Question

Сформулировать правило, которое связывает деление и умножение

Answer 1

Если одно число умножить на другое (например: 5*5=25) то если ответ разделить на любой множитель получится другой множитель.

Answer 2

The Rule Relating Division and Multiplication

The rule that relates division and multiplication is known as the inverse relationship between division and multiplication. This rule states that division is the inverse operation of multiplication, and multiplication is the inverse operation of division.

When two numbers are multiplied together, the result is called the product. The product can be divided by one of the numbers to obtain the other number. Similarly, when two numbers are divided, the result is called the quotient. The quotient can be multiplied by one of the numbers to obtain the other number.

In mathematical notation, the inverse relationship between division and multiplication can be expressed as follows:

If a × b = c, then c ÷ a = b and c ÷ b = a.

This means that if we multiply two numbers, a and b, to obtain a product c, we can divide c by either a or b to obtain the other number.

For example, let's consider the equation 6 × 2 = 12. According to the inverse relationship, we can divide 12 by either 6 or 2 to obtain the other number:

- 12 ÷ 6 = 2 - 12 ÷ 2 = 6

Similarly, if we have a division equation, we can multiply the quotient by either of the numbers to obtain the dividend.

It's important to note that the inverse relationship between division and multiplication holds true for real numbers, as well as for other number systems like rational numbers, integers, and fractions.

Example Application

To further illustrate the inverse relationship between division and multiplication, let's consider the following example:

Question: What is the value of 6 ÷ 2(1+2)?

To solve this expression, we need to follow the order of operations, which states that we should perform the operations inside parentheses first, then multiplication and division from left to right.

1. First, we evaluate the expression inside the parentheses: 1 + 2 = 3. 2. Next, we perform the multiplication: 2(3) = 6. 3. Finally, we perform the division: 6 ÷ 6 = 1.

Therefore, the value of 6 ÷ 2(1+2) is 1.

It's worth noting that this example can be subject to different interpretations due to the ambiguity of the expression. Different conventions and interpretations may yield different results. However, following the order of operations and applying the inverse relationship between division and multiplication, the result is 1.

Conclusion

The inverse relationship between division and multiplication states that division is the inverse operation of multiplication, and multiplication is the inverse operation of division. This means that if two numbers are multiplied together to obtain a product, the product can be divided by either of the numbers to obtain the other number. Similarly, if two numbers are divided, the quotient can be multiplied by either of the numbers to obtain the dividend.