1. Describe two ways the numbers in each proportion are related. a) 5:20 = 125:500 b) 10:1 = 120:12 c) 75:25 = 300: 100
d) 1:3 = 16:48
2. Multiply between ratios to determine each value of n.
a) 2:5 = 8:n b) 2:n = 6:9 c) n:5 = 12:20
d) 8:n = 4:15
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3. Multiply within ratios to determine each value of z.
a) 4:8 = 3:2 b) 5:2 = 6:18 c) z: 14 = 10:20
d) 3:21 = z:56

Each value has been identified below.

Step-by-step 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.

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step-by-step explanation: