Final answer:
Option c) 8 + 10 can be rewritten as an addition problem of two integers with the same sign because both numbers are positive.
Step-by-step explanation:
To rewrite an addition problem with two integers of the same sign, we need to look for options that match the rules of addition. According to the given rules:
Based on these rules, option c) 8 + 10 can be rewritten as an addition problem of two integers with the same sign because both numbers are positive. When analyzing the question of which option could be rewritten as an addition problem of two integers with the same sign, we must consider the basic rules of addition for integers with different signs. When two positive numbers are added together, the sum is positive, and similarly, when two negative numbers are added together, the sum is negative.
For example:
Two positive numbers: 3 + 2 equals 5 (both numbers have a +ve sign, and the answer is also +ve).
Two negative numbers: -4 + (-2) equals -6 (both numbers have a -ve sign, and the answer is also -ve).
However, when numbers with opposite signs are added, we subtract the smaller number from the larger one, and the resulting sum takes on the sign of the larger number:
Oposite signs: -5 + 3 equals -2.
When dealing with subtraction, the operation can be converted into an addition problem by changing the sign of the number being subtracted. For instance, to subtract 3 from 5, we write it as 5 + (-3) which equals 2.
Now, applying this knowledge to the options provided, we can see that:
Option a), b) and d) don't represent addition problems explicitly.
Option c) 8 + 10 is a clear example of addition between two positive numbers, which can be rewritten as an addition problem with two integers with the same sign.
Thus, the correct option is c) 8 + 10, where two positive integers with the same sign (+) are being added to produce a positive result.