A mother bought two packs of sweets. One pack had 22 sweets, and the other had 18 sweets. She shared all the sweets equally between her two children. Which expression below tells you how many sweets each child received? 22 plus 18, 12 plus nine, 11 plus 10, or 11 plus nine?
We might expect in a question like this to be asked how many sweets each child received and then to give an answer in one number. But we can see that all four possible answers are additions. We don’t actually have one number as the answer. So, in other words, we’re being asked, how would you find the answer to the problem? Which addition would you use?
Let’s read through the problem again slowly to understand what it’s describing. The problem described a mother who’s bought two packets of sweets. We’re told that one pack had 22 sweets in it and the other had 18 sweets. Now, if we were being asked to find the total number of sweets that were in both packs, we know that we’d have to add the two numbers together, 22 plus 18.
But there’s another sentence in our problem that we need to consider. The mother shared all the sweets equally between her two children. So, instead of two whole packets, each of the children now receives half a packet each. Half of the first packet of sweets is equal to 22 divided by two. We know that half of 20 is 10. So, half of 22 must be 11; 11 plus 11 makes 22. Each child gets 11 sweets.
But there’s also a second pack to think about. This pack contains 18 sweets. And so, to find half of 18, we need to divide 18 by two. Each child gets the equivalent of 18 divided by two sweets. And we know 18 divided by two equals nine. Half of 18 is nine, and nine plus nine equals 18.
So, each child receives half of the first packet of sweets and also half of the second packet of sweets, 11 plus nine. And if we look at our list of possible answers, we can see 11 plus nine is there. The expression that tells us how many sweets each child received is equivalent to half of 22 plus half of 18, or in other words 11 plus nine.