Mathematics, 01.09.2020 17:01 markmlg122

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

Answers: 2

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Answer from: buchaell000

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 $\times$ 125 = 5 $\times$ 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; $\frac{5}{125}$ is equal to $\frac{20}{500}$ or not.

$\frac{5}{125} = \frac{20}{500}$

$\frac{1}{25} = \frac{1}{25}$

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 $\times$ 120 = 10 $\times$ 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; $\frac{10}{120}$ is equal to $\frac{1}{12}$ or not.

$\frac{10}{120} = \frac{1}{12}$

$\frac{1}{12} = \frac{1}{12}$

This shows that the given proportion is related.

One way of describing that the given ratios are in proportion is;

Product of means = Product of extremes

25 $\times$ 300 = 75 $\times$ 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; $\frac{75}{300}$ is equal to $\frac{25}{100}$ or not.

$\frac{75}{300} = \frac{25}{100}$

$\frac{1}{4} = \frac{1}{4}$

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 $\times$ 16 = 1 $\times$ 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; $\frac{1}{16}$ is equal to $\frac{3}{48}$ or not.

$\frac{1}{16} = \frac{3}{48}$

$\frac{1}{16} = \frac{1}{16}$

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 $\times$ 8 = 2 $\times$ n

40 = 2n

$n=\frac{40}{2}$ = 20

Hence, the value of n is 20.

(b) 2 : n = 6 : 9

As we know that Product of means = Product of extremes

n $\times$ 6 = 2 $\times$ 9

6n = 18

$n=\frac{18}{6}$ = 3

Hence, the value of n is 3.

As we know that Product of means = Product of extremes

5 $\times$ 12 = n $\times$ 20

60 = 20n

$n=\frac{60}{20}$ = 3

Hence, the value of n is 3.

(d) 8 : n = 4 : 15

As we know that Product of means = Product of extremes

n $\times$ 4 = 8 $\times$ 15

4n = 120

$n=\frac{120}{4}$ = 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 $\times$ 3 = 4 $\times$ z

24 = 4z

$z=\frac{24}{4}$ = 6

Hence, the value of z is 6.

(b) 5 : z = 6 : 18

As we know that Product of means = Product of extremes

z $\times$ 6 = 5 $\times$ 18

6z = 90

$z=\frac{90}{6}$ = 15

Hence, the value of z is 15.

As we know that Product of means = Product of extremes

14 $\times$ 10 = z $\times$ 20

140 = 20z

$z=\frac{140}{20}$ = 7

Hence, the value of z is 7.

(d) 3 : 21 = z : 56

As we know that Product of means = Product of extremes

21 $\times$ z = 3 $\times$ 56

21z = 168

$z=\frac{168}{21}$ = 8

Hence, the value of z is 8.

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Answer from: Quest

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1. Describe two ways the numbers in each proportion are related. a) 5:20 = 125:500 b) 10:1 = 120:12...