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Commutative Laws
The "Commutative Laws" say we can swap numbers over and still get the same answer ...
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... when we add:
a + b = b + a
... or when we multiply:
a × b = b × a
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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
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And we write it like this:
a × (b + c) = a × b + a × c
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Try the calculations yourself:
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3 × (2 + 4) = 3 × 6 = 18
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3×2 + 3×4 = 6 + 12 = 18
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Either way gets the same answer.
In English we can say:
We get the same answer when we:
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multiply a number by a group of numbers added together, or
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do each multiply separately then add them
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