions:
Order these fractions from smallest to largest:
Drag fractions to reorder them
How to order fractions:
- Find a common denominator for all fractions
- Convert each fraction to an equivalent fraction with that denominator
- Compare the numerators to determine the order
- Arrange from smallest numerator to largest
Simplifying Fractions
Simplifying fractions means reducing them to their smallest form. To simplify a fraction:
- Find the Greatest Common Divisor (GCD) of the numerator and denominator
- Divide both numerator and denominator by the GCD
- The fraction is now in simplest form!
Example: Simplify 4/8
GCD of 4 and 8 is 4
4÷4 = 1, 8÷4 = 2
Simplified fraction: 1/2
Simplify this fraction:
Equivalent Fractions 🎉
Imagine you have a 🍎 apple cut into 2 pieces—that’s 1/2. If you cut each of those pieces in half again, now you have 4 pieces, but still the same apple! That’s why 1/2 = 2/4.
🔍 How to Find Them
-
Multiply top and bottom by the same number
e.g. 1 × 2 = 2, 2 × 2 = 4 → 2/4 -
Divide top and bottom by the same number (only if they divide evenly!)
e.g. 6 ÷ 3 = 2, 9 ÷ 3 = 3 → 2/3
📊 Examples Table
| Start | Operation | Result |
|---|---|---|
| 1/2 | ×2 ⇒ (1×2)/(2×2) | 2/4 |
| 1/2 | ×3 ⇒ (1×3)/(2×3) | 3/6 |
| 1/2 | ×4 ⇒ (1×4)/(2×4) | 4/8 |
🔑 Key idea: Changing how many pieces you cut into doesn’t change the amount you have—just the size of each piece!
✏️ Your Turn!
Pick any fraction you know, choose a number (like 2 or 5), and multiply both its top and bottom. What new fraction did you get? Draw or use little pictures (🍩, 🍓, 🎈) to show why they’re the same!
Equivalent Fractions Practice
Mixed Numbers & Improper Fractions
Mixed numbers combine whole numbers and fractions, while improper fractions have numerators larger than denominators.
To convert mixed to improper:
Multiply whole number by denominator, then add numerator.
Example: 2 1/3 = (2×3 + 1)/3 = 7/3
To convert improper to mixed:
Divide numerator by denominator - quotient is whole number, remainder is numerator.
Example: 7/3 = 2 remainder 1 = 2 1/3
Conversion Practice
Convert to improper fraction: 2 1/3
Multiplying & Dividing Fractions
Multiplication: Multiply numerators together and denominators together
Example: 2/3 × 3/4 = (2×3)/(3×4) = 6/12 = 1/2
Division: Multiply by the reciprocal of the second fraction (flip numerator and denominator)
Example: 2/3 ÷ 3/4 = 2/3 × 4/3 = 8/9
Always simplify your final answer!
Fraction Multiplication with Pie Charts
Each pie chart represents a fraction. When we have multiple identical fractions, we can multiply them together. Count the number of pie charts and the shaded parts in each to write the multiplication equation.