Lesson Plan: Subtracting Fractions with Unlike Denominators

Lesson Summary

This 50-minute lesson focuses on subtracting fractions with unlike denominators and solving related word problems. Students will learn the process of finding common denominators and subtracting fractions step-by-step. The lesson incorporates various multimedia resources from Media4Math.com, including visual aids and interactive activities. A 10-question quiz with an answer key is provided at the end to assess student understanding of the concepts covered.

Lesson Objectives

• Subtract fractions with unlike denominators
• Solve word problems involving subtraction 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

• Adding fractions with unlike denominators
• Subtracting fractions with like denominators

Key Vocabulary

• Unlike denominators: Fractions with different bottom numbers
• Difference: The result of subtracting one number or fraction from another
• Common denominator: A common multiple of the denominators of two or more fractions
• Least common denominator (LCD): The smallest common denominator for a set of fractions

Multimedia Resources

• A collection of fraction definitions: https://www.media4math.com/Definitions--Fractions
• A collection of video definitions on the topic of fractions: https://www.media4math.com/MathVideoCollection--FractionsVocabulary
• A slide show of definitions on the topic of fractions: https://www.media4math.com/library/slideshow/fraction-definitions

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.

• Students use calculators to convert fractions to decimals and estimate differences of fractions with unlike denominators. 
• For example, estimate $\frac{3}{4}$ - $\frac{1}{3}$ by converting to decimals (0.75 - 0.33 ≈ 0.42).

Fraction Bars Activity

• Display images of fraction subtraction with unlike denominators using fraction bars. 
• Ask students to describe what they observe and how the visual representations help them understand the concept.

 $\frac{1}{3}$ - $\frac{1}{4}$ = $\frac{1}{12}$

Number Line Activity

• Provide students with blank number lines from 0 to 1. 
• Have them mark fractions like $\frac{1}{4}$, $\frac{1}{3}$, $\frac{1}{2}$, $\frac{2}{3}$, and $\frac{3}{4}$ on the number line. 
• Then, ask them to visualize and estimate differences between pairs of fractions, such as $\frac{3}{4}$ - $\frac{1}{3}$ or $\frac{2}{3}$ - $\frac{1}{4}$, using the number line.

$\frac{3}{4}$ - $\frac{1}{3}$ = $\frac{5}{12}$

Teach

Subtracting fractions with unlike denominators requires finding a common denominator before performing the subtraction. This process ensures that we are working with equivalent fractions that represent the same parts of a whole.

Steps for subtracting fractions with unlike denominators:

1. Find the least common denominator (LCD) of the fractions.
2. Convert each fraction to an equivalent fraction with the LCD.
3. Subtract the numerators while keeping the common denominator.
4. Simplify the result if necessary.

Example 1: Subtracting fractions where one denominator is a multiple of the other

Subtract: $\frac{3}{8}$ - $\frac{1}{4}$

• Step 1: The LCD of 8 and 4 is 8.
• Step 2: Convert $\frac{1}{4}$ to an equivalent fraction with denominator 8: $\frac{1}{4} = \frac{2}{8}$.
• Step 3: Subtract the numerators: $\frac{3}{8} - \frac{2}{8} = \frac{1}{8}$.

Therefore, $\frac{3}{8} - \frac{1}{4} = \frac{1}{8}$. Notice that in this example one denominator is a multiple of the other.

Example 2: Subtracting simple fractions with unlike denominators using fraction bars

Subtract: $\frac{3}{4}$ - $\frac{1}{3}$ using fraction bars.

$\frac{3}{4}$ - $\frac{1}{3}$ =  $\frac{5}{12}$

You can also solve by finding the LCD:

• Step 1: Find the LCD of 4 and 3, which is 12.
• Step 2: Convert each fraction to an equivalent fraction with denominator 12: $\frac{3}{4} = \frac{9}{12}$, $\frac{1}{3} = \frac{4}{12}$.
• Step 3: Subtract the numerators: $\frac{9}{12} - \frac{4}{12} = \frac{5}{12}$.
• Step 4: The fraction $\frac{5}{12}$ is already in its simplest form.

Therefore, $\frac{3}{4} - \frac{1}{3} = \frac{5}{12}$.

Example 3: Subtracting an improper fraction by a proper fraction

Subtract: $\frac{7}{4}$ - $\frac{5}{8}$

• Step 1: Find the LCD of 4 and 8, which is 8.
• Step 2: Convert $\frac{7}{4}$ to an equivalent fraction with denominator 8: $\frac{7}{4} = \frac{14}{8}$.
• Step 3: Subtract the numerators: $\frac{14}{8} - \frac{5}{8} = \frac{9}{8}$.
• Step 4: Convert $\frac{9}{8}$ to a mixed number: $1\frac{1}{8}$.

Therefore, $\frac{7}{4} - \frac{5}{8} = 1\frac{1}{8}$.

Example 4: Real-world application

A quilter has $\frac{5}{8}$ yard of fabric and uses $\frac{3}{10}$ yard for a project. How much fabric is left?

• Step 1: Find the LCD of 8 and 10, which is 40.
• Step 2: Convert each fraction to an equivalent fraction with denominator 40: $\frac{5}{8} = \frac{25}{40}$, $\frac{3}{10} = \frac{12}{40}$.
• Step 3: Subtract the numerators: $\frac{25}{40} - \frac{12}{40} = \frac{13}{40}$.

