201 Likes, 2 Comments - Tribe Alive (@tribealive) on Instagram: “Friends that color block together stay together. We are the Service Employees International Union (SEIU), a union of about 2 million diverse members in healthcare, the public sector and property services who believe in and fight for our Vision for a Just Society: where all workers are valued and all people respected—no matter where we come from or what color we are; where all families and communities can thrive; and where we leave a better. Suppose you are given the two functions f (x) = 2x + 3 and g(x) = –x 2 + 5.Composition means that you can plug g(x) into f (x).This is written as '(f o g)(x)', which is pronounced as 'f-compose-g of x'.And '( f o g)(x)' means 'f (g(x))'.That is, you plug something in for x, then you plug that value into g, simplify, and then plug the result into f. Bind us together, Lord, bind us together With cords that cannot be broken. Bind us together, Lord, bind us together, Lord, Bind us together in love.
Wow! What a mouthful of words! But the ideas are simple.
Commutative Laws
The 'Commutative Laws' say we can swap numbers over and still get the same answer .
. when we add:
Example:
. or when we multiply:
a × b = b × a
Example:
Commutative Percentages!
Because a × b = b × a it is also true that a% of b = b% of a
Why 'commutative' . ?
Because the numbers can travel back and forth like a commuter.
Associative Laws
The 'Associative Laws' say that it doesn't matter how we group the numbers (i.e. which we calculate first) .
. when we add:
Delux mouse driver for mac. . or when we multiply: Blocs 3 2 4 cylinder.
(a × b) × c = a × (b × c)
Examples:
This: | (2 + 4) + 5 = 6 + 5 = 11 |
Has the same answer as this: | 2 + (4 + 5) = 2 + 9 = 11 |
This: | (3 × 4) × 5 = 12 × 5 = 60 |
Has the same answer as this: | 3 × (4 × 5) = 3 × 20 = 60 |
Uses:
Together 3 3 7 24
Sometimes it is easier to add or multiply in a different order:
What is 19 + 36 + 4?
![Together 3 3 7 21 Together 3 3 7 21](https://i.ytimg.com/vi/taJQMMCn638/maxresdefault.jpg)
19 + 36 + 4 = 19 + (36 + 4)
= 19 + 40 = 59
= 19 + 40 = 59
Or to rearrange a little:
What is 2 × 16 × 5?
2 × 16 × 5 = (2 × 5) × 16
= 10 × 16 = 160
= 10 × 16 = 160
Distributive Law
![Together Together](https://st3.idealista.pt/news/arquivos/styles/news_detail/public/2018-09/carros_0.jpg?sv=wmyJVjrj&itok=RAvHwf4e)
The 'Distributive Law' is the BEST one of all, but needs careful attention.
This is what it lets us do:
3 lots of (2+4) is the same as 3 lots of 2 plus 3 lots of 4
So, the 3× can be 'distributed' across the 2+4, into 3×2 and 3×4
And we write it like this:
a × (b + c) = a × b + a × c
Try the calculations yourself:
- 3 × (2 + 4) = 3 × 6 = 18
- 3×2 + 3×4 = 6 + 12 = 18
Either way gets the same answer.
In English we can say:
We get the same answer when we:
- multiply a number by a group of numbers added together, or
- do each multiply separately then add them
Uses:
Sometimes it is easier to break up a difficult multiplication:
Example: What is 6 × 204 ?
6 × 204 = 6×200 + 6×4
= 1,200 + 24
= 1,224
Or to combine: https://movavi-mac-cleaner-2-4-2.peatix.com.
Example: What is 16 × 6 + 16 × 4?
16 × 6 + 16 × 4 = 16 × (6+4)
= 16 × 10
= 160
We can use it in subtraction too:
Example: 26×3 - 24×3
We could use it for a long list of additions, too:
Example: 6×7 + 2×7 + 3×7 + 5×7 + 4×7
6×7 + 2×7 + 3×7 + 5×7 + 4×7
= (6+2+3+5+4) × 7
= 20 × 7
= 140
= (6+2+3+5+4) × 7
= 20 × 7
= 140
And those are the Laws . . .
. . . but don't go too far!
The Commutative Law does not work for subtraction or division:
Example:
- 12 / 3 = 4, but
- 3 / 12 = ¼
The Associative Law does not work for subtraction or division:
Example:
- (9 – 4) – 3 = 5 – 3 = 2, but
- 9 – (4 – 3) = 9 – 1 = 8
The Distributive Law does not work for division:
Example:
- 24 / (4 + 8) = 24 / 12 = 2, but
- 24 / 4 + 24 / 8 = 6 + 3 = 9
Summary
Together 3 3 7 25
Commutative Laws: | a + b = b + a a × b = b × a |
Associative Laws: | (a + b) + c = a + (b + c) (a × b) × c = a × (b × c) |
Distributive Law: | a × (b + c) = a × b + a × c |