Final answer:
The product of the two negative numbers −214 and −213 is positive 45562, according to the rule that the multiplication of two negative numbers results in a positive number.
Step-by-step explanation:
The student has asked to multiply two negative numbers, specifically −214 and −213. When multiplying two negative numbers, the result is always positive, according to the rule that states that the product of two negative numbers has a positive sign. So, to solve −214∙(−213), we multiply the absolute values of the numbers (ignoring the negative signs) and then assign a positive sign to the result.
The multiplication of the absolute values of −214 and −213 is 214∙2013. Therefore, the final answer is +45562, as both negative signs cancel each other out.
The rules for multiplication of integers are:
- When two positive numbers are multiplied, the result is positive (, 2x3 = 6).
- When two negative numbers are multiplied, the result is positive (, (-4) x (-3) = 12).
- When a positive and a negative number are multiplied, the result is negative (, (-3) x 2 = -6 or 4 x (-4) = -16).
Hence, the answer to the multiplication of −214 and −213 is +45562.