Goals
1. Understand the addition and subtraction of fractions with both equal and different denominators.
2. Apply problem-solving skills to practical scenarios involving fractions in our daily life.
3. Create various fraction-based problems to enhance understanding.
Contextualization
Fractions play a critical role in our daily lives, whether it's while cooking in the kitchen, splitting a bill at a dhaba with friends, or figuring out discounts during a sale. For instance, when a recipe requires 1/2 cup of sugar and a pinch of salt, you're working with fractions. Likewise, when sharing a pizza or a cake with friends, fractions help ensure everyone enjoys their fair share.
Subject Relevance
To Remember!
Addition of Fractions with Equal Denominators
Adding fractions with equal denominators is quite simple—you retain the denominator and just sum the numerators. This is a basic concept necessary for solving problems involving equal parts.
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Retain the same denominator.
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Sum only the numerators.
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If possible, simplify the resulting fraction.
Addition of Fractions with Different Denominators
When adding fractions with different denominators, it's important to first establish a common denominator before adding the numerators. This method requires identifying common multiples and is useful in various real-life situations.
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Find the least common multiple (LCM) of the denominators.
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Convert each fraction to share the common denominator.
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Add the numerators of the adjusted fractions.
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If possible, simplify the resulting fraction.
Subtraction of Fractions with Equal Denominators
Subtracting fractions with equal denominators is similar to addition. Here, you keep the denominator constant and subtract the numerators, which is beneficial for addressing problems that involve taking away equal parts.
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Retain the same denominator.
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Subtract only the numerators.
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If possible, simplify the resulting fraction.
Subtraction of Fractions with Different Denominators
In order to subtract fractions with different denominators, you first need to find a common denominator. This process is crucial for situations where you're dealing with parts that aren’t directly comparable.
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Find the least common multiple (LCM) of the denominators.
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Convert each fraction to share the common denominator.
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Subtract the numerators of the adjusted fractions.
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If possible, simplify the resulting fraction.
Practical Applications
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Modifying recipes in cooking by adjusting ingredient measurements for varying servings.
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Sharing bills: Determining each person's contribution to a common bill.
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Engineering and construction: Ensuring precise measurements in projects that involve division and sum of parts.
Key Terms
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Fractions: A representation of a part of a whole.
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Numerator: The top part of a fraction indicating how many parts we possess.
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Denominator: The bottom part of a fraction indicating how many parts the whole is divided into.
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Least Common Multiple (LCM): The smallest common multiple among two or more numbers, used to determine common denominators.
Questions for Reflections
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In what ways can being proficient in adding and subtracting fractions simplify your daily activities?
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Can you name professions that regularly incorporate fractions into their work, and how does this impact their efficiency?
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Have you faced any hurdles in understanding fraction concepts? What strategies can you adopt to overcome them?
Adjusting Recipes: A Culinary Challenge
To solidify your grasp on adding and subtracting fractions, you will modify a recipe to cater to a different number of servings. This challenge will allow you to apply your understanding of fractions in an everyday context.
Instructions
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Select a recipe involving fractions (for instance, using 1/2 cup of sugar, 1/4 teaspoon of salt).
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Determine how many people the original recipe caters to and the new serving size you want.
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Calculate the new ingredient amounts, utilising addition and subtraction of fractions where necessary.
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Document each step of your calculations to reach the new ingredient quantities.
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Share your modified recipe with your classmates or family and describe how you calculated the new amounts.
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For an added challenge, try adjusting the recipe without using a calculator and double-check your results.
