Adding Fractions with Related Denominators
Grade 4 Eureka Math students add fractions with related denominators by creating equivalent fractions. When denominators are related—one is a multiple of the other—only the smaller denominator needs to be converted. For example, 1/2 + 1/4: multiply 1/2 by 2/2 to get 2/4, then add to get 3/4. Similarly, 2/3 + 1/6 becomes 4/6 + 1/6 = 5/6. This skill develops flexible thinking about equivalent fractions before students encounter unrelated denominators requiring the least common multiple.
Key Concepts
To add fractions with related, unlike denominators, first find a common denominator by creating an equivalent fraction for the term with the smaller denominator. Then, add the numerators. $$\frac{a}{b} + \frac{c}{d} = \frac{a \times k}{b \times k} + \frac{c}{d}$$ where $d$ is a multiple of $b$ and $d = b \times k$.
Common Questions
What are related denominators?
Related denominators are denominators where one is a multiple of the other, such as 2 and 4, or 3 and 6. One fraction can be converted to match the other without finding an LCM.
How do you add 1/2 and 1/4?
Convert 1/2 to an equivalent fraction with denominator 4: 1/2 = 2/4. Then add: 2/4 + 1/4 = 3/4.
How do you add 2/3 and 1/6?
Convert 2/3 to sixths: 2/3 = 4/6. Then add: 4/6 + 1/6 = 5/6.
Why must fractions have a common denominator before adding?
Fractions with different denominators represent pieces of different sizes. You cannot combine different-sized pieces until they are the same unit.
What comes after learning related-denominator addition in Grade 4?
Students progress to finding the least common denominator for unrelated denominators, then to adding any two fractions.