Adding Unlike Fractions with a Rectangular Model
A rectangular fraction model helps add unlike fractions by partitioning a rectangle vertically by one denominator and horizontally by the other, creating a common denominator equal to the product of the two denominators. This visual method reveals the equivalent fractions needed for addition. This Grade 5 math skill from Eureka Math Chapter 16 covers making like units pictorially for fraction addition.
Key Concepts
To add two fractions $\frac{a}{b}$ and $\frac{c}{d}$ using a rectangular model, partition a whole rectangle vertically into $b$ parts and horizontally into $d$ parts. This creates a common denominator of $b \times d$. The sum is then calculated by adding the equivalent fractions: $$\frac{a}{b} + \frac{c}{d} = \frac{a \times d}{b \times d} + \frac{c \times b}{d \times b} = \frac{ad + cb}{bd}$$.
Common Questions
How do you use a rectangular model to add unlike fractions?
Draw a rectangle and partition it vertically by the first denominator and horizontally by the second. The total number of small boxes is the common denominator, and you can count the boxes for each fraction to add them.
What is an example using a rectangular model for 1/2 + 1/3?
Partition a rectangle into 2 columns and 3 rows, creating 6 equal boxes. The fraction 1/2 covers 3 boxes (equals 3/6) and 1/3 covers 2 boxes (equals 2/6). The sum is 5/6.
How does the rectangular model show the common denominator?
The total number of small boxes in the rectangle equals the product of the two denominators, which serves as a common denominator for both fractions.
What is an example using a rectangular model for 1/4 + 2/3?
Partition a rectangle into 4 columns and 3 rows (12 boxes total). The 1/4 covers 3 boxes (equals 3/12) and 2/3 covers 8 boxes (equals 8/12). The sum is 11/12.