Aula 1 - Operações com números inteiros para o Banco do Brasil CESGRANRIO

Introduction

This tutorial provides a step-by-step guide on performing operations with integers, specifically tailored for the Banco do Brasil CESGRANRIO exam preparation. The material includes practical examples from previous exams and aims to enhance your mathematical skills, particularly in handling integer operations.

Step 1: Understanding Integer Operations

• Addition and Subtraction: Familiarize yourself with the basic rules of adding and subtracting integers.

  • Positive + Positive = Positive
  • Negative + Negative = Negative
  • Positive + Negative = Subtract the smaller value from the larger value, keep the sign of the larger.

• Multiplication and Division: Understand how to multiply and divide integers.

  • Positive × Positive = Positive
  • Negative × Negative = Positive
  • Positive × Negative = Negative
  • Division follows similar rules as multiplication.

Step 2: Practice with Real Problems

• Problem Example 1: From Cesgranrio 2016, consider a scenario where 9 people were invited to a basketball event. Use integer operations to analyze attendance:

  • Write down how many people attended versus how many were invited.

• Problem Example 2: From Cesgranrio 2014, a boy is on the eighth step of a staircase:

  • If he climbs 3 steps, how many steps does he have to climb to reach the top? Use integers to represent steps.

Step 3: Solving Coin Problems

• Example Problem: Pedro has 3 coins of 50 cents and 12 coins of 5 cents.
  • Calculate the total value:
    • Total from 50 cent coins: ( 3 \times 0.50 = R$ 1.50 )
    • Total from 5 cent coins: ( 12 \times 0.05 = R$ 0.60 )
    • Combine both values: ( 1.50 + 0.60 = R$ 2.10 )

Step 4: Analyzing Deposits

• Example Problem: Fernando deposited R$ 1,176.00 over three months.
  • Determine the average monthly deposit:
    • Average = Total Deposited / Number of Months = ( R$ 1,176.00 / 3 = R$ 392.00 )

Step 5: Working with Remainders

• Example Problem: If a number is divided by 6 and leaves a remainder of 2, find possible values for this number.
  • Represent the number as ( x = 6n + 2 ) where ( n ) is a non-negative integer.

Step 6: Adding Powers of Two

• Example Problem: Simplifying ( 2^{103} + 2^{102} ):
  • Factor out the common term:
    • ( 2^{102}(2 + 1) = 2^{102} \times 3 )

Step 7: Solving Real-world Problems

• Example Problem: Calculate the total amount of money that siblings Paulo, Rui, and Marcelo have together:
  • If they have R$ 470.00, each sibling can be represented by a variable, and you can set up equations based on any additional information provided.

Conclusion

This tutorial has provided a structured approach to mastering integer operations, showcasing practical applications through example problems. Continue practicing these concepts with various problems to strengthen your understanding and prepare effectively for the Banco do Brasil CESGRANRIO exam. Consider reviewing additional resources or engaging in practice exams for further preparation.