Sequential Percent Changes
成绩单
顺序百分比更改。所以这是关于当我们有百分比的增加和减少。
There are a few common mistakes involving percent increases and decreases and the test loves to exploit these common oversights.
They love to write problems where people make very predictable mistakes. These mistakes center on scenarios.
两个或更多的变化是按照顺序进行的。例如，你可能会有一定的价格上涨百分之二，并且 然后，员工会以一定的员工折扣购买，这样你就可以得到百分之百的上涨，百分之一的下降，他们是如何组合的？ 例如，这里有一个典型的问题。一件物品最初要花一百美元。
The beginning of the year, the price increased by 30%. After the increase, an employee purchased it with a 30% decrease, a 30% discount. What price did the employee pay? So pause the video right now, work on this on your own, and then restart. When you're ready. The first thing I'll say is that the answer is not $100.
这就是陷阱的答案。这是可预测的错误答案。 超过一半的人参加考试将guess that, and they will be wrong. 这是整个学科中最常见的错误。上下或下的百分比相同 then up, does not put you back in the same place.
People think, oh a 30% up, 30% down they cancel. They absolutely do not, you do not wind up back in the same place. We answer this using a product of multipliers. Though a, a 30% increase, that's a multiplier of 1.3, a 30% decrease is a multiplier by, of .7. And so, we just multiply 100 by each one of those multipliers.
So, 100*1.3*.7 gives us 91, and that's the actual price that the employ. Employee paid. Now this might be anti-intuitive for some people. Let's think about this. Starts out at 100, a 30% increase means it goes up to 130. Well then the employee comes along with a 30% discount, but they're not getting a 30% discount on the price of 100, they're getting a 30% discount on a price of.
130和30%的130大于100的30%，这就是为什么它下降的数量大于它上升的数量的原因， 这就是为什么员工最终支付的价格不到100美元。还有一个问题。 年初，一项商品价格上涨了30%。增加后，员工以40%的折扣购买。
雇员支付的价格是。换言之，比原价低多少百分比， what percent below the price before the increase. So, again pause the video, take a moment to work this out on your own. The first thing I'll talk about here is the mistake.
人们会说，常见的错误是，高达30%，然后下跌40%，30负40是负10%。 Must be a 10% decrease. Guaranteed, more than half, maybe even three quarters of the people who take the test, will fall into this trap. It's as if the test writers just set up a huge.
蝴蝶网。人们都会跑进去的。 In hordes. It's absolutely 100% predictable. How many people make this mistake. That's why it's so important to recognize this, and understand not to make it.
当您在一行中有两个或更多%的更改时。不要添加或减去百分比。 那永远是错误的。你永远不想增加或减掉百分比的增减。 相反，你做什么？当然，我们使用乘法器。
We always use. Use multipliers for percent increases and decreases. So a percent, a 30% increase that's a 1.3 multiplier. A 40% decrease that's a 0.6 multiplier. 我们只需把这两个乘法器相乘。它们乘到0.78。
0.78是22%的乘数。减少。 And so, this means that what we having going on here is a 22% decrease. The price that the employee paid, was 22% less than the original price. Here's another.
The price of a stock increased 20% in January, dropped 50% in February and increased 40% in March. So in other words, that's the first quarter of the year. Find the percent change for 这三个月期间，第一季度的百分比发生变化。所以，再次暂停这里的视频，看看你是否能解决这个问题。
我要说的第一件事是，当然是错误的答案，问题， the very predictable mistake that more than half the people who take the test will make, they're just gonna do plus 30 minus 50 plus 40. 它给我们正面10，所以一定是10%的增长。这是人们会犯的错误。
同样，一个非常可预测的错误，当测试作者能够写出一个有这样一个可预测错误的问题时，他们绝对喜欢它。 这就是为什么理解这个错误的本质是如此重要，所以你不会落入这个陷阱。 当然，我们还要用乘法器。乘数为20%，增加1.2。
50%的乘数下降，即0.5。乘数为40%，增加1.4%。 我们要把这三个乘以。为了简单起见，我先把最后一个也乘以。 .5，或一半。那是1.4给我的。
and then .7 times 1.2, gives me .84. That is the multiplier for a 16% decrease. And so that's what's happened here: for the first quarter of the year, the stock. Decreased 16%. 所以在这个话题中，理解错误的本质是非常重要的， 非常诱人的错误，以及理解正确的事情是做什么。
第一个错误是，增减相同的百分比是不可能的。把我们带回原来的起点。 Mistake number two, in a series of percent changes, never add and subtract the individual percent, that will be wrong 100% of the time. 相反，我们要做的是找出乘法器，把所有的乘法器相乘在一起。
阅读完整的成绩单
两个或更多的变化是按照顺序进行的。例如，你可能会有一定的价格上涨百分之二，并且 然后，员工会以一定的员工折扣购买，这样你就可以得到百分之百的上涨，百分之一的下降，他们是如何组合的？ 例如，这里有一个典型的问题。一件物品最初要花一百美元。
The beginning of the year, the price increased by 30%. After the increase, an employee purchased it with a 30% decrease, a 30% discount. What price did the employee pay? So pause the video right now, work on this on your own, and then restart. When you're ready. The first thing I'll say is that the answer is not $100.
