1 00:00:00,000 --> 00:00:02,133 16乘100就是16后边加两个0 2 00:00:00,000 --> 00:00:01,000 16乘10是160 3 00:00:00,000 --> 00:00:01,000 16乘2是32 4 00:00:00,000 --> 00:00:01,666 16乘5 早算好的 是80 5 00:00:00,000 --> 00:00:02,133 16乘50 就是16乘5 再乘个10 6 00:00:00,000 --> 00:00:01,000 16乘5是80 7 00:00:00,000 --> 00:00:01,400 16除1000是多少？ 8 00:00:00,000 --> 00:00:01,533 16除108是多少呢？ 9 00:00:00,000 --> 00:00:01,333 16除268是多少？ 10 00:00:00,000 --> 00:00:01,000 16除28 11 00:00:00,000 --> 00:00:01,000 2-1=1 12 00:00:00,000 --> 00:00:01,000 2乘了一个10 13 00:00:00,000 --> 00:00:01,000 8-0=8 10-8=2 14 00:00:00,000 --> 00:00:01,000 8-0=8 8-0=8 15 00:00:00,000 --> 00:00:01,133 8-0=8 8-2=6 5-3=2 16 00:00:00,000 --> 00:00:01,000 8-6=2 2-1=1 17 00:00:00,000 --> 00:00:01,000 80+5=85 85+1=86 18 00:00:00,000 --> 00:00:01,666 800太大了 320也太大 19 00:00:00,000 --> 00:00:02,066 800还是太大了 超过588了 20 00:00:00,000 --> 00:00:02,666 一开始可以给16取6和3两个乘数 21 00:00:00,000 --> 00:00:03,533 一直运算下去直到剩下的部分小于16为止 22 00:00:00,000 --> 00:00:03,133 不是非得求出小于268的16的最大倍数 23 00:00:00,000 --> 00:00:01,000 乘以5再乘10 24 00:00:00,000 --> 00:00:01,000 也就是- 25 00:00:00,000 --> 00:00:01,000 也就是乘50 26 00:00:00,000 --> 00:00:02,200 但最后的结果都是一样的 27 00:00:00,000 --> 00:00:01,200 你可能要问了 28 00:00:00,000 --> 00:00:03,133 假设我们只知道16的这两个乘法式子 29 00:00:00,000 --> 00:00:01,400 先是800的这部分 30 00:00:00,000 --> 00:00:02,200 再来看 16除588是多少呢？ 31 00:00:00,000 --> 00:00:01,800 剩下28 这个就简单了 32 00:00:00,000 --> 00:00:01,133 剩下余数是12 33 00:00:00,000 --> 00:00:03,933 只要保证写的数和16的乘积在268以内就可以了 34 00:00:00,000 --> 00:00:02,200 只要把右边的数都加起来 35 00:00:00,000 --> 00:00:02,266 可以返回头来看- 16乘5是80 36 00:00:00,000 --> 00:00:01,000 商1 37 00:00:00,000 --> 00:00:02,266 因为100乘16就是1600 太大了 38 00:00:00,000 --> 00:00:01,133 好 16乘50是800 39 00:00:00,000 --> 00:00:02,000 如何把被除数分解运算 40 00:00:00,000 --> 00:00:01,200 就用这个320吧 41 00:00:00,000 --> 00:00:01,000 就用这个吧 42 00:00:00,000 --> 00:00:01,400 就用这个试试吧 43 00:00:00,000 --> 00:00:02,200 希望大家能喜欢这个方法 44 00:00:00,000 --> 00:00:01,333 当然肯定不是10 45 00:00:00,000 --> 00:00:01,000 得800 46 00:00:00,000 --> 00:00:01,800 我是怎么知道的呢？ 47 00:00:00,000 --> 00:00:02,533 或者说 16乘以这两个数的10倍 48 00:00:00,000 --> 00:00:01,000 教我们 49 00:00:00,000 --> 00:00:01,000 然后28减16 50 00:00:00,000 --> 00:00:01,000 然后是320 51 00:00:00,000 --> 00:00:01,000 然后相减 52 00:00:00,000 --> 00:00:01,000 然后相减 53 00:00:00,000 --> 00:00:03,866 用5是因为800远比320更接近我们讨论的这个数 54 00:00:00,000 --> 00:00:01,866 直接用10吧 10乘16是160 55 00:00:00,000 --> 00:00:01,000 相减 56 00:00:00,000 --> 