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

Lesson 3: Solve multi-step word problems; assess reasonableness of solutions using benchmark numbers.

In this Grade 5 Eureka Math lesson from Chapter 18, students solve multi-step word problems involving mixed numbers and fractions, applying subtraction with unlike denominators across multiple sequential steps. Students use tape diagrams to organize information and benchmark numbers to assess whether their solutions are reasonable. The lesson builds fraction computation fluency while developing problem-solving strategies for real-world contexts like race times and measurement.

Section 1

Solve Multi-Step Fraction Word Problems

Property

Multi-step word problems require performing two or more mathematical operations to find the solution.
To solve, first identify the different parts of the problem and the question being asked.
Then, plan the sequence of operations (e.g., addition, subtraction) needed to arrive at the final answer.

Examples

  • Marta had 4124\frac{1}{2} pounds of flour. She used 1341\frac{3}{4} pounds for a cake and 1181\frac{1}{8} pounds for cookies. To find how much flour she had left, first add the amounts used (134+118=2781\frac{3}{4} + 1\frac{1}{8} = 2\frac{7}{8}), then subtract that total from the starting amount (412−278=1584\frac{1}{2} - 2\frac{7}{8} = 1\frac{5}{8} pounds).
  • A race is 10 miles long. Carlos ran 3123\frac{1}{2} miles and then walked for 2132\frac{1}{3} miles. To find how much farther he has to go, first add the distance covered (312+213=5563\frac{1}{2} + 2\frac{1}{3} = 5\frac{5}{6}), then subtract that from the total race distance (10−556=41610 - 5\frac{5}{6} = 4\frac{1}{6} miles).

Explanation

Solving multi-step word problems combines several skills into one process. You must first read and understand the entire problem to map out a solution plan. This often involves breaking the problem down into smaller, single-step parts. By executing each step in the correct order, you can solve complex problems that require more than one calculation.

Lesson overview

Expand to review the lesson summary and core properties.

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Section 1

Solve Multi-Step Fraction Word Problems

Property

Multi-step word problems require performing two or more mathematical operations to find the solution.
To solve, first identify the different parts of the problem and the question being asked.
Then, plan the sequence of operations (e.g., addition, subtraction) needed to arrive at the final answer.

Examples

  • Marta had 4124\frac{1}{2} pounds of flour. She used 1341\frac{3}{4} pounds for a cake and 1181\frac{1}{8} pounds for cookies. To find how much flour she had left, first add the amounts used (134+118=2781\frac{3}{4} + 1\frac{1}{8} = 2\frac{7}{8}), then subtract that total from the starting amount (412−278=1584\frac{1}{2} - 2\frac{7}{8} = 1\frac{5}{8} pounds).
  • A race is 10 miles long. Carlos ran 3123\frac{1}{2} miles and then walked for 2132\frac{1}{3} miles. To find how much farther he has to go, first add the distance covered (312+213=5563\frac{1}{2} + 2\frac{1}{3} = 5\frac{5}{6}), then subtract that from the total race distance (10−556=41610 - 5\frac{5}{6} = 4\frac{1}{6} miles).

Explanation

Solving multi-step word problems combines several skills into one process. You must first read and understand the entire problem to map out a solution plan. This often involves breaking the problem down into smaller, single-step parts. By executing each step in the correct order, you can solve complex problems that require more than one calculation.