Question 694524: (-2+5)2
Answer by RedemptiveMath(80)   (Show Source):
You can put this solution on YOUR website! This problem uses a property that we call the distributive property. If you distributed food in a cafeteria, you would give food to each person that walked through the line. This problem is no different. The number we distribute is the number that is outside the parentheses "(" and ")". You can think of that number as the food. The numbers inside the parentheses can be thought of as people. The that is outside the parentheses, or the food, affects every number inside the parentheses, or the people. The way the outside number affects the inside number is through multiplication. So, looking at our problem:
(-2+5)2 = -2 * 2 +5 * 2.
The asterisk "*" means multiplication. Here we can see that the number 2 (outside number, food) is multiplying the inside numbers -2 and 5 (people). If you remember the different properties of multiplying numbers, then the next part should be simple:
-2 * 2 +5 * 2 = -4 + 10.
When you use the distributive property, you MUST be cautious of the signs of the numbers inside the parentheses. The two signs you'll likely deal with are negative "-" and positive "+". As mentioned earlier, you must remember the properties of multiplying numbers such as positives and negatives. In the step above, I got -4 by multiplying -2 and 2. 2 times 2 is 4, and since one of the signs of the numbers is negative, the product must also be negative. That is why -2 times 2 gives us -4. (A negative times a positive equals a negative). Looking at the next multiplication piece, +5 times 2 gives us +10. Another way you could write the steps above is to let the outside number 2 keep its sign when we multiply:
(-2+5)2 = -2 * +2 +5 * +2 = -4 + 10.
We know the outside number to be positive because it has no sign written next to it. If a number is outside parentheses or has no number to the left of it, and if the number is positive, then the sign is usually just implied. That is, it is supposed to be common understanding that these numbers are positive. Negative numbers are given their signs a whole lot more than positive numbers are given theirs. So, what we've done is the distributive property. However, we are not done yet. Looking at the piece -4 + 10, we can see that there is still one more step to take: We must combine the two numbers together. Since we are dealing with addition and 10 (from +10) is greater than 4 (from -4),
-4 + 10 = +6 or 6 (you don't have to write the plus sign in your final answer).
Remember, the rule states that if you have an addition (or subtraction) problem between two numbers of different signs (positive and negative), then the resulting number (the sum from addition or difference from subtraction) takes the sign of the greater number in the operation. For example, in -4 + 10 the number 10 is greater than 4. Therefore, the resulting number 6 takes the sign of the biggest number between 10 and 4 (which is 10). 6 is positive.
NOTE: In the step -4 + 10, the two numbers are combined according to the sign of the second number. Since 10 is positive, we add the two terms together. If 10 was negative, we would subtract the two numbers together (-4 - 10 = -14).
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