Lesson Plan: Subtracting Mixed Numbers

Lesson Summary

This 50-minute lesson focuses on teaching students how to subtract mixed numbers with like and unlike denominators. Students will build on their understanding of fractions, mixed numbers, and borrowing concepts. Through hands-on activities, multimedia resources from Media4Math.com, and structured examples, students will master the subtraction of mixed numbers. The lesson concludes with a 10-question quiz and an answer key to assess understanding.

Lesson Objectives

  • Subtract mixed numbers with like and unlike denominators.
  • Solve word problems involving subtraction of mixed numbers.

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

  • Understanding of mixed numbers.
  • Subtracting fractions with like and unlike denominators.
  • Borrowing concept in subtraction.

Key Vocabulary

Multimedia Resources

 

 

Warm Up Activities

Choose from one or more of these activities:

Calculator Activity

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

  • Estimate the difference of two mixed numbers using the fraction calculator. 
  • With the Desmos calculator, use the round() formula.
  • Note the two ways of estimating the mixed number differences.

 

Fractions

 

Multimedia Slide Show

Use Media4Math’s Fraction Definitions Slide Show https://www.media4math.com/library/slideshow/fraction-definitions to introduce or review key fraction concepts.

Pizza Fractions Activity

Provide pizza fractions that model mixed numbers and ask students how to find the difference. For example, if there are  \(2 \frac{1}{2} \) pizzas and  \(1 \frac{1}{4} \) pizzas are eaten, how much is left? Use pizza fraction visual models to solve.

 

FractionsFractions

 

 To see the collection of pizza fraction clip art images, go to this collection: https://www.media4math.com/MathClipArtCollection--EquivalentFractionModelsPizzaSlices

 

 

Teach

Introduction

Explain that subtracting mixed numbers involves three steps:

  1. Subtract the fractional parts (after finding a common denominator, if needed).
  2. Subtract the whole number parts.
  3. Borrow from the whole number part if the fractional part of the minuend is smaller than that of the subtrahend.

Example 1: Subtracting with Like Denominators

Problem: \(4 \frac{3}{8} - 2 \frac{1}{8}\)

  1. Subtract the fractional parts: \( \frac{3}{8} - \frac{1}{8} = \frac{2}{8} \).
  2. Subtract the whole numbers: \(4 - 2 = 2\).
  3. Combine the results: \(2 \frac{2}{8}\).
  4. Simplify the fraction: \(2 \frac{1}{4}\).

Example 2: Subtracting with Unlike Denominators

Problem: \(5 \frac{2}{3} - 3 \frac{5}{6}\)

  1. Find a common denominator: The LCM of 3 and 6 is 6. 
  2. Rewrite the fractions: \( \frac{2}{3} = \frac{4}{6} \), \( \frac{5}{6} \) remains the same.
  3. Subtract the fractional parts: \( \frac{4}{6} - \frac{5}{6} \). Since \( \frac{4}{6} < \frac{5}{6} \), borrow 1 from the whole number (making it \(4\)) and convert it into \( \frac{6}{6} \). New fraction: \( (\frac{6}{6} + \frac{4}{6}) - \frac{5}{6} = \frac{5}{6} \).
  4. Subtract the whole numbers (remember that 1 was borrowed from the 5): \(4 - 3 = 1\).
  5. Combine the results: \(1 \frac{5}{6}\).

Example 3: Real-World Application

Problem: A baker has \(6 \frac{3}{4}\) cups of flour. After baking a cake, \(2 \frac{5}{8}\) cups are used. How much flour remains?

  1. Find a common denominator: The LCM of 4 and 8 is 8. 
  2. Rewrite the fractions: \( \frac{3}{4} = \frac{6}{8} \), \( \frac{5}{8} \) remains the same.
  3. Subtract the fractional parts: \( \frac{6}{8} - \frac{5}{8} = \frac{1}{8} \).
  4. Subtract the whole numbers: \(6 - 2 = 4\).
  5. Combine the results: \(4 \frac{1}{8}\) cups of flour remain.