Therefore, the quilter has $\frac{13}{40}$ yard of fabric left.

Example 5: Real-world application

A baker has $\frac{9}{10}$ cup of sugar and uses $\frac{2}{5}$ cup for a recipe. How much sugar is left?

• Step 1: Find the LCD of 10 and 5, which is 10.
• Step 2: Convert $\frac{2}{5}$ to an equivalent fraction with denominator 10: $\frac{2}{5} = \frac{4}{10}$.
• Step 3: Subtract the numerators: $\frac{9}{10} - \frac{4}{10} = \frac{5}{10}$.
• Step 4: Simplify $\frac{5}{10}$ to $\frac{1}{2}$.

Therefore, the baker has $\frac{1}{2}$ cup of sugar left.

Multimedia Resources

Here are some tutorial videos that provide additional examples: 

• Adding Fractions by Using Equivalent Fractions I: https://www.media4math.com/library/39462/asset-preview
• Adding Fractions by Using Equivalent Fractions II: https://www.media4math.com/library/39461/asset-preview
• Adding Mixed Numbers by Using Equivalent Fractions: https://www.media4math.com/library/39460/asset-preview
• Subtracting Fractions Using Equivalent Fractions: https://www.media4math.com/library/39458/asset-preview
• Subtracting Mixed Using Equivalent Fractions: https://www.media4math.com/library/39456/asset-preview

Review

In this lesson, we focused on subtracting fractions with unlike denominators. Key takeaways include:

• To subtract fractions with unlike denominators, always find the least common denominator first.
• Convert fractions to equivalent fractions with the LCD.
• Perform the subtraction and simplify the result if necessary.

Review of Vocabulary:

• Unlike denominators: Fractions with different denominators, requiring adjustment to subtract.
• Least common denominator (LCD): The smallest common multiple of the denominators.
• Equivalent fractions: Fractions that represent the same value, used to align denominators.

Review Example 1: Subtracting fractions with unlike denominators

Subtract: $\frac{7}{12}$ - $\frac{1}{6}$

• Step 1: Find the LCD of 12 and 6, which is 12.
• Step 2: Convert $\frac{1}{6}$ to an equivalent fraction: $\frac{1}{6} = \frac{2}{12}$.
• Step 3: Subtract the numerators: $\frac{7}{12} - \frac{2}{12} = \frac{5}{12}$.

Therefore, $\frac{7}{12} - \frac{1}{6} = \frac{5}{12}$.

Review Example 2: Subtracting mixed numbers

Subtract: $2\frac{1}{4} - 1\frac{2}{3}$

• Step 1: Convert to improper fractions: $2\frac{1}{4} = \frac{9}{4}$, $1\frac{2}{3} = \frac{5}{3}$.
• Step 2: Find the LCD of 4 and 3, which is 12.
• Step 3: Convert to equivalent fractions: $\frac{9}{4} = \frac{27}{12}$, $\frac{5}{3} = \frac{20}{12}$.
• Step 4: Subtract the numerators: $\frac{27}{12} - \frac{20}{12} = \frac{7}{12}$.

Therefore, $2\frac{1}{4} - 1\frac{2}{3} = \frac{7}{12}$.

Review Example 3: Real-world application

Maria has $\frac{5}{6}$ of a cup of flour. She uses $\frac{1}{4}$ of a cup for a recipe. How much flour does she have left?

• Step 1: Find the LCD of 6 and 4, which is 12.
• Step 2: Convert to equivalent fractions: $\frac{5}{6} = \frac{10}{12}$, $\frac{1}{4} = \frac{3}{12}$.
• Step 3: Subtract the numerators: $\frac{10}{12} - \frac{3}{12} = \frac{7}{12}$.

Therefore, Maria has $\frac{7}{12}$ of a cup of flour left.

Multimedia Resources

• A collection of fraction definitions: https://www.media4math.com/Definitions--Fractions
• A collection of video definitions on the topic of fractions: https://www.media4math.com/MathVideoCollection--FractionsVocabulary
• A slide show of definitions on the topic of fractions: https://www.media4math.com/library/slideshow/fraction-definitions

Quiz

Directions: Solve the following problems involving subtraction of fractions with unlike denominators. Show your work and simplify your answers when possible.

1. $\frac{5}{6} - \frac{1}{3}$
2. $\frac{3}{4} - \frac{2}{5}$
3. $\frac{7}{8} - \frac{1}{2}$
4. $\frac{2}{3} - \frac{1}{4}$
5. $\frac{4}{5} - \frac{3}{10}$
6. $\frac{11}{12} - \frac{2}{3}$
7. $\frac{5}{8} - \frac{3}{16}$
8. $\frac{7}{6} - \frac{5}{12}$
9. $\frac{3}{5} - \frac{2}{15}$
10. $\frac{13}{20} - \frac{7}{10}$

Answer Key

1. $\frac{1}{2}$
2. $\frac{7}{20}$
3. $\frac{3}{8}$
4. $\frac{5}{12}$
5. $\frac{1}{2}$
6. $\frac{1}{4}$
7. $\frac{7}{16}$
8. $\frac{1}{4}$
9. $\frac{7}{15}$
10. $\frac{3}{20}$