Lesson Plan: Adding Fractions with Unlike Denominators

Lesson Summary

This 50-minute lesson teaches students to add fractions with unlike denominators. Students will learn to find a common denominator, rewrite fractions as equivalent fractions, and add them effectively. This lesson aligns with Common Core Standard CCSS.Math.Content.5.NF.A.1. Multimedia resources from Media4Math.com are integrated throughout to support learning. The lesson concludes with a 10-question quiz, complete with an answer key.

Lesson Objectives

  • Add fractions with unlike denominators.
  • Solve word problems involving addition of fractions with unlike denominators.

Common Core Standards

  • CCSS.Math.Content.5.NF.A.1: Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators.

Prerequisite Skills

  • Finding common denominators.
  • Adding fractions with like denominators.

Key Vocabulary

Multimedia Resources

 

 

Warm Up Activities

Choose from one or more of the following activities.

Calculator Activity

Use any fraction calculator for this activity. Desmos.com has a freely available calculator.

  • Estimation with Decimals: Write several pairs of fractions with unlike denominators on the board, such as \(\frac{2}{5}\) and \(\frac{3}{4}\). 
  • Have students convert the fractions to decimals using calculators. 
  • Ask them to estimate the sum and compare their estimates with the actual sums calculated later.

 

Fractions

 

Fraction Bars Activity

  • Adding with Fraction Bars: Provide students with physical or digital fraction bars. Ask students to model fractions with unlike denominators (e.g., \(\frac{1}{3}\) and \(\frac{1}{4}\)) and visually show the sum.

 

Fractions

 

Benchmark Fractions Activity

Use Benchmark Fractions to Compare: Divide students into groups. 

  • Give each group a fraction comparison problem (e.g., compare \(\frac{3}{7} and \frac{3}{5}\)). 
  • Have them use a fraction number line that shows benchmark fraction \(\frac{1}{2}\).

 

Fractions

 

  • Have them estimate the relative size of the fractions relative to the benchmark.

 

Fractions

 

  • Using the relative locations on the number line, have them compare the fractions:

\(\frac{3}{7} < \frac{3}{5}\)

 

 

Teach

Introduction to Adding Fractions with Unlike Denominators:

  • Begin by reviewing the concept of fractions and their components: numerators and denominators. Ensure that students understand the role of denominators in determining the size of the fractional parts.
  • Discuss why fractions with unlike denominators cannot be directly added. Use real-world examples, such as combining different units of measurement, to illustrate the need for a common denominator. For instance, explain how adding \(\frac{1}{4}\) of a pizza to \(\frac{1}{3}\) of another pizza requires making the parts the same size.
  • Introduce the concept of Least Common Multiple (LCM) and how it is used to find a common denominator. Demonstrate finding the LCM using simple numbers, such as 4 and 3, and explain that the LCM is the smallest multiple shared by both numbers.
  • Explain the process of rewriting fractions as equivalent fractions with the common denominator. Use visual aids, such as fraction bars or circles, to help students see how the fractions change but remain equivalent.
  • Reinforce the importance of maintaining the value of a fraction when converting it to an equivalent fraction. Highlight that while the numbers in the fraction may change, the represented value remains the same.

Example 1: One Denominator is a Multiple of the Other

Add: \(\frac{3}{4} + \frac{5}{8}\)

  • Identify that denominator 8 is a multiple of denominator 4, so the LCM is 8.
  • Rewrite \(\frac{3}{4}\) as \(\frac{6}{8}\) (by multiplying both numerator and denominator by 2).
  • Add: \(\frac{6}{8} + \frac{5}{8} = \frac{11}{8}\).
  • Convert to a mixed number: \(\frac{11}{8} = 1\frac{3}{8}\).

Example 2: Adding Simple Fractions

Add: \(\frac{1}{4} + \frac{2}{3}\)

  • Find the LCM of 4 and 3, which is 12.
    • 4: 4, 8, 12
    • 3: 3, 6, 9, 12
  • This makes the LCD 12.
  • Rewrite fractions using the LCD: \(\frac{1}{4} = \frac{3}{12}\) and \(\frac{2}{3} = \frac{8}{12}\).
  • Add: \(\frac{3}{12} + \frac{8}{12} = \frac{11}{12}\).

Example 3: Sums reater than 1

Add: \(\frac{5}{6} + \frac{4}{5}\)

  • Find the LCM of 6 and 5
    • 6: 6, 12, 18, 24, 30
    • 5: 5, 10, 15, 20, 25, 30
  • This means the LCD is 30.
  • Rewrite fractions: \(\frac{5}{6} = \frac{25}{30}\) and \(\frac{4}{5} = \frac{24}{30}\).
  • Add: \(\frac{25}{30} + \frac{24}{30} = \frac{49}{30}\).
  • Convert to a mixed number: \(\frac{49}{30} = 1\frac{19}{30}\).

