The 'Like Units' Rule for Adding Fractions
Fractions can only be added when they have the same denominator (like units), because only same-sized pieces can be directly combined. The denominator represents the unit size, and fractions with different denominators represent different-sized pieces that cannot be added until converted to a common unit. This Grade 5 math skill from Eureka Math Chapter 16 covers making like units pictorially for fraction addition.
Key Concepts
To add fractions, they must have like units, meaning a common denominator. You can only add the numerators when the denominators are the same. $$\frac{a}{c} + \frac{b}{c} = \frac{a+b}{c}$$.
Common Questions
Why do fractions need a common denominator to add?
The denominator tells you the size of each piece. You can only add pieces of the same size, just like you can add 3 apples plus 2 apples but not 3 apples plus 2 oranges without finding a common unit.
What does the like units rule for fractions mean?
The like units rule means fractions can only be added directly when their denominators are the same, because the denominators represent the unit (size) of each piece being added.
What is wrong with adding 1/2 plus 1/4 directly?
Halves and fourths are different-sized pieces. You must convert 1/2 to 2/4 (creating like units) before adding: 2/4 plus 1/4 equals 3/4.
How do you add fractions with unlike denominators?
First convert both fractions to equivalent fractions with a common denominator, then add the numerators while keeping the common denominator.