Outline scenarios where contrasting quantities merge to produce 0 such as a hydrogen atom with 0 charge due to its differently charged particles. Comprehend p + q as a number |q| units away from p, towards positive/negative based on q's sign. Assert that a number and its inverse add up to 0 and use this to explain sums of rational numbers. Rational numbers subtraction can be understood as adding the negative of a number, and the gap between two points on a number line as the absolute value of their difference, this concept is applicable in practical scenarios.

Use operational properties as methods for adding and subtracting rational numbers. Extend the concept of multiplication from fractions to rational numbers, ensuring operational properties, specifically the distributive law, continue to hold. Use these principles to explain how rational number multiplication operates. Remember integers can be divided as long as the divisor isn't 0, and every integer division (with non-zero divisor) results in a rational number, this can be interpreted in real life situations.

Utilize operational rules as methods to multiply and divide rational numbers. Change a rational number into a decimal via long division; understand that the decimal of a rational number ends in 0s or repeats eventually. Apply