这就是陷阱的答案。这是可预测的错误答案。 超过一半的人参加考试将guess that, and they will be wrong. 这是整个学科中最常见的错误。上下或下的百分比相同 then up, does not put you back in the same place.
People think, oh a 30% up, 30% down they cancel. They absolutely do not, you do not wind up back in the same place. We answer this using a product of multipliers. Though a, a 30% increase, that's a multiplier of 1.3, a 30% decrease is a multiplier by, of .7. And so, we just multiply 100 by each one of those multipliers.
So, 100*1.3*.7 gives us 91, and that's the actual price that the employ. Employee paid. Now this might be anti-intuitive for some people. Let's think about this. Starts out at 100, a 30% increase means it goes up to 130. Well then the employee comes along with a 30% discount, but they're not getting a 30% discount on the price of 100, they're getting a 30% discount on a price of.
130和30%的130大于100的30%，这就是为什么它下降的数量大于它上升的数量的原因， 这就是为什么员工最终支付的价格不到100美元。还有一个问题。 年初，一项商品价格上涨了30%。增加后，员工以40%的折扣购买。
雇员支付的价格是。换言之，比原价低多少百分比， what percent below the price before the increase. So, again pause the video, take a moment to work this out on your own. The first thing I'll talk about here is the mistake.
人们会说，常见的错误是，高达30%，然后下跌40%，30负40是负10%。 Must be a 10% decrease. Guaranteed, more than half, maybe even three quarters of the people who take the test, will fall into this trap. It's as if the test writers just set up a huge.
蝴蝶网。人们都会跑进去的。 In hordes. It's absolutely 100% predictable. How many people make this mistake. That's why it's so important to recognize this, and understand not to make it.
当您在一行中有两个或更多%的更改时。不要添加或减去百分比。 那永远是错误的。你永远不想增加或减掉百分比的增减。 相反，你做什么？当然，我们使用乘法器。
We always use. Use multipliers for percent increases and decreases. So a percent, a 30% increase that's a 1.3 multiplier. A 40% decrease that's a 0.6 multiplier. 我们只需把这两个乘法器相乘。它们乘到0.78。
0.78是22%的乘数。减少。 And so, this means that what we having going on here is a 22% decrease. The price that the employee paid, was 22% less than the original price. Here's another.
The price of a stock increased 20% in January, dropped 50% in February and increased 40% in March. So in other words, that's the first quarter of the year. Find the percent change for 这三个月期间，第一季度的百分比发生变化。所以，再次暂停这里的视频，看看你是否能解决这个问题。
我要说的第一件事是，当然是错误的答案，问题， the very predictable mistake that more than half the people who take the test will make, they're just gonna do plus 30 minus 50 plus 40. 它给我们正面10，所以一定是10%的增长。这是人们会犯的错误。
同样，一个非常可预测的错误，当测试作者能够写出一个有这样一个可预测错误的问题时，他们绝对喜欢它。 这就是为什么理解这个错误的本质是如此重要，所以你不会落入这个陷阱。 当然，我们还要用乘法器。乘数为20%，增加1.2。
50%的乘数下降，即0.5。乘数为40%，增加1.4%。 我们要把这三个乘以。为了简单起见，我先把最后一个也乘以。 .5，或一半。那是1.4给我的。
and then .7 times 1.2, gives me .84. That is the multiplier for a 16% decrease. And so that's what's happened here: for the first quarter of the year, the stock. Decreased 16%. 所以在这个话题中，理解错误的本质是非常重要的， 非常诱人的错误，以及理解正确的事情是做什么。
第一个错误是，增减相同的百分比是不可能的。把我们带回原来的起点。 Mistake number two, in a series of percent changes, never add and subtract the individual percent, that will be wrong 100% of the time. 相反，我们要做的是找出乘法器，把所有的乘法器相乘在一起。
