Question

verify the closure property addition and multiplication of rational numbers -5/7 and 8/9​

Answer 1

Answer:

Under addition :-

-8/9 + 3/5 = -40/45 + 27/45 = -30/45

3/5 + -8/9 = 27/45 + -40/45 = -30/45

Therefore it is closed under addition.

Under Subtraction :-

-8/9 - 3/5 = -40/45 - 27/45 = -67/45

3/5 + 8/9 = 27/45 + 40/45 = 67/45

Therefore it is not closed under subtraction.

Under Multiplication :-

-8/9 × 3/5 = -8/15

3/5 × -8/9 = -8/15

Therefore it is closed under subtraction.

Under Division :-

-8/9 ÷ 3/5 = -8/9 × 5/3 = -40/27

3/5 ÷ -8/9 = 3/5 × -9/8 = -27/40

Therefore it is not closed under division.

Hence the numbers are closed under commutative property in addition and multiplication.