Was really just trying to make her method from 44x60 work and thinking less about common sense
51x38
22:20 Hellomed: Peach: Make 51 equal to 61. Then 6x3x8.5x13
22:20 Hellomed: Closest I’ve gotten
22:20 Hellomed: 51x38
22:21 Hellomed: 1989 vs 19386x8.5=51
I say 3x13 without fully knowing why (Why peach?)
In your 44x60 you did 4x6x11x10
once you know the “trick” it’s easy. Care to explain?
OKAY FURTHER:
51x38
- 6 x 3 x 8.5 x 11
- to get rid of 1/2 make it 6x3x8x15
I did it like this
51x 38
(1x 8) + (1x 30) + (5 x 8 x 10) + (5× 3 x 100)
8+30+400+1500
1938
Factor what you can (without throwing decimals in)
If you can't factor further, multiply the individual numbers then add together like I did there ^
The blood on my hands covered the holes
I see it now this is just my doubling and halving method Xena.
Double 50, halve 38 and multiply.
And add 1 x 38.
This is a good observation, you can make a similar one about peaches.
What does it mean?
Hint: How many steps does it take to multiply n-digit numbers?
I see it now this is just my doubling and halving method Xena.
Double 50, halve 38 and multiply.
And add 1 x 38.
This is a good observation, you can make a similar one about peaches.
What does it mean?
Hint: How many steps does it take to multiply n-digit numbers?
It’s the equality property of equations (divide by two is same as multiplying by 1/2 right?)
Peach said:(1x 8) + (1x 30) + (5 x 8 x 10) + (5× 3 x 100)
8+30+400+150051x38
I’m honestly having trouble recognizing multiplying by 10 and 100. Could you illustrate this? Otherwise I might have had this method down pat.
Edit: I see 5 and 3 are in 100ths place and 1 and 8 in 10ths place
last edit on
1/18/2023 6:11:45 AM
Peach said:51x 38(1x 8) + (1x 30) + (5 x 8 x 10) + (5× 3 x 100)
8+30+400+1500
Med
I’m honestly having trouble recognizing multiplying by 10 and 100. Could you illustrate this? Otherwise I might have had this method down pat.
Edit: I see 5 and 3 are in 100ths place and 1 and 8 in 10ths place
last parentheses would be (50 x30) I factored that to (5 x 10 x 3 x 10) and just went ahead and multipled the 10s
10ths and 100ths place are for decimals (with a th). 5 and 3 are in the 10s place and 8 is in the 1s place
The blood on my hands covered the holes
last edit on
1/18/2023 12:09:14 PM
I see it now this is just my doubling and halving method Xena.
Double 50, halve 38 and multiply.
And add 1 x 38.
This is a good observation, you can make a similar one about peaches.
What does it mean?
Hint: How many steps does it take to multiply n-digit numbers?
It’s the equality property of equations (divide by two is same as multiplying by 1/2 right?)
I see it now this is just my doubling and halving method Xena.
Double 50, halve 38 and multiply.
And add 1 x 38.
This is a good observation, you can make a similar one about peaches.
What does it mean?
Hint: How many steps does it take to multiply n-digit numbers?
It’s the equality property of equations (divide by two is same as multiplying by 1/2 right?)
I'll just tell you.
Peaches and Xenas methods are fundamentally equivalent.
They can both be described via the expression ac10^n + 10^(n/2)[ad + bc] + bd
In Xenas case she is using her times tables but implicitly what is actually happening is that expression, where
a = 5, b = 1, c = 3, and d = 8.
They theoretically take the same amount of time to compute, that is n^2 time.
There are faster methods, each a little more schizo than the last, but there is one you can express similarly to the expression they are using.
You could compute via ac10^n + 10^(n/2)[(a + b)(c + d) - ac - bd] + bd
This expression looks similar, and even more complicated, but you'll notice that two of the multiplications are repeated - that is ac and bd are done twice. However, technically those extra multiplications would only take place once given you would just store those values in memory (your own or a computers). As such, you are actually reducing the number of necessary multiplications to just three instead of four by trading one for extra additions/subtractions and multiplication is technically a more costly operation.
This reduces the time-complexity to n^1.58.
If you want to learn more about this look into this wiki, this particular improvement is known as Karatsuba Multiplication.
last edit on
1/18/2023 6:32:16 PM
This is no more difficult than memorizing
— [-b+/-(b2-4ac)1/2]/2a and all of my Chemistry
if I had to I could do it.*
Sometimes with math you don’t need the explanation in words.
So we decided n above is #of digits to be multiplied
For ac10^n + 10^(n/2)[ad + bc] + bd
and 15x32
a=1 b=5 c=3 d=2 where n=2