I am trying to get better at math, the highest math I have is Algebra. For some reason I just can't do math. I have this homework helpers book about basic math and pre-algebra to help me understand math. Its talking about negative integers and distributive property. I was following along just fine until I got to this example it asked me to work out. 25x96 Now I thought I had this, so I went about to do this: (25x90) + (25x6) to get my answer but then I read how the book does it and I am completely lost. This is how the book did it: 25x96 = 25 x (100-4) = 25x100 + 25 x (-4) = 2,500 - 100 = 2,400 Where did they get this 100-4, I realize it equals 96 but what? Can anyone explain to me why it went by 100? What am I missing here?
yes, precisely. They needed an example for multiplying the opposit of a sum. the way you did was multyplying sums. Nothing wrong with it at all, but not what they wanted to explain. Actually the 100-4 makes sense. You can multiply by 100 by simply adding two 0es or shifting the decimal point (or in Europe the decimal comma) two digits to the right. This is a mechanical step that doesn't require much thinking and goes quickly. Then they substract the rest. Imagine their example as: there are 25 boxes with 100 cupcakes each. Someone steals 4 cupcakes from every box. How many are left? See? Now it makes perfect sense (and a belly ache for the thief LOL)
They are also demonstrating that numbers can be defined many ways. 96 can be defined as 100-4 (that's where they got it from, to answer your question). Of course, 96 could also be defined as 90+6 or 8(12), etc.
Because it's easier that way. That's how I figured it out in my own head before I looked at the answer in your post. I recognized from experience that 96 is a multiple of 4 (sometimes it's just a matter of practice and experience, which is why they have us memorize multiplication tables -- or at least they did when I was a kid), and when I was trying to remind myself what it factored down to, I realized, "Hey, 96 is only 4 less than 100, and I know that 100 divided by 4 is 25, so 96 divided by 4 must therefore be 24." Which was an easy way of figuring it out. (Otherwise I would've broken it down as 80 + 16, which is (20 + 4) x 4, and that would've given me the answer.) And that meant that 25 x 96 could also be written as 25 x (4 x 24), and you just move the parentheses and it's (25 x 4) x 24 = 100 x 24 = 2400. It's just an easier and more intuitive route to the solution. So that's two different points where it was possible to get to 100, and that made it much easier to solve those parts. We use base-10 mathematics because we have ten fingers, so anytime you can rearrange an equation to get a 10 or 100 or the like in there, it makes it easier to solve.
Yes. I have learned recently to not worry so much about finding an answer but learning the process and many different ways to look at it, one of the reasons I bought this book, saw it the reviews that it explained different ways to do math.
When I signed up I was told there would be no math. I think it's in the FAQ. My math score was so low on my SATs, I think they had to go negative.
This is very true. There are lots of "tricks" you can use - like knowing the digits of anything divisible by 3 will, themselves, sum up to something divisible by 3. For example: 1386486 Sum the digits: 36. Sum the digits again: 9. So it's divisible by 3. Similarly anything divisible by 9 can have its digits added up to something divisible by 9. (So 1386486 above is divisible by 9.) You learn them mostly through experience, but also sometimes through being taught them.
Book method makes perfect sense. It's stupid-easy to figure out what 100 x anything is, so you can get to 2500 instantly. Then, since you only needed 96 of them instead of 100, just take 4 back off, so -100. Breaking it into 90 and 6 doesn't help...
As thestrangequark said, the point isn't about results, the point is about understanding the process. Sure, having a car means you don't have to walk everywhere, but the existence of cars doesn't mean we don't need to learn how to walk.
^excellent comparism! Sorry but I just can't resist: according to this theory all Britons used to have 12 fingers and got two amputated since the 1960s.
We use 12 a lot because of lunar cycles (roughly 12 months in a year), and because it has a lot of divisors that make it mathematically useful (2, 3, 4, 6). Ten only factors into 2 and 5; it's actually a pretty bad number to choose as a numerical base. But we use it anyway, and it's because we have ten fingers and thus have a natural inclination to count in tens (which is not to say that we're incapable of doing otherwise; some cultures have had base-60 or base-20 mathematics, but those are still multiples of ten).
My ancestors were astucious enough to know that they have also 10 toes and they used a base 20 system that survived a little in my language and in the collective culture. For exemple, there is a hospital in Paris called les quinze-vingts (the 15-20) because it hosted 300 patients when it was created during the Middle Ages. Another exemple : 80 = quatre-vingt = 4-20 litterally.
But then you all started designing fabulous footwear and, alas, the base 20 system met its end. It's glorious, kitten-heeled end.