00:00:01,200 相减 8-0=8 6-6=0 57 00:00:00,000 --> 00:00:01,400 算的还是正确的 58 00:00:00,000 --> 00:00:01,000 结果也乘10 59 00:00:00,000 --> 00:00:01,600 结果就是50+20+10+5+1 60 00:00:00,000 --> 00:00:01,933 结果是-- 50+20=70 70+10=80 61 00:00:00,000 --> 00:00:01,000 肯定不是100 62 00:00:00,000 --> 00:00:01,000 试试5吧 63 00:00:00,000 --> 00:00:01,133 这一步剩下-- 64 00:00:00,000 --> 00:00:01,200 这一步剩下268 65 00:00:00,000 --> 00:00:02,000 这个估算得多接近呢？ 66 00:00:00,000 --> 00:00:02,000 这个估算是非常粗略的 67 00:00:00,000 --> 00:00:03,666 这么做的话 怎么知道16除1388到底是多少？ 68 00:00:00,000 --> 00:00:01,800 这就是结果 商86 余12 69 00:00:00,000 --> 00:00:01,000 这种方法 70 00:00:00,000 --> 00:00:02,800 这种方法不必求那个正好的答案 71 00:00:00,000 --> 00:00:01,800 这种方法的优点在于 72 00:00:00,000 --> 00:00:02,333 这边已经算过了16乘以5是80 73 00:00:00,000 --> 00:00:02,400 这边相应的结果可能不一样 74 00:00:00,000 --> 00:00:01,333 这里我可以写60 75 00:00:00,000 --> 00:00:02,466 那么 16除1000到底是多少呢？ 76 00:00:00,000 --> 00:00:01,933 那么-- 我换个颜色写-- 77 00:00:00,000 --> 00:00:01,466 那么13-8=5 剩下588 78 00:00:00,000 --> 00:00:01,466 那么16乘20就是320 79 00:00:00,000 --> 00:00:01,466 那么16乘50就是800 80 00:00:00,000 --> 00:00:01,800 这次的题目是16除1388 81 00:00:00,000 --> 00:00:01,200 我要做的就是 82 00:00:00,000 --> 00:00:03,200 首先给大家示范一下求商的传统做法 83 00:00:00,000 --> 00:00:02,600 然后再介绍一种用估算来求商 84 00:00:00,000 --> 00:00:01,000 的新方法 85 00:00:00,000 --> 00:00:03,600 那么一般拿到这个题 大家会先看 16除1商0 86 00:00:00,000 --> 00:00:01,400 然后接着向右看 87 00:00:00,000 --> 00:00:01,466 16除13是多少呢？ 88 00:00:00,000 --> 00:00:02,533 还是0 再往右看一位就是138了 89 00:00:00,000 --> 00:00:01,333 16是可以除138的 90 00:00:00,000 --> 00:00:01,600 那么商是多少呢？ 91 00:00:00,000 --> 00:00:01,066 可以先试试9 92 00:00:00,000 --> 00:00:02,000 计算的过程我写在右边 93 00:00:00,000 --> 00:00:01,333 16乘以9-- 6・9=54 94 00:00:00,000 --> 00:00:01,066 1乘9是9 9+5=14 95 00:00:00,000 --> 00:00:01,466 乘积是144 太大了 96 00:00:00,000 --> 00:00:01,266 比138大了 不行 97 00:00:00,000 --> 00:00:03,000 所以来试试8 乘以8应该就比138小了 98 00:00:00,000 --> 00:00:01,066 在上边写个8 99 00:00:00,000 --> 00:00:01,866 注意 这里是要用试的 100 00:00:00,000 --> 00:00:03,200 要保证最后写上的数字是正确无误的 101 00:00:00,000 --> 00:00:01,666 所以这里一定要写8 102 00:00:00,000 --> 00:00:01,000 8乘6是48 103 00:00:00,000 --> 00:00:01,066 8乘1是8 8+4=12 104 00:00:00,000 --> 00:00:01,400 所以8乘16得到128 105 00:00:00,000 --> 00:00:02,133 138-128 求得这一步的余数 106 00:00:00,000 --> 00:00:01,000 8-8=0 3-2=1 107 00:00:00,000 --> 00:00:01,133 两个1一减成0 108 00:00:00,000 --> 00:00:01,000 所以剩10 109 00:00:00,000 --> 00:00:02,800 但被除数中还有一个8 把8拿下来 110 00:00:00,000 --> 00:00:03,266 凑成了108 然后还是和刚才一样的步骤 111 00:00:00,000 --> 00:00:03,866 先把上一步的进位擦掉 免得影响之后的运算 112 00:00:00,000 --> 00:00:02,133 然后就是求16除108是多少 113 00:00:00,000 --> 00:00:02,000 大家可以大体估算一下 114 00:00:00,000 --> 00:00:02,933 肯定不是8 因为8乘16刚算过了是128 115 00:00:00,000 --> 00:00:03,466 所以是不是7呢？