Group and Combine Like Fractions
When solving multi-term fraction problems, reorder terms to group fractions with common denominators first and combine them before dealing with unlike denominators. This simplifies the calculation using the commutative and associative properties. This Grade 5 math skill from Eureka Math Chapter 18 covers further applications of fraction operations.
Key Concepts
Property When solving multi term problems with fractions, you can reorder the terms to group fractions with common denominators. This strategy simplifies the calculation. For example: $\frac{a}{c} + \frac{b}{d} \frac{e}{c} = (\frac{a}{c} \frac{e}{c}) + \frac{b}{d}$.
Examples For the expression $\frac{3}{8} + \frac{2}{3} \frac{1}{8}$, group the like fractions first: $(\frac{3}{8} \frac{1}{8}) + \frac{2}{3} = \frac{2}{8} + \frac{2}{3}$ To solve $4\frac{1}{5} \frac{3}{4} + \frac{2}{5}$, group the terms with a denominator of 5: $(4\frac{1}{5} + \frac{2}{5}) \frac{3}{4} = 4\frac{3}{5} \frac{3}{4}$.
Explanation When an expression has multiple fractions, look for an opportunity to reorder the terms and group fractions that already have the same denominator. By combining these "like fractions" first, you simplify the problem before dealing with unlike denominators. This strategy makes the calculation more efficient and reduces the chance of errors. It is an application of the commutative and associative properties of addition.
Common Questions
How do you group and combine like fractions?
Reorder the terms to place fractions with the same denominator next to each other, combine those like fractions first, then handle remaining unlike fractions.
What is an example of grouping like fractions?
For 3/8 + 2/3 - 1/8, group the eighths first: (3/8 - 1/8) + 2/3 equals 2/8 + 2/3. This is simpler than working left to right through unlike denominators.
Why is grouping like fractions a good strategy?
Combining fractions with the same denominator is straightforward, so grouping them first simplifies the problem and reduces errors when working with unlike denominators.
What math properties does grouping like fractions apply?
Regrouping fractions uses the commutative property (changing order) and associative property (changing grouping) of addition, both valid for adding and subtracting fractions.