As others have mentioned, there are faster, easier, more natural ways to get to the answer, ways that are also less likely to induce silly arithmetics mistakes. Here's one: 4¹¹ - 2 = 2¹¹ x 2¹¹ - 2 = 2048 x 2048 - 2 = 4194304 - 2 = 4194302 Even if you don't know the value of 2¹¹ by heart, it's pretty easy to figure out by starting from a lower power of 2 (one that you do know), and work your way back up to 2¹¹. For instance: 2⁵ = 32, 2⁶ = 64, 2⁷ = 128, [...] 2¹¹ = 2048. Solving the whole thing shouldn't take much more than a couple of minutes (if that), and is certainly not Harvard-level math.
Surely you don't think any of these problems are entrance exams to anywhere (well, U of Phoenix perhaps). That's just to hook you into the problem. Colleges have mostly made the SAT voluntary. You can't charge $82k a year and make folks jump through hoops for the privilege.
You should encourage your students/readers to improve their thinking power by your presentation and show them how shortcuts can be used.That is the duty of a teacher.
It is also the duty of the teacher to make sure that students master the fundamentals so that when the shortcut is introduced, it makes sense. Shortcuts without comprehension will lead to train wrecks.
note that 1024 is an easy number to multiply by because the parts of the multiplication are 1,2,4 which are all easy Note also that adding numbers in columns is easier than in rows. so 4^10= 1024² = 1024000 20480 4096 + -------- 1048576 ×4 -------- 4000000 . 160000 32000 2000 280 24 -------- 4194304 = 4¹¹ 4¹¹-2 = 4194302 3 minutes not 13
As others have mentioned, there are faster, easier, more natural ways to get to the answer, ways that are also less likely to induce silly arithmetics mistakes. Here's one:
4¹¹ - 2
= 2¹¹ x 2¹¹ - 2
= 2048 x 2048 - 2
= 4194304 - 2
= 4194302
Even if you don't know the value of 2¹¹ by heart, it's pretty easy to figure out by starting from a lower power of 2 (one that you do know), and work your way back up to 2¹¹. For instance: 2⁵ = 32, 2⁶ = 64, 2⁷ = 128, [...] 2¹¹ = 2048.
Solving the whole thing shouldn't take much more than a couple of minutes (if that), and is certainly not Harvard-level math.
Surely you don't think any of these problems are entrance exams to anywhere (well, U of Phoenix perhaps). That's just to hook you into the problem.
Colleges have mostly made the SAT voluntary. You can't charge $82k a year and make folks jump through hoops for the privilege.
4^11-2= 2^22-2= 2^10x2^10x2^2-2= 1024x1024x4-2= 1048576x4-2= 4194304-2= 4194302 ...[all people knows 2^10=1024]
That's how I soled it. This vido makes no sense. The Internet is a weird place where everyone can be an expert in anything.
You should encourage your students/readers to improve their thinking power by your presentation and show them how shortcuts can be used.That is the duty of a teacher.
Absolutely!✅💯😍🙏🤩🔥💪
It is also the duty of the teacher to make sure that students master the fundamentals so that when the shortcut is introduced, it makes sense. Shortcuts without comprehension will lead to train wrecks.
Incredible.
Thanks for your support and feedback. I'm glad you found it helpful 🙏💕💯🤩🥰
不把問題搞得千迴百折，如何表現老師的厲害？😂
🤣🤣🤣💪🔥
note that 1024 is an easy number to multiply by because the parts of the multiplication are 1,2,4 which are all easy
Note also that adding numbers in columns is easier than in rows.
so 4^10= 1024²
=
1024000
20480
4096 +
--------
1048576
×4
--------
4000000
. 160000
32000
2000
280
24
--------
4194304 = 4¹¹
4¹¹-2 =
4194302
3 minutes not 13
The power of knowing that 2^10 = 1024 is great
4^11 - 2
[(2^11) * (2^11)] - 2 👍
(2048 * 2048) - 2
4,194,304 - 2
4,194,302✅