ESA - MATEMÁTICA BÁSICA - AULA 7 - FRAÇÃO E MMC | CONDUTA MILITAR

Introduction

This tutorial covers the basics of fractions and the least common multiple (MMC), essential topics for students preparing for the Escola de Sargentos das Armas (ESA) or the Escola Preparatória de Cadetes do Exército (ESPCEX). Understanding these concepts will help improve your mathematical skills and boost your confidence for exams.

Step 1: Understanding Fractions

• Definition of a Fraction: A fraction consists of two parts, the numerator (top number) and the denominator (bottom number).
• Types of Fractions:
  • Proper Fractions: Numerator is smaller than the denominator (e.g., 1/2).
  • Improper Fractions: Numerator is larger than or equal to the denominator (e.g., 5/4).
  • Mixed Numbers: A whole number combined with a proper fraction (e.g., 1 1/2).

Practical Tips

• Visualize fractions using pie charts or number lines to better understand their values.
• Always simplify fractions by dividing both the numerator and denominator by their greatest common divisor (GCD).

Step 2: Operations with Fractions

• Addition:

  • To add fractions, make sure they have a common denominator.
    1. Find the least common denominator (LCD).
    2. Convert each fraction to have this denominator.
    3. Add the numerators and keep the common denominator.

• Subtraction:

  • Follow the same steps as addition but subtract the numerators.

• Multiplication:

  • Multiply the numerators together and the denominators together.
    • Example: (\frac{a}{b} \times \frac{c}{d} = \frac{a \times c}{b \times d})

• Division:

  • Multiply by the reciprocal of the second fraction.
    • Example: (\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c})

Common Pitfalls to Avoid

• Forgetting to simplify fractions after performing operations.
• Confusing addition and multiplication of fractions; remember the different rules for each.

Step 3: Understanding the Least Common Multiple

• Definition: The least common multiple (MMC) of two or more numbers is the smallest number that is a multiple of each of the numbers.
• Finding MMC:
  1. List the multiples of each number.
  2. Identify the smallest common multiple.
  3. Alternatively, use the prime factorization method:
     • Factor each number into primes.
     • Take the highest power of each prime and multiply them together.

Example

• For the numbers 4 and 6:
  • Multiples of 4: 4, 8, 12, 16, 20...
  • Multiples of 6: 6, 12, 18, 24...
  • MMC is 12.

Conclusion

Mastering fractions and the least common multiple is crucial for success in mathematics, especially for exams like the ESA/ESPCEX. Practice these concepts regularly to build confidence. Consider exploring additional resources or practice exercises to further enhance your understanding. Good luck with your studies!