Algebra II Homework Help

[V1rus.112]

PROJECT: CREATING AN ALGORITHM
Imagine working with a younger sibling or student who is having trouble multiplying by 9s. Create an algorithm to help the student learn how to do this easily. Then notate whether the given algorithm is equivalent or not. You may need to use outside resources to help you.

Basically, I was going to say something like, just add 9 to 0 however many times it's multiplied. The only real part I don't understand is in bold. How do I notate whether my "algorithm is equivalent or not?"

[MikeM709]

I like 9's because you can use your fingers easily.

[new420]

well i have no idea what an algorithm is, but just say if its multiplied by a number lower than 9, just take the number under it as 10s digit, minus the number from 9 and thats the ones digit. (9*6, 5, 9-5, 4). if its higher than 9, take the number under it, slap a 0 on it and minus however much from it to take the original number to 10 (9*22, 21, 210, 210-12). after that just write "I NOTATE THIS ALGORITHM...EQUIVALENT!" i have no idea if this helped whatsoever, but good luck with your shit.

[Reclaimer]

I like 9's because you can use your fingers easily.

I only have 8 fingers though ;)

[Spartennum117]

I like 9's because you can use your fingers easily.

I only have 8 fingers though ;)

toes.

Also, sorry i can't really help you :/

[Rob`]

I'm pretty sure that by "Then notate whether the given algorithm is equivalent or not. You may need to use outside resources to help you." they just mean explain why the algorithm works and that the teacher is cool with you using google to find an algorithm to use. I suspect the point of the exercise is to explain why the algorithm you give works, not to come up with an algorithm.

Personally I'd probably write out something similar to New420's method as step by step instructions - your method of "just add 9" sucks. - and then add notations explaining why it works.

Oh and when you don't understand the question you can just ask the teacher what the question is asking you to do. I don't think they'd murder you then and there.

well i have no idea what an algorithm is

A nerdy way of saying "set of instructions" only with if statements and loops and stuff, so perhaps a bit more complicated than your typical set of instructions.

[ImSpartacus]

Let y be a whole number [1,10]
Let x by the product of y and 9.

9y = x
10(y-1)+(10-y) = x

That works from numbers 1 through 10. After that, it gets too complicated to teach a kid, but still works.

The first term represents the number in the tens column. The second term represents the number in the ones column.

Given:
10(y-1)+(10-y) = x
9y = x

Subsitution:
10(y-1)+(10-y) = 9y

Algebraic Properties:
10(y-1)+(10-y) = 9y
10y-10 + 10-y = 9y
10-y + 10-10 = 9y
9y = 9y

[Gosu]

/wayovermyhead

[V1rus.112]

Ok, so I'm doing summer school, and now that I check back on the assignment the teacher changed the status from "Assigned" to "Skipped." Cool!

[ImSpartacus]

/wayovermyhead

9x1 = 09
9x2 = 18
9x3 = 27
9x4 = 36
9x5 = 45
9x6 = 54
9x7 = 63
9x8 = 72
9x9 = 81
9x10 = 90

Tens Place Digits:
0
1
2
3
4
5
6
7
8
9

Ones Place Digits:
9
8
7
6
5
4
3
2
1
0

See the pattern?

Using only "9" and the numbers [1,10], you can algebraically figure out how to get both the Ones Place Digit and the Tens Place Digit. Then you just add those two together and you get the correct number. If this were Excel, I could explain it a little better.

I'll try a different, but still equivalent, equation.

10(y-1) + 1(10-y) = 9y

These two numbers dictate the place. One marks the Tens Place, another marks the Ones Place.
These numbers are just there to take the y value and make it into the correct digit.
This is the desired result, 9 times the number. It just shows that they are equivalent.

[Gosu]

I can't believe I managed to pass maths, I've completely forgotten most of it.