This guide provides useful resources for a wide variety of math topics. It is targeted at students enrolled in a math course or any other Centennial course that requires math knowledge and skills.

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- Basic Laws
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The **Commutative Law** states that even if we switch the order of the numbers, the resulting answer is the same. The commutative law holds for addition and multiplication.

The **Commutative Law of Addition**: a + b = b + a

`Example`

The **Commutative Law of Multiplication**: a × b = b × a

`Example`

The commutative law does not hold for subtraction or division.

For instance:

- 3 - 2 ≠ 2 - 3
- 2 ÷ 3 ≠ 3 ÷ 2

__Uses of Commutative Law__

It is sometimes easier to compute the answer to a multiplication or addition question by switching the order of numbers.

`Example`

For addition question: In the question 3 + 44 + 17, it is easier if we add 17 and 3 first, so 3 + 44 + 17 = 44 + 3 + 17 = 44+20 = 64

`Example`

For multiplication question: In the question, 5 × 10 × 6, it is easier if we multiply 6 and 5 first, so 5 × 10 × 6 = 10 × 5 × 6 = 10 × 30 = 300

The **Associative Law** states that even if we group numbers differently, the answer is still the same. The associative law holds for addition and multiplication.

The **Associative Law of Addition**: (a + b) + c = a + (b + c)

`Example`

The **Associative Law of Multiplication**: (a × b) × c = a × (b × c)

`Example`

The associative law does not hold for subtraction or division.

For instance,

- (5 - 10) - 4 = -5 - 4 = -9 but 5 - (10 - 4) = 5 - 6 = -1
- (8 ÷ 4) ÷ 2 = 2 ÷ 2 = 1 but 8 ÷ (4 ÷ 2) = 8 ÷ 2 = 4

__Uses of Associative Law__

It is sometimes easier to add or multiply if we group numbers differently.

`Example`

For addition: In the question, 23 + 45 + 5, it is easier to add 45 and 5 first, rather than adding 23 and 45 first. So, 23 + 45 + 5 = 23 + (45 + 5) = 23 + 50 = 73

`Example`

For multiplication: In the question, 15 × 5 × 2, it is easier to first multiply 5 and 2 rather than 15 and 5. So, 15 × 5 × 2 = 15 × (5 × 2) = 15 × 10 = 150

The **Distributive Law**: a × (b + c) = a × b + a × c and a × (b - c) = a × b - a × c.

`Example`

_{The distributive law }_{does not hold }_{for division. }

_{For instance, 16 ÷ (8 + 2) = 16 ÷ 10 = 1.6 but 16 ÷ 8 + 16 ÷ 2 = 2 + 8 = 10. }

_{The }_{correct way}_{ is 16 ÷ (8 + 2) = 16 ÷ 10 = 1.6.}

__Uses of Distributive Law__

A difficult multiplication question’s numbers can be broken up or combined, resulting in an easier multiplication question using the distributive law.

Example where we break up a number: In the question, 3 × 502, 502 can be broken up into (500 + 2) and so the question becomes, 3 × (500 + 2) and using the distributive law, this is equal to 3 × 500 + 3 × 2 = 1500 + 6 = 1506

Example where we combine numbers: In the question, 15 × 3 + 15 × 7, we can combine 3 and 7, so 15 × 3 + 15 × 7 = 15 × (3 + 7) = 15 × 10 = 150

- Last Updated: Oct 2, 2024 4:11 PM
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