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Principles3 (Management and control), 4 (Financial prudence) and (in so far as it relates to disclosing to theFCA) 11 (Relations with regulators) take into account the activities of members of afirm'sgroup. Compliance by another personto whom thePrinciplesapply withPrinciples3, 4 and 11 can also be.

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:

.. or when we multiply:

(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:

Sometimes it is easier to add or multiply in a different order:

What is 19 + 36 + 4?

19 + 36 + 4 = 19 + (36 + 4)
= 19 + 40 = 59

Or to rearrange a little:

What is 2 × 16 × 5?

2 × 16 × 5 = (2 × 5) × 16
= 10 × 16 = 160

Distributive Law

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 ?

Principle 3 Finance

6 × 204 = 6×200 + 6×4
= 1,200 + 24
= 1,224

Or to combine:

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

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

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

The Right to recognition before the law

Everyone has the right to recognition everywhere as a person before the law. Persons of diverse sexual orientations and gender identities shall enjoy legal capacity in all aspects of life. Each person’s self-defined sexual orientation and gender identity is integral to their personality and is one of the most basic aspects of self-determination, dignity and freedom. No one shall be forced to undergo medical procedures, including sex reassignment surgery, sterilisation or hormonal therapy, as a requirement for legal recognition of their gender identity. No status, such as marriage or parenthood, may be invoked as such to prevent the legal recognition of a person’s gender identity. No one shall be subjected to pressure to conceal, suppress or deny their sexual orientation or gender identity.