Mastering Fractions: Types, Operations, and Real-Life
School
Seneca College**We aren't endorsed by this school
Course
MAT 111
Subject
Mathematics
Date
Dec 11, 2024
Pages
2
Uploaded by ChiefGalaxyOpossum52
Understanding FractionsWhat is a Fraction?A fraction represents a part of a whole. It consists of two numbers: the numerator (the top part) and the denominator (the bottom part). The numerator indicates how many parts are being considered, while the denominator indicates the total number of equal parts that make up the whole.Example: In the fraction \frac{3}{4} , 3 is the numerator (indicating 3 parts) and 4 is the denominator (indicating 4 equal parts in total).Types of Fractions1.Proper Fractions: The numerator is less than the denominator.•Example: \frac{2}{5} 2.Improper Fractions: The numerator is greater than or equal to the denominator.•Example: \frac{5}{3} or \frac{4}{4} 3.Mixed Numbers: A combination of a whole number and a proper fraction.•Example: 2 \frac{1}{2} Equivalent FractionsFractions that represent the same value but have different numerators and denominators are called equivalent fractions. To find equivalent fractions, multiply or divide both the numerator and denominator by the same non-zero number.Example:•\frac{1}{2} = \frac{2}{4} = \frac{3}{6} Simplifying FractionsTo simplify a fraction, divide both the numerator and the denominator by their greatest common divisor (GCD).Example:•Simplifying \frac{8}{12} :•GCD of 8 and 12 is 4.•\frac{8 \div 4}{12 \div 4} = \frac{2}{3} Operations with Fractions
1.Addition and Subtraction:•Same Denominator: Add or subtract the numerators and keep the denominator.•Example: \frac{2}{5} + \frac{1}{5} = \frac{3}{5} •Different Denominators: Find a common denominator, convert, then add or subtract.•Example: \frac{1}{4} + \frac{1}{6} •Common denominator is 12:•\frac{1}{4} = \frac{3}{12} •\frac{1}{6} = \frac{2}{12} •\frac{3}{12} + \frac{2}{12} = \frac{5}{12} 2.Multiplication:•Multiply the numerators and denominators.•Example: \frac{2}{3} \times \frac{4}{5} = \frac{8}{15} 3.Division:•Multiply by the reciprocal of the divisor.•Example: \frac{2}{3} \div \frac{4}{5} = \frac{2}{3} \times \frac{5}{4} = \frac{10}{12} = \frac{5}{6} (simplified)Applications of FractionsFractions are used in various real-life situations, such as cooking (measuring ingredients), construction (measuring lengths), and finance (calculating discounts or interest rates).Example Problems1.Adding Fractions:•\frac{3}{8} + \frac{1}{4} :•Convert \frac{1}{4} to \frac{2}{8} .•\frac{3}{8} + \frac{2}{8} = \frac{5}{8} .2.Subtracting Fractions:•\frac{7}{10} - \frac{1}{5} :•Convert \frac{1}{5} to \frac{2}{10} .•\frac{7}{10} - \frac{2}{10} = \frac{5}{10} = \frac{1}{2} .3.Multiplying Fractions:•\frac{3}{4} \times \frac{2}{5} = \frac{6}{20} = \frac{3}{10} (simplified).4.Dividing Fractions:•\frac{1}{2} \div \frac{3}{4} = \frac{1}{2} \times \frac{4}{3} = \frac{4}{6} = \frac{2}{3} (simplified).ConclusionUnderstanding fractions is fundamental in mathematics. Mastery of fractions enables individualsto perform calculations accurately and apply them in various contexts, from everyday tasks to advanced mathematical concepts.