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Understanding Fractions: Shaded and Unshaded Parts
Let's discover what fractions are through shaded and unshaded parts!
A fraction shows parts of a whole. The top number tells how many parts are shaded, the bottom tells total parts!
Numerator: 1 (shaded parts)
Denominator: 4 (total parts)
Numerator: 3 (shaded parts)
Denominator: 8 (total parts)
Numerator: 5 (shaded parts)
Denominator: 6 (total parts)
Visualizing Fractions
Let's Explore Fraction Visualization. Try changing numerator and denominator.
Comparing Fractions - Theory
Rule 1: Fractions with Same Denominator
When two fractions have the same denominator (bottom number), the fraction with the larger numerator (top number) is bigger.
Example: 5/8 > 3/8 because 5 parts > 3 parts (both divided into 8 equal pieces)
Rule 2: Fractions with Same Numerator
When two fractions have the same numerator (top number), the fraction with the smaller denominator is bigger because each piece is larger.
Example: 3/4 > 3/8 because dividing into 4 pieces makes bigger pieces than dividing into 8 pieces
Rule 3: Unit Fractions (Numerator is 1)
For unit fractions (fractions with 1 as numerator), the fraction with the smaller denominator is larger.
Example: 1/2 > 1/4 > 1/8 (half of a pizza is bigger than a quarter)
Rule 4: Unlike Fractions
When fractions have different numerators and denominators, convert them to have a common denominator first.
Example: 2/3 vs 3/4 → Convert: 8/12 vs 9/12 → So 2/3 < 3/4
Comparing Fractions - Practice
Choose which fraction is larger using the buttons below!
Fraction A
Fraction B
How to Solve This Step by Step
Fraction Color Wheel Game
Color the correct number of sections in the wheel to match the target fraction!
How to Identify Fractions
Proper Fractions
Definition: A fraction where the numerator (top number) is smaller than the denominator (bottom number).
How to identify: Count the total shaded parts and the total equal parts. If shaded parts < total parts, it's a proper fraction.
Since 3 < 5, this is a proper fraction.
Improper Fractions
Definition: A fraction where the numerator (top number) is greater than or equal to the denominator (bottom number).
How to identify: Count ALL shaded parts across ALL figures. Then count how many parts are in ONE complete figure. If total shaded ≥ parts in one figure, it's improper.
Total shaded = 2×6 + 2 = 14 shaded parts out of 6 parts per figure = 14/6
Since 14 > 6, this is an improper fraction.
Mixed Fractions (Mixed Numbers)
Definition: A combination of a whole number and a proper fraction.
How to identify: Count the number of COMPLETELY shaded figures (whole number). Then count the additional shaded parts in the partial figure (proper fraction).
Answer: 2 3/5 (two and three-fifths)
Whole number = 2, Numerator = 3, Denominator = 5
Quick Tips
✓ Always count the parts carefully
✓ Make sure all parts are equal in size
✓ For mixed fractions: count whole figures first, then the partial one
✓ For improper fractions: count ALL shaded parts across ALL figures
Fraction Comparison Guide
- Same Denominator: When denominators are the same, the fraction with the larger numerator is bigger.
- Example: 3/4 > 1/4 because both have 4 parts, and 3 shaded parts is more than 1 shaded part.
- Visual Check: Look at the shaded areas - the fraction with more shaded area is larger.