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The negative sign is so that the rate of your reactants is positive. We want to work with positive reaction rates, so we use the negative sign to make the reactants rate positive. Without the negative sign, we'd end up with a negative value because the [R] is decreasing. The final concentration is smaller than the initial for the reactant, and since rate deals with change in concentration, the rate for the reactants would be negative. We don't want that so we add the negative sign.
you are finding the average rate of consumption. So, because the reactants are being consumed the delta A or R is going to be negative. For chemical kinetics, the rate is always going to be positive, hence the negative sign.
The reason why we want rates to be positive is because it is the standard convention. It makes it easier to compare rates of formation and consumption to each other without the distraction of the negative sign. Another way to think about it is that we generally don't report our speed in daily life with negative numbers (which indicates direction), so we don't express rate with a negative number here as well.
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