Example 4: Adding Mixed Numbers

Add: \(1\frac{1}{2} + 2\frac{2}{5}\)

  • Convert to improper fractions: \(\frac{3}{2}\) and \(\frac{12}{5}\).
  • Find the LCM of 2 and 5
    • 2: 2, 4, 6, 8, 10
    • 5: 5, 10
  • The LCD is 10.
  • Rewrite fractions: \(\frac{3}{2} = \frac{15}{10}\) and \(\frac{12}{5} = \frac{24}{10}\).
  • Add: \(\frac{15}{10} + \frac{24}{10} = \frac{39}{10} = 3\frac{9}{10}\).

Example 5: Real-World Application

Add: Combine \(\frac{3}{4}\) cup of sugar and \(\frac{2}{5}\) cup of flour.

  • Find the LCM of 4 and 5, which is 20.
  • Rewrite fractions: \(\frac{3}{4} = \frac{15}{20}\) and \(\frac{2}{5} = \frac{8}{20}\).
  • Add: \(\frac{15}{20} + \frac{8}{20} = \frac{23}{20} = 1\frac{3}{20}\).

Multimedia Resources

Here are some additional worked-out examples for adding fractions: Student Tutorial: Adding Fractions

 

Review

Introduction: In this section, we will revisit the key concepts and vocabulary introduced in the lesson. We will reinforce the importance of finding common denominators, rewriting fractions as equivalent fractions, and combining them accurately. By practicing these steps, students will solidify their understanding of adding fractions with unlike denominators. Additionally, we will review the following key vocabulary to ensure students fully grasp the terms used throughout the lesson:

  • Unlike denominators: Fractions with different denominators that require a common denominator to perform operations like addition or subtraction.
  • Common denominator: A shared multiple of the denominators of two or more fractions, used to make the denominators the same for calculation.
  • Equivalent fractions: Fractions that represent the same value or part of a whole, even though the numerators and denominators may differ.
  • Sum: The result of adding two or more numbers or fractions together.

With these concepts in mind, we will proceed to solve additional examples and reinforce the process of adding fractions with unlike denominators.

Example 1: \(\frac{5}{8} + \frac{3}{10}\)

  • LCM = 40.
  • Rewrite fractions: \(\frac{5}{8} = \frac{25}{40}\), \(\frac{3}{10} = \frac{12}{40}\).
  • Add: \(\frac{25}{40} + \frac{12}{40} = \frac{37}{40}\).

Example 2: \(2\frac{1}{4} + 1\frac{3}{5}\)

  • Convert to improper fractions: \(\frac{9}{4}\) and \(\frac{8}{5}\).
  • LCM = 20. Rewrite: \(\frac{9}{4} = \frac{45}{20}\), \(\frac{8}{5} = \frac{32}{20}\).
  • Add: \(\frac{45}{20} + \frac{32}{20} = \frac{77}{20} = 3\frac{17}{20}\).

Example 3: Combining Measurements

  • Problem: Combining \(\frac{2}{3}\) liter and \(\frac{5}{6}\) liter.
  • LCM = 6. Rewrite: \(\frac{2}{3} = \frac{4}{6}\), \(\frac{5}{6}\) remains the same.
  • Add: \(\frac{4}{6} + \frac{5}{6} = \frac{9}{6} = 1\frac{1}{2}\).

Multimedia Resources

Here are some tutorial videos that provide additional examples: 

 

 

Quiz

Directions: Solve each problem. Show your work.

  1. \(\frac{1}{3} + \frac{2}{5}\)
  2. \(\frac{5}{6} + \frac{3}{8}\)
  3. \(2\frac{1}{4} + \frac{1}{3}\)
  4. \(\frac{4}{5} + \frac{2}{7}\)
  5. \(1\frac{2}{3} + 2\frac{3}{4}\)
  6. \(\frac{1}{6} + \frac{5}{12}\)
  7. \(3\frac{1}{8} + 1\frac{1}{6}\)
  8. \(\frac{7}{9} + \frac{2}{5}\)
  9. Real-world: Combining \(\frac{1}{2}\) cup of oil with \(\frac{3}{7}\) cup of syrup.
  10. Real-world: Combining \(\frac{2}{3}\) mile with \(\frac{4}{5}\) mile.

Answer Key

  1. \(\frac{11}{15}\)
  2. \(1\frac{19}{24}\)
  3. \(2\frac{11}{12}\)
  4. \(\frac{38}{35}\)
  5. \(4\frac{5}{12}\)
  6. \(\frac{7}{12}\)
  7. \(4\frac{7}{24}\)
  8. \(1\frac{28}{45}\)
  9. \(\frac{17}{14}\)
  10. \(1\frac{11}{15}\)