Introduction aux Fractions

Introduction to Fraction of a Quantity

• A fraction represents a part of a whole.
• It consists of a numerator (top number) and a denominator (bottom number).
• The denominator represents the total number of equal parts the whole is divided into.
• The numerator represents the number of parts being considered.

Calculating a Fraction of a Quantity

• To find a fraction of a quantity, multiply the quantity by the fraction.
• For example, to find 1/3 of 12, multiply 12 by 1/3: (12 * (1/3)) = 4

Example scenarios and applications

• Sharing: If a pizza is cut into 8 slices, and you eat 2/8 of it, you've eaten 2 slices.
• Discounts: If a shirt is priced at $20 and there's a 25% discount, the discount is (20 * 25/100) = $5. Applying the discount means the final price is (20 - 5) = $15.
• Recipes: If a recipe calls for 3/4 cup of flour, and you want to make half the recipe, you need (3/4 * 1/2) = 3/8 cup of flour.

Different Types of Fractions

• Proper fractions: The numerator is smaller than the denominator (e.g., 2/3).
• Improper fractions: The numerator is greater than or equal to the denominator (e.g., 5/3).
• Mixed numbers: A combination of a whole number and a fraction (e.g., 1 2/3).

Converting Between Fractions, Decimals, and Percentages

• Fractions, decimals, and percentages are different ways to represent the same value.
• Converting between them involves understanding their relationship.

Solving Problems Involving Fractions of a Quantity

• Identify the given quantity: The whole amount.
• Identify the fraction: The part of the whole being considered.
• Multiply the quantity by the fraction: This results in the desired portion of the quantity.
• Example: Find 2/5 of 20. (20 * (2/5)) = 8

Key Considerations

• Ensure the fraction is in the simplest form.
• When dealing with mixed numbers, convert them to improper fractions before calculating.
• Pay close attention to the units involved in the problem statements.
• Fractions can represent parts of a quantity, rates, ratios, and proportions. They can be used in virtually any field that deals with divisions of amounts.

Simplifying Fractions

• Simplify fractions by dividing both the numerator and denominator by their greatest common divisor (GCD).
• This process makes the fraction easier to understand and work with while retaining the same value.

Word Problems

• Word problems that involve fractions of a quantity require careful reading and understanding of the problem situation to determine what the problem is asking – not just what numbers are given. Identify and translate the necessary components into a mathematical equation.
• It's critical to show your steps.