Question

Name all sets to which each number belongs. -5/3

Answer 1

See explanations

Explanation:

1. Rational numbers are subset of the real numbers.

The given number
`-(5)/(3)` belongs to the set of rational numbers and real numbers.

2. First simplify
`√(49)` to obtain
`√(7^2)=7`.

The natural numbers are subsets of whole numbers, integers and real numbers.

Therefore
`√(49)=7` belongs to the set of natural numbers
`\mathbb N`,whole numbers
`\mathbb W`, integers
`\mathbb Z`, the rational numbers
`\mathbb Q` and the real numbers
`\mathbb R`.

3. The given number is
`0.\bar 6`.

We can rewrite this as
`0.\bar6=(2)/(3)`.

Hence
`0.\bar 6` is a subset of the rational numbers
`\mathbb Q`, and the real numbers
`\mathbb R`

4. The given number is
`\pi`.

In decimals:
`\pi\approx 3.141592663589....`.

This number does not terminate and /or recur.

It belongs to the set of irrational numbers,
`\mathbb P`

5. The given number
`-(36)/(4)=-9` is a subset of the integers
`\mathbb Z`, the rational numbers
`\mathbb Q` and the real numbers
`\mathbb R`.

6. The given number
`1.125=(9)/(8)` is a subset of the rational numbers
`\mathbb Q` and the real numbers
`\mathbb R`.

7. See attachment

8. A number
`-(1)/(3)`and its additive inverse
`(1)/(3)`, summing up to zero.

`-(1)/(3)+(1)/(3)=0`......The inverse property of addition.

9. The commutative property of multiplication says that; the order in which we multiply two real numbers does not matter.

`(9\cdot -4)\cdot 7=7\cdot (9\cdot -4)`.......commutative property of multiplication.

10. Let
`a,b,c \in \mathbb R`, then the distributive property of multiplication over subtraction says that:

`a(b-c)=a\cdot b- a\cdot c`

`6(2x-1)=6\cdot 2x-6\cdot 1`

11. Let
`a\in \mathbb R`, then the identity property of multiplicatio says that, any real number multiplied by itself is the same number.

`a\cdot 1=1\cdot a=a`

`5x^2\cdot 1=5x^2`