Rational
Numbers

01 Identity

Identity Property

Addition

Adding 0 to any rational number leaves it unchanged.

12 +0 =0 + 12 = 12
0 is the additive identity

Multiplication

Multiplying any rational number by 1 leaves it unchanged.

12 ×1 =1 × 12 = 12
1 is the multiplicative identity
02 Inverse

Inverse Property

Addition (Additive Inverse)

Adding a number to its negative gives 0.

−12 + 12 = 0
½ and −½ are additive inverses

Multiplication (Reciprocal)

Multiplying a number by its reciprocal gives 1.

23 × 32 = 1
⅔ and 3/2 are multiplicative inverses
03 Commutative

Commutative Property

Addition

Changing the order of addition doesn't change the sum.

12 + 23 = 23 + 12
a/b + c/d = c/d + a/b

Multiplication

Changing the order of multiplication doesn't change the product.

12 × 23 = 23 × 12
a/b × c/d = c/d × a/b
04 Associative

Associative Property

Addition

Changing the grouping of addition doesn't change the sum.

( ab + cd ) + ef = ab + ( cd + ef )

Multiplication

Changing the grouping of multiplication doesn't change the product.

( ab × cd ) × ef = ab × ( cd × ef )
05 Closure

Closure Property

Addition

The sum of two rational numbers is always a rational number.

12 + 23 = 76
7/6 is still rational ✓

Multiplication

The product of two rational numbers is always a rational number.

12 × 23 = 13
1/3 is still rational ✓
Quiz

Quick Quiz

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