Answer:
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Step-by-step explanation:
1. Rational numbers are subset of the real numbers.
The given number [tex]-\frac{5}{3}[/tex] belongs to the set of rational numbers and real numbers.
2. First simplify [tex]\sqrt{49}[/tex] to obtain [tex]\sqrt{7^2}=7[/tex].
The natural numbers are subsets of whole numbers, integers and real numbers.
Therefore [tex]\sqrt{49}=7[/tex] belongs to the set of natural numbers [tex]\mathbb N[/tex],whole numbers [tex]\mathbb W[/tex], integers [tex]\mathbb Z[/tex], the rational numbers [tex]\mathbb Q[/tex] and the real numbers [tex]\mathbb R[/tex].
3. The given number is [tex]0.\bar 6[/tex].
We can rewrite this as [tex]0.\bar6=\frac{2}{3}[/tex].
Hence [tex]0.\bar 6[/tex] is a subset of the rational numbers [tex]\mathbb Q[/tex], and the real numbers [tex]\mathbb R[/tex]
4. The given number is [tex]\pi[/tex].
In decimals: [tex]\pi\approx 3.141592663589....[/tex].
This number does not terminate and /or recur.
It belongs to the set of irrational numbers, [tex]\mathbb P[/tex]
5. The given number [tex]-\frac{36}{4}=-9[/tex] is a subset of the integers [tex]\mathbb Z[/tex], the rational numbers [tex]\mathbb Q[/tex] and the real numbers [tex]\mathbb R[/tex].
6. The given number [tex]1.125=\frac{9}{8}[/tex] is a subset of the rational numbers [tex]\mathbb Q[/tex] and the real numbers [tex]\mathbb R[/tex].
7. See attachment
8. A number [tex]-\frac{1}{3}[/tex]and its additive inverse [tex]\frac{1}{3}[/tex], summing up to zero.
[tex]-\frac{1}{3}+\frac{1}{3}=0[/tex]......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.
[tex](9\cdot -4)\cdot 7=7\cdot (9\cdot -4)[/tex].......commutative property of multiplication.
10. Let [tex]a,b,c \in \mathbb R[/tex], then the distributive property of multiplication over subtraction says that:
[tex]a(b-c)=a\cdot b- a\cdot c[/tex]
[tex]6(2x-1)=6\cdot 2x-6\cdot 1[/tex]
11. Let [tex]a\in \mathbb R[/tex], then the identity property of multiplicatio says that, any real number multiplied by itself is the same number.
[tex]a\cdot 1=1\cdot a=a[/tex]
[tex]5x^2\cdot 1=5x^2[/tex]
