Question

Измените неравенства так чтобы получились равенства. Сколько способов выполнения задания найдено? Дети выполнили задание с неравенством 6+2 <9 так: Оля 6+2=8 Саша 6+3=9 Катя 7+2=9 Денис 6+2=9-1 Кто из них прав? Как рассуждал каждый? Выберете одно неравенство. Измените его разными способами так,чтобы получились равенства.

Answer 1

Прав Денис, так как он нашел значение левой части и уровнял его с правой

Answer 2

Task: Changing Inequalities to Equations

To solve the given task, we need to change the inequality "6 + 2 < 9" into an equation. The children attempted to solve it in the following ways:

- Olya: 6 + 2 = 8 - Sasha: 6 + 3 = 9 - Katya: 7 + 2 = 9 - Denis: 6 + 2 = 9 - 1

Let's analyze each child's reasoning and determine who is correct.

1. Olya's reasoning: Olya added 6 and 2, which equals 8. However, the original inequality was "6 + 2 < 9," which means the sum should be less than 9. Since 8 is not less than 9, Olya's solution is incorrect.

2. Sasha's reasoning: Sasha added 6 and 3, which equals 9. This solution satisfies the original inequality "6 + 2 < 9" because 9 is equal to 9. Therefore, Sasha's solution is correct.

3. Katya's reasoning: Katya added 7 and 2, which equals 9. Similar to Sasha's solution, this also satisfies the original inequality "6 + 2 < 9" because 9 is equal to 9. Therefore, Katya's solution is correct.

4. Denis's reasoning: Denis subtracted 1 from 9, which equals 8. However, the original inequality was "6 + 2 < 9," which means the sum should be less than 9. Since 8 is not less than 9, Denis's solution is incorrect.

Based on the analysis, both Sasha and Katya provided correct solutions to the inequality "6 + 2 < 9" by changing it into an equation.

Now, let's choose one inequality and change it in different ways to obtain equations.

Let's take the inequality "3x + 5 > 10" as an example.

1. Changing the inequality into an equation by subtracting 5 from both sides: 3x + 5 - 5 = 10 - 5 This simplifies to: 3x = 5

2. Changing the inequality into an equation by dividing both sides by 3: (3x + 5) / 3 = 10 / 3 This simplifies to: x + 5/3 = 10/3

3. Changing the inequality into an equation by subtracting 10 from both sides: 3x + 5 - 10 = 10 - 10 This simplifies to: 3x - 5 = 0

These are just a few examples of how we can change an inequality into an equation. There are many other ways to manipulate inequalities to obtain equations, depending on the specific inequality and the desired outcome.

In conclusion, the children who correctly solved the inequality "6 + 2 < 9" by changing it into an equation were Sasha and Katya. Each child had their own reasoning, but only Sasha and Katya's solutions satisfied the original inequality. Additionally, we explored different ways to change an inequality into an equation using the example "3x + 5 > 10."