还是要在旁边运算一下 116 00:00:00,000 --> 00:00:01,466 16乘以7-- 6乘7是42 117 00:00:00,000 --> 00:00:01,066 1乘7是7 7+4=11 118 00:00:00,000 --> 00:00:01,000 乘积是112 119 00:00:00,000 --> 00:00:02,800 比108大 不合适 所以应该就是6了 120 00:00:00,000 --> 00:00:02,200 我们在旁边写的这些过程 121 00:00:00,000 --> 00:00:04,466 是为了确定商的每一位-- 通过验证发现这一位不是7 122 00:00:00,000 --> 00:00:03,333 所以在乘积不超过108的情况下 6应该是 123 00:00:00,000 --> 00:00:01,400 可取的最大的数 124 00:00:00,000 --> 00:00:01,000 6乘6是36 进3 125 00:00:00,000 --> 00:00:02,266 或者也可以说向十位送个3 126 00:00:00,000 --> 00:00:01,466 6乘1是6 6+3=9 9+3=12 127 00:00:00,000 --> 00:00:01,600 然后还是相减 8-6=2 128 00:00:00,000 --> 00:00:03,466 这里可以直接是10-9=1 当然也可以用借位 129 00:00:00,000 --> 00:00:03,200 把0向前借1凑成10 前边这个1就没有了 130 00:00:00,000 --> 00:00:01,000 10-9=1 余12 131 00:00:00,000 --> 00:00:03,466 我们不需要求小数 所以这样就算做完了 132 00:00:00,000 --> 00:00:01,866 因为16比12大 除不了12 133 00:00:00,000 --> 00:00:01,800 所以16除1388 商86 余12 134 00:00:00,000 --> 00:00:01,600 下边是得到的余数 135 00:00:00,000 --> 00:00:01,800 这么做是完全正确的 136 00:00:00,000 --> 00:00:03,400 这应该是你在学校里学到的求商的方法 137 00:00:00,000 --> 00:00:01,400 今天我要做的是 138 00:00:00,000 --> 00:00:03,200 给大家介绍一种做长除更有趣的方法 139 00:00:00,000 --> 00:00:01,600 还是以16除1388为例 140 00:00:00,000 --> 00:00:03,000 这种方法给了我们很多估算的空间 141 00:00:00,000 --> 00:00:02,000 或者说需要大家去猜测 142 00:00:00,000 --> 00:00:02,200 我们做的 就是不停的猜-- 143 00:00:00,000 --> 00:00:02,133 来试16乘各种数积是多少 144 00:00:00,000 --> 00:00:02,000 要做到乘积小于被除数 145 00:00:00,000 --> 00:00:02,600 同时也不是一位一位的向右看 146 00:00:00,000 --> 00:00:01,800 而是整体考虑被除数 147 00:00:00,000 --> 00:00:03,266 不过在做之前 我要先处理另外一件事 148 00:00:00,000 --> 00:00:02,400 这个对于我们解题非常重要 149 00:00:00,000 --> 00:00:02,200 先求一下16乘以2和16乘以5 150 00:00:00,000 --> 00:00:01,733 2和5我都是随便取的 151 00:00:00,000 --> 00:00:01,600 只是用来估算而已 152 00:00:00,000 --> 00:00:03,266 不一定非要这两个 随便两个数都可以 153 00:00:00,000 --> 00:00:02,400 以后我再示范用其他数字的 154 00:00:00,000 --> 00:00:01,000 16乘以2是32 155 00:00:00,000 --> 00:00:02,266 16乘以5- 6乘5加5乘10 50+30=80 156 00:00:00,000 --> 00:00:01,000 这两个结果 157 00:00:00,000 --> 00:00:02,600 在这边解题的时候要牢牢记住 158 00:00:00,000 --> 00:00:01,800 那么首先要考虑的是 159 00:00:00,000 --> 00:00:01,200 使劲猜就行了 160 00:00:00,000 --> 00:00:01,200 16除1388是多少 161 00:00:00,000 --> 00:00:01,000 或者说