Learn on PengiEureka Math, Grade 5Chapter 18: Further Applications

Lesson 2: Strategize to solve multi-term problems.

In this Grade 5 Eureka Math lesson from Chapter 18, students learn strategies for solving multi-term addition and subtraction problems involving fractions and mixed numbers with unlike denominators. Students practice identifying like units, rearranging terms, and recognizing compatible numbers to simplify expressions such as combining thirds, fifths, eighths, and halves efficiently. The lesson builds on prerequisite skills like making like units and extends to multi-step word problems requiring students to determine whether a part or whole is unknown.

Section 1

Group and Combine Like Fractions

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: ac+bd−ec=(ac−ec)+bd\frac{a}{c} + \frac{b}{d} - \frac{e}{c} = (\frac{a}{c} - \frac{e}{c}) + \frac{b}{d}

Examples

  • For the expression 38+23−18\frac{3}{8} + \frac{2}{3} - \frac{1}{8}, group the like fractions first: (38−18)+23=28+23(\frac{3}{8} - \frac{1}{8}) + \frac{2}{3} = \frac{2}{8} + \frac{2}{3}
  • To solve 415−34+254\frac{1}{5} - \frac{3}{4} + \frac{2}{5}, group the terms with a denominator of 5: (415+25)−34=435−34(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.

Lesson overview

Expand to review the lesson summary and core properties.

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Section 1

Group and Combine Like Fractions

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: ac+bd−ec=(ac−ec)+bd\frac{a}{c} + \frac{b}{d} - \frac{e}{c} = (\frac{a}{c} - \frac{e}{c}) + \frac{b}{d}

Examples

  • For the expression 38+23−18\frac{3}{8} + \frac{2}{3} - \frac{1}{8}, group the like fractions first: (38−18)+23=28+23(\frac{3}{8} - \frac{1}{8}) + \frac{2}{3} = \frac{2}{8} + \frac{2}{3}
  • To solve 415−34+254\frac{1}{5} - \frac{3}{4} + \frac{2}{5}, group the terms with a denominator of 5: (415+25)−34=435−34(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.