Mathematical operation

23 Sep

KEY 1. Order does not matter.

Commutative Law of Addition When adding numbers
a + b = b + a For example, 2 + 5 is the same as 5 + 2

Is 123 + 569 = 569 + 123 ?
Is 0.675 + 3.49 = 3.49 + 0.675 ?
Is 4.2 + 7.9 = 7.9 + 4.2 ?

Commutative Law of Multiplication When multiplying numbers
ab = ba For example, 2 x 5 is the same as 5 x 2

Is 4.2 x 7.9 = 7.9 x 4.2 ?
Is 123 x 569 = 569 x 123 ?
Is 0.675 x 3.49 = 3.49 x 0.675 ?

KEY 2. Can be group in any way.

Associative Law of Addition When adding numbers
a + ( b + c ) = ( a + b ) + c For example, (3 + 4) + 5 gives the same result as 3 + (4 + 5)

Is (4.3 + 2.6) + 7.2 = 4.3 + (2.6 + 7.2) ?

Associative Law of Multiplication When multiplying numbers
a(bc) = (ab)c For example, 3 x (4 x 5) gives the same result as (3 x 4) x 5

Is 20 × 32 × 5 = (20 × 5) × 32 ?
Is (0.675 × 3.49) × 1.1 = 3.49 × (0.675 × 1.1) ?
Is (4.2 × 7.9) × 2.9 = 7.9 × (4.2 × 2.9) ?

Note: Subtraction and division are NOT commutative or associative operations!

Distributive Law The Distributive Law provides a useful way of removing parentheses
a (b + c) = ab + ac 2(x+3) can be written as 2•x + 2•3 = 2x + 6. It also allows us to
“factor” an expression: 3x + 21 can be written as 3 • x + 3 • 7
which can then be written as 3(x + 7 )

4 × 19 + 6 × 19 = (4 + 6) × 19 = 10 × 19 = 190

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