ATIVIDADE 01 - MATEMÁTICA - 7º ANO

Summary

In this educational video, the teacher presents a problem about organizing the maximum number of baskets using various packages of food items, such as rice, flour, sugar, and coffee. The goal is to evenly distribute the items without any leftovers. The teacher introduces two key mathematical concepts: the Least Common Multiple (LCM) and the Greatest Common Divisor (GCD), demonstrating both techniques using examples. Ultimately, students learn how to apply the GCD to determine how many rice packages each basket should contain, concluding that each basket will have 4 packages of rice. The video serves as a practical application of these mathematical principles.

Takeaways

• 😀 The problem involves organizing food items into baskets without leaving any package behind.
• 😀 The goal is to find the maximum number of baskets that can be created using the available packages.
• 😀 The lesson focuses on two key concepts: Minimum Common Multiple (MCM) and Maximum Common Divisor (MCD).
• 😀 MCM is the smallest number that is a multiple of each of the given numbers, used to determine the size of the baskets.
• 😀 MCD is the largest number that divides each of the given numbers exactly, helping to figure out how many packages fit per basket.
• 😀 To find the MCM of 5, 8, and 10, lists of multiples are created, and the smallest common multiple (40) is identified.
• 😀 Another method to calculate MCM involves prime factorization, which in this case also results in 40.
• 😀 MCD can be found by listing the divisors of the numbers involved (24, 36, 18) and selecting the largest common divisor (6).
• 😀 Prime factorization can also be used to find the MCD, where the common prime factors (2 and 3) are multiplied to get 6.
• 😀 After calculating the MCD (48) between the rice packages and other food items, the number of rice packages per basket is found by dividing 192 by 48, resulting in 4 packages per basket.

Q & A

What is the main problem discussed in the video?

The main problem is how to distribute packages of rice, flour, sugar, and coffee into baskets without leaving any packages behind, and determining how many packs of rice should be placed in each basket.

What mathematical concepts are introduced in the video?

The video introduces the concepts of Least Common Multiple (LCM) and Greatest Common Divisor (GCD), which are used to solve the distribution problem.

How is the Least Common Multiple (LCM) defined in the video?

The LCM is defined as the smallest natural number that is a multiple of all given numbers simultaneously, excluding zero.

What are the two methods to find the LCM discussed in the video?

The two methods to find the LCM are listing the multiples of the numbers and using prime factorization.

How is the LCM of 5, 8, and 10 calculated in the video?

The LCM of 5, 8, and 10 is found by listing their multiples and identifying the smallest common multiple, which is 40.

How does prime factorization help in finding the LCM?

Prime factorization helps by breaking down the numbers into their prime factors, and then multiplying the highest powers of all prime factors involved to obtain the LCM.

What is the concept of the Greatest Common Divisor (GCD) explained in the video?

The GCD is the largest natural number that can divide each of the given numbers without leaving a remainder.

What are the two methods to find the GCD discussed in the video?

The two methods to find the GCD are listing the divisors of the numbers and using prime factorization.

How is the GCD of 24, 36, and 18 calculated in the video?

The GCD of 24, 36, and 18 is found by listing their divisors and identifying the largest common divisor, which is 6.

What is the solution to the problem of distributing the rice packages into baskets?

The solution is to use the GCD of the numbers representing the food packages, which is 48. Dividing 192 rice packages by 48 gives 4, meaning each basket will contain 4 packages of rice.