Here are some cards. Positive 7.6, negative 7.6, positive 7.2, negative 7.2.
This question has a part a and part b. First, we’ll consider part a. For the equation below, choose a card such that the answer is as large as possible and calculate the answer. 2.5 plus blank.
We want to make this sum as large as possible. And we know that we’re dealing with addition. To make it as large as possible when we’re adding, we need to add the largest card. That means we can eliminate the two negative cards and then ask which is larger, positive 7.6 or positive 7.2? 7.6 is larger than 7.2. The largest sum possible could be found by adding 7.6 to 2.5.
To add them, we can line them up vertically. Six plus five is 11. Write down one and carry a one. Seven plus two is nine plus the one we carried over is 10. Bring down the decimal. And we find our sum is 10.1.
Moving on to part b, we start with the same four cards. For the equation below, choose a card such that the answer is as large as possible and calculate the answer.
At first, it looks like nothing has changed. But then, we notice that in part b, we are subtracting a value from 2.5 instead of adding. Our goal hasn’t changed. We still want to make the value as large as possible. To maximize the result, we want to choose the smallest possible value. If we’re doing subtraction and we want to keep our value as large as possible, then we should subtract the smallest amount we can. That means that this time we won’t consider the positive options as the two negative options are less than the positive option.
Out of negative 7.6 and negative 7.2, which value is smaller? Remember when we consider these values on a number line, on the left of zero for negative numbers, the closer the value is to zero, the larger it is. This means that negative 7.2 is larger than negative 7.6. Since negative 7.6 is the smallest value possible, we’ll plug that in here and we have 2.5 minus negative 7.6. To subtract that negative, we can add 2.5 plus 7.6 which is the same result we found for part a, 10.1. 2.5 minus negative 7.6 equals 10.1.