Summary

Subtracting mixed numbers involves borrowing when necessary and ensuring fractions have a common denominator. Practice with real-world scenarios enhances understanding.

Multimedia Resources

 

Review

The review section revisits the key concepts and vocabulary introduced during the lesson. Begin by summarizing the steps for subtracting mixed numbers and addressing any common challenges students encountered. Reinforce the importance of ensuring fractions have a common denominator before subtraction and highlight the borrowing process when the fractional part of the minuend is smaller than the fractional part of the subtrahend.

Key Vocabulary Review

  • Mixed number: A number that consists of a whole number and a fraction.
  • Improper fraction: A fraction where the numerator is greater than or equal to the denominator.
  • Borrowing: The process of taking a unit from the whole number part of a mixed number when subtracting.
  • Difference: The result of subtracting one number or fraction from another.

Example 1

Problem: \(7 \frac{1}{4} - 3 \frac{3}{4}\)

  1. Because \(\frac{1}{4} < \frac{3}{4}\), borrow 1 from the whole number: \(7\) becomes \(6\), and \( \frac{1}{4} \) becomes \( \frac{5}{4} \).
  2. Subtract the fractions: \( \frac{5}{4} - \frac{3}{4} = \frac{2}{4} \).
  3. Subtract the whole numbers (recall that 1 is borrowed from 7): \(6 - 3 = 3\).
  4. Combine and simplify: \(3 \frac{2}{4}\) = \(3 \frac{1}{2}\).

Example 2

Problem: \(8 \frac{5}{6} - 4 \frac{1}{3}\)

  1. Find a common denominator: Rewrite \( \frac{1}{3} \) as \( \frac{2}{6} \).
  2. Subtract the fractions: \( \frac{5}{6} - \frac{2}{6} = \frac{3}{6} \).
  3. Subtract the whole numbers: \(8 - 4 = 4\).
  4. Combine and simplify: \(4 \frac{3}{6}\) = \(4 \frac{1}{2}\).

Example 3

Problem: \(6 \frac{2}{5} - 2 \frac{4}{5}\)

  1. Subtract the fractional parts. Since \( \frac{2}{5} <  \frac{4}{5}\), borrow 1. So \( \frac{2}{5}\) becomes So \( \frac{7}{5}\)
  2. Subtract the fractions: \( \frac{7}{5} - \frac{4}{5} = \frac{3}{5} \).
  3. Subtract the whole numbers (recall that 1 was borrowed from 6): \(5 - 2 = 3\).
  4. Combine: \(3 \frac{3}{5}\).

Multimedia Resources

 

 

Quiz

Directions: Subtract the following mixed numbers. Show your work.

  1. \(5 \frac{2}{5} - 3 \frac{1}{5}\)
  2. \(6 \frac{3}{4} - 4 \frac{2}{4}\)
  3. \(8 \frac{5}{6} - 2 \frac{1}{3}\)
  4. \(9 \frac{7}{8} - 5 \frac{4}{8}\)
  5. \(7 \frac{3}{5} - 4 \frac{2}{5}\)
  6. \(10 \frac{3}{4} - 8 \frac{5}{6}\)
  7. \(12 \frac{6}{8} - 7 \frac{5}{8}\)
  8. \(6 \frac{2}{3} - 3 \frac{4}{6}\)
  9. \(4 \frac{1}{2} - 2 \frac{3}{4}\)
  10. \(5 \frac{5}{8} - 3 \frac{6}{8}\)

Answer Key

  1. \(2 \frac{1}{5}\)
  2. \(2 \frac{1}{4}\)
  3. \(6 \frac{1}{2}\)
  4. \(4 \frac{3}{8}\)
  5. \(3 \frac{1}{5}\)
  6. \(1 \frac{11}{12}\)
  7. \(4 \frac{1}{8}\)
  8. \(2\)
  9. \(1 \frac{3}{4}\)
  10. \(1 \frac{7}{8}\)