Hello! Today we'll learn how to solve the chicken and rabbit cage problem. This is a fun math problem that even second-grade students can understand. We have chickens with 2 legs and rabbits with 4 legs in a cage, and we need to figure out how many of each animal there are.
Now let's learn the assumption method to solve this problem. Step one: assume all animals in the cage are chickens. Step two: calculate how many legs there would be if they were all chickens. Step three: compare the actual number of legs with our assumed number. This method makes the problem much easier to solve.
Let's work through a real example. We have 10 animals in a cage with a total of 26 legs. How many chickens and how many rabbits are there? First, assume all 10 animals are chickens. That would give us 10 times 2 equals 20 legs. But we actually have 26 legs, so 26 minus 20 equals 6 extra legs. These 6 extra legs come from rabbits, because each rabbit has 2 more legs than a chicken.
Now let's complete the solution. We found 6 extra legs, and since each rabbit has 2 more legs than a chicken, we divide 6 by 2 to get 3 rabbits. Then we subtract 3 rabbits from the total 10 animals to get 7 chickens. Let's verify: 7 chickens have 14 legs, 3 rabbits have 12 legs, and 14 plus 12 equals 26 legs total. Perfect! So the answer is 7 chickens and 3 rabbits.
小朋友们好！今天我们来学习一个有趣的数学问题叫做鸡兔同笼。这是一个古老的中国数学问题。我们会学到一个简单的方法来解决这类问题。准备好了吗？让我们开始吧！
现在让我们看一个具体的例子。有一个笼子里关着鸡和兔子。从上面数，一共有8个头。从下面数，一共有22条腿。问笼子里有几只鸡？几只兔子？我们知道每只鸡有1个头2条腿，每只兔子有1个头4条腿。
让我们用假设法来解决这个问题。第一步，假设8只动物都是鸡，那么腿数就是8乘以2等于16条。第二步，比较腿数。实际有22条腿，假设只有16条腿，差了6条腿。第三步，每只兔子比鸡多2条腿，所以兔子数量是6除以2等于3只。最后，鸡的数量是8减去3等于5只。
现在让我们验证一下答案是否正确。我们得到的答案是5只鸡和3只兔子。验证头数：5只鸡加3只兔子等于8个头，正确！验证腿数：5只鸡乘以2条腿等于10条腿，3只兔子乘以4条腿等于12条腿，总共10加12等于22条腿，也正确！所以我们的答案是对的。
让我们总结一下解题的方法。鸡兔同笼问题的解题口诀是：第一，假设全是鸡，算出腿数。第二，实际腿数减去假设腿数。第三，差数除以2得到兔子数量。第四，总数减去兔子数得到鸡的数量。第五，最后验证答案对不对。记住这个方法，以后遇到类似问题就不怕啦！你学会了吗？