Goals
1. Compare fractions of whole quantities, for instance, half of 50 and a third of 60.
2. Identify which fraction is larger between two whole numbers.
3. Order fractions in ascending or descending order.
4. Develop logical reasoning and mathematical skills.
5. Apply fraction concepts in everyday situations.
Contextualization
Fractions are woven into our daily lives, from sharing a pizza with friends to measuring out ingredients for a lekker recipe. Getting a grip on how to compare fractions helps us make better choices. Picture needing to divide a cake among your classmates and wanting to ensure that everyone gets a fair share. Knowing how to compare fractions will help you figure out the best way to divide it evenly.
Subject Relevance
To Remember!
Comparing Fractions with Different Denominators
When comparing fractions with different denominators, it’s key to find a common denominator. This makes it simpler to convert the fractions into equivalent forms with the same denominator, allowing for a straightforward comparison of their numerators.
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Find the least common multiple (LCM) of the denominators.
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Convert each fraction so they have the same denominator.
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Look at the numerators of the equivalent fractions to see which is larger or smaller.
Transforming Fractions to Common Denominators
Transforming fractions to a common denominator is a handy technique for making comparison easier. By ensuring fractions share the same denominator, it becomes visually clearer and mathematically simpler to determine which fraction holds a greater value.
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Calculate the LCM of the original denominators.
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Multiply the numerator and denominator of each fraction by the required factor to achieve the common denominator.
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Double-check if you’ve transformed correctly by comparing the resulting fractions.
Application of Fractions in Everyday Contexts
Fractions are regularly encountered in daily life, through cooking, construction, and finance. Knowing how to apply fractions in these scenarios ensures you make more accurate and informed choices.
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In cooking, to modify recipes and maintain the right proportions of ingredients.
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In building work, to figure out how much material is required for a project.
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In finance, to assess and compare the performance of different investments.
Practical Applications
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A civil engineer calculates how much cement and sand to mix for concrete, ensuring the correct ratios for the strength required.
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A chef tweaks a recipe to accommodate a different number of guests, adjusting ingredient amounts proportionally using fractions.
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A financial analyst assesses fractions to compare the performance of various investment options, aiding in making savvy investment choices.
Key Terms
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Fractions: Mathematical symbols representing parts of a whole.
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Denominator: The lower part of a fraction that indicates into how many equal parts the whole is divided.
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Numerator: The upper part of a fraction that shows how many of the whole parts are being considered.
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Least Common Multiple (LCM): The smallest common multiple of two or more numbers, used for identifying common denominators.
Questions for Reflections
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How might the skill of comparing fractions be useful in your daily life and future career?
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Can you think of a recent moment where you unconsciously used fractions? Describe it.
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In what ways can understanding fractions aid in making informed and fair decisions across different professional contexts?
Practical Challenge: Adjusting a Recipe
In this challenge, you'll step into the chef's shoes and adjust a recipe to serve a different number of people.
Instructions
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Select a recipe that you enjoy and list the ingredients along with their quantities.
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Determine how many people the original recipe is meant to serve.
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Decide how many people you wish to adjust the recipe for.
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Calculate the new amounts of each ingredient, using fractions to maintain the correct proportions.
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Compare your new fractions with the originals and explain your reasoning.
