NÃO ERRE MAIS MATEMÁTICA! TODO CONCURSEIRO DEVE SABER. PARTE 1 DE 2. PASSO A PASSO.

Summary

In this math tutorial, Professor D provides helpful tricks for tackling fundamental and high school-level math problems, covering topics like the Least Common Multiple (LCM), Greatest Common Divisor (GCD), order of operations (PEMDAS), and percentage calculations. Through engaging examples, the professor explains how to identify when to use LCM and GCD, how to apply the correct order of operations, and how to calculate percentage changes. The video aims to equip viewers with practical techniques for effectively solving math problems in exams, emphasizing the importance of repetition and understanding key concepts.

Takeaways

• 😀 Understanding LCM (Least Common Multiple): The script explains that when two events (like buses passing at regular intervals) happen together, you can calculate the next time they will meet by finding the LCM of their intervals. In this case, the buses pass every 15 and 20 minutes, and their next meeting time is 60 minutes later.
• 😀 Identifying LCM Questions: Look for keywords such as 'together,' 'at the same time,' or 'next time' to identify LCM-related problems in math exams.
• 😀 Steps for Finding LCM: The script outlines a step-by-step process for finding the LCM of two numbers (15 and 20) by prime factorization, resulting in an LCM of 60 minutes.
• 😀 Maximizing Efficiency with Prime Factorization: The importance of breaking down numbers into prime factors to easily find their LCM is emphasized.
• 😀 Understanding GCD (Greatest Common Divisor): The script also teaches how to solve problems involving GCD, using the example of cutting three pieces of iron (15m, 24m, and 27m) into the largest possible pieces without leftover material.
• 😀 Identifying GCD Questions: Keywords such as 'largest possible size' or 'same size pieces' signal that a GCD approach should be used.
• 😀 Steps for Finding GCD: Prime factorization is again used for GCD, with the factors of 15, 24, and 27 being analyzed. The GCD is determined to be 3, which leads to determining the number of pieces that can be cut from the iron.
• 😀 Order of Operations (PEMDAS): The script emphasizes the importance of the correct order of operations in math problems. The acronym 'PENDAS' helps remember the sequence: Parentheses, Exponents, Multiplication/Division, Addition/Subtraction.
• 😀 Solving an Expression with PEMDAS: An example is given where the expression '2^3 x 4^2 + 8 - 2' is solved step-by-step, applying PEMDAS to get the final result of 1,042.
• 😀 Percentage Problems Simplified: The script explains a simple technique for solving percentage problems, such as finding 14% of 700 by using the formula: 'percentage ÷ 100 x number.' This leads to the solution of 98 for the given example.

Q & A

What is the key concept being explained in the beginning of the transcript?

The transcript starts by explaining how to solve a mathematical problem related to finding the least common multiple (LCM) of two bus schedules. It introduces the method of identifying problems involving 'simultaneously' or 'together' as LCM problems.

How do we recognize when to use the least common multiple (LCM) in a math problem?

The transcript suggests that when a math problem contains keywords such as 'simultaneously', 'together', or 'next time', it likely involves LCM. These words indicate that the problem is asking for the first time two events will occur together again.

How do you find the LCM of 15 and 20, as shown in the script?

To find the LCM of 15 and 20, the transcript demonstrates factorization: 15 factors into 3 × 5, and 20 factors into 2² × 5. The LCM is obtained by multiplying the highest powers of each prime factor, resulting in 2² × 3 × 5 = 60.

What does the script teach about the greatest common divisor (GCD)?

The script explains that the GCD is used when the problem asks for the 'largest possible' or 'same size' parts. It provides an example with the numbers 15, 24, and 27, showing how to find the GCD by dividing them by common factors like 3, and concluding that the GCD is 3.

What key strategy does the script suggest for solving problems involving percentages?

The key strategy for solving percentage problems is to compare with the original total. The script uses the example of Anderson's height increase, where the original height (1.65 meters) represents 100%, and the new height (1.98 meters) is compared to find the percentage increase.

What is the macete (trick) for solving problems involving the word 'por' in math?

The script teaches that 'por' in mathematical problems means 'division'. This helps identify the operation when calculating percentages or other fractions, as shown in the example with 14% of 700.

How is the order of operations explained in the script?

The script introduces the acronym 'PENDAS' to remember the order of operations: Parentheses, Exponents, Multiplication/Division (from left to right), and Addition/Subtraction (from left to right). It uses an example to illustrate the correct sequence of operations when simplifying a complex mathematical expression.

What does the 'PENDAS' acronym stand for, and how is it applied?

'PENDAS' stands for Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right). It is used to remember the order in which operations should be performed in a math expression. The script uses it to solve an example involving exponents, multiplication, and addition.

How does the script demonstrate solving a problem involving both multiplication and exponents?

The script shows how to solve a problem like 2³ × 4² + 8 - 2, by first resolving the parentheses, then calculating exponents (2³ = 8 and 4² = 16), followed by multiplication, and finally performing the addition and subtraction in the correct order.

How does the script explain calculating the percentage increase in Anderson's height?

The script explains that to calculate the percentage increase in Anderson's height, you compare the original height (1.65m) to the new height (1.98m). Using a rule of three, it finds that Anderson’s height increased by 120%, meaning a 20% increase from his original height.