Answer:
Each value has been identified below.
Explanation:
(1) We have to describe two ways the numbers in each proportion are related;
(a) 5 : 20 = 125 : 500
One way of describing that the given ratios are in proportion is;
Product of means = Product of extremes
20
125 = 5
500
2500 = 2500
This shows that the given proportion is related.
Another way of describing that the given ratios are in proportion is;
As 5 : 20 = 125 : 500
We will check that;
is equal to
or not.

This shows that the given proportion is related.
(b) 10 : 1 = 120 : 12
One way of describing that the given ratios are in proportion is;
Product of means = Product of extremes
1
120 = 10
12
120 = 120
This shows that the given proportion is related.
Another way of describing that the given ratios are in proportion is;
As 10 : 1 = 120 : 12
We will check that;
is equal to
or not.

This shows that the given proportion is related.
(c) 75 : 25 = 300 : 100
One way of describing that the given ratios are in proportion is;
Product of means = Product of extremes
25
300 = 75
100
7500 = 7500
This shows that the given proportion is related.
Another way of describing that the given ratios are in proportion is;
As 75 : 25 = 300 : 100
We will check that;
is equal to
or not.

This shows that the given proportion is related.
(d) 1 : 3 = 16 : 48
One way of describing that the given ratios are in proportion is;
Product of means = Product of extremes
3
16 = 1
48
48 = 48
This shows that the given proportion is related.
Another way of describing that the given ratios are in proportion is;
As 1 : 3 = 16 : 48
We will check that;
is equal to
or not.

This shows that the given proportion is related.
(2) Now we have to determine each value of n in the following given ratios;
(a) 2 : 5 = 8 : n
As we know that Product of means = Product of extremes
5
8 = 2
n
40 = 2n
= 20
Hence, the value of n is 20.
(b) 2 : n = 6 : 9
As we know that Product of means = Product of extremes
n
6 = 2
9
6n = 18
= 3
Hence, the value of n is 3.
(c) n : 5 = 12 : 20
As we know that Product of means = Product of extremes
5
12 = n
20
60 = 20n
= 3
Hence, the value of n is 3.
(d) 8 : n = 4 : 15
As we know that Product of means = Product of extremes
n
4 = 8
15
4n = 120
= 30
Hence, the value of n is 30.
(3) Now we have to determine each value of z in the following given ratios;
(a) 4 : 8 = 3 : z
As we know that Product of means = Product of extremes
8
3 = 4
z
24 = 4z
= 6
Hence, the value of z is 6.
(b) 5 : z = 6 : 18
As we know that Product of means = Product of extremes
z
6 = 5
18
6z = 90
= 15
Hence, the value of z is 15.
(c) z : 14 = 10 : 20
As we know that Product of means = Product of extremes
14
10 = z
20
140 = 20z
= 7
Hence, the value of z is 7.
(d) 3 : 21 = z : 56
As we know that Product of means = Product of extremes
21
z = 3
56
21z = 168
= 8
Hence, the value of z is 8.