Fractions in Action: Applying Addition and Subtraction in Daily Life

Objectives

1. Understand addition and subtraction of fractions with like and unlike denominators.

2. Apply practical problem-solving involving fractions in everyday life.

3. Create problems using fractions to strengthen understanding.

Contextualization

Fractions are an essential part of mathematics that we use in various situations in our daily lives, such as in the kitchen when following recipes, dividing a restaurant bill among friends, or even calculating discounts on purchases. These operations of adding and subtracting fractions are fundamental for dealing with these situations accurately and effectively. For example, when following a recipe that calls for 1/2 cup of sugar and 1/4 teaspoon of salt, you are working with fractions. Similarly, when sharing a pizza among friends, you use fractions to ensure that everyone receives a fair share.

Relevance of the Theme

Understanding fractions is crucial in various professions and everyday situations. Engineers use fractions to make precise measurements in construction projects; chefs adjust recipes using fractions; and accountants apply fractions to calculate taxes and other finances. Understanding fractions can open doors to a wide range of careers and improve your skills in daily tasks. Therefore, mastering the operations of adding and subtracting fractions is essential not only for academic success but also for an efficient practical and professional life.

Addition of Fractions with Like Denominators

Adding fractions with like denominators is a simple process where you keep the denominator and add the numerators. This concept is fundamental for solving problems that involve equal parts of a whole.

• Keep the same denominator.

• Add only the numerators.

• Simplify the resulting fraction, if possible.

Addition of Fractions with Unlike Denominators

To add fractions with unlike denominators, it is necessary to find a common denominator before adding the numerators. This process involves using common multiples and can be applied in various practical situations.

• Find the least common multiple (LCM) of the denominators.

• Convert each fraction to have the common denominator.

• Add the numerators of the converted fractions.

• Simplify the resulting fraction, if possible.

Subtraction of Fractions with Like Denominators

Subtracting fractions with like denominators follows a process similar to addition. You keep the denominator constant and subtract the numerators, which is useful for solving problems that involve removing equal parts from a whole.

• Keep the same denominator.

• Subtract only the numerators.

• Simplify the resulting fraction, if possible.

Subtraction of Fractions with Unlike Denominators

To subtract fractions with unlike denominators, you must first find a common denominator. This process is essential for dealing with problems of removing parts that are not directly comparable.

• Find the least common multiple (LCM) of the denominators.

• Convert each fraction to have the common denominator.

• Subtract the numerators of the converted fractions.

• Simplify the resulting fraction, if possible.

Practical Applications

• Adjusting recipes in cooking: Converting ingredient measurements for different servings.
• Splitting bills: Calculating each individual's share in a shared bill.
• Engineering and construction: Making precise measurements in projects that require division and addition of parts.

Key Terms

• Fractions: Representation of a part of a whole.

• Numerator: The upper part of a fraction indicating how many parts we have.

• Denominator: The lower part of a fraction indicating into how many parts the whole is divided.

• Least Common Multiple (LCM): The smallest common multiple between two or more numbers, used to find common denominators.

Questions

• How can the ability to add and subtract fractions make your daily life easier?

• What professions do you know that regularly use fractions and how does that impact their work?

• Have you encountered difficulties in understanding any concept related to fractions? How can you overcome them?

Conclusion

To Reflect

In this summary, we explored how the addition and subtraction of fractions are applicable in both everyday situations and various professional contexts. Understanding these mathematical operations not only enhances our academic skills but also prepares us to tackle real challenges, such as adjusting culinary recipes, calculating bill splits, and making precise measurements in engineering projects. By mastering fractions, you will be better equipped to handle practical problems efficiently and collaboratively.

Mini Challenge - Adjusting Recipes: A Culinary Challenge

To consolidate your understanding of adding and subtracting fractions, you will adjust a recipe to serve a different number of people. This challenge will help you apply your knowledge of fractions in a practical and everyday context.

• Choose a recipe that uses fractions (e.g., 1/2 cup of sugar, 1/4 teaspoon of salt).
• Determine how many people the original recipe serves and how many people you want to adjust the recipe for.
• Calculate the new quantities of each ingredient, using addition and subtraction of fractions when necessary.
• Record each calculation step to arrive at the new measures.
• Share your adjusted recipe with colleagues or family and explain how you arrived at the results.
• For an extra challenge, try adjusting the recipe without a calculator and check your results.