CHECK IF THE GIVEN RATIOS ARE EQUIVALENT

A proportion is a statement that two quantities are equal.

Method 1 :

If two ratios are equal, then

Method 2 :

Multiply both parts of one of the ratio by some constant and check, we get the other ratio.

Method 3 :

Divide both parts of one of the ratio by some constant and check, we get the other ratio.

Which of the following pairs of ratios are equal?

(1)  16 : 20, 4 : 5

(2)  3 : 5, 21 : 35

(3) 2 : 7, 8 : 21

(4)  5 : 6, 30 : 36

(5) 12 : 16, 18 : 24

(6)  15 : 35, 21 : 56

(7)  18 : 27, 6 : 4

(8)  2 : 2 1/2 , 32 : 40

(9)  1 : 1  1/3, 15 : 20

(10)  4 : 6, 20 : 30 

1. Solution :

16 : 20, 4 : 5

2. Solution :

3 : 5, 21 : 35

=  3(7) : 5(7)

=  21 : 35

So, the given ratios are equal.

3. Solution :

2 : 7, 8 : 21

Product of extremes  =  Product of means

7(21)  =  7(8)

147  ≠  56

So, the given ratios are not equal.

4. Solution :

5 : 6, 30 : 36

Multiplying both parts of the first ratio by 6, we get

=  5(6) : 6(6)

=  30 : 36

We get the second ratio. So, they are equal ratios.

5. Solution :

12 : 16, 18 : 24

Divide the first ratio by 4, so we get

12/4 : 16/4  ==>  3 : 4

Divide the second ratio by 6, so we get

18/6 : 24/6  ==>  3 : 4

So, both are equal ratios.

6. Solution :

15 : 35, 21 : 56

Divide the first ratio by 5, so we get

15/5 : 35/5  ==>  3 : 7

Divide the second ratio by 7, so we get

21/7 : 56/7  ==>  3 : 8

So, they are not equal ratios.

7. Solution :

18 : 27, 6 : 4

Divide the first ratio by 9, so we get

18/9 : 27/9  ==>  2 : 3

Divide the second ratio by 2, so we get

6/2 : 4/2  ==>  3 : 2

So, they are not equal ratios.

8. Solution :

2 : 2 1/2 , 32 : 40

Let us change the mixed fraction into improper fraction.

2 : 2 1/2  ==>  2 : 5/2

Multiplying both parts by 2, we get

4 : 5

Divide both parts of the second ratio 32 : 40 by 8

=  32/8 : 40/8

=  4 : 5

We get the same answers. So, they are equal ratios.

9. Solution :

1 : 1  1/3  ==>  1 : 4/3

Multiplying both parts by 3, we get

3 : 4

Divide both parts of the second ratio 15 : 20 by 5, we get

=  15/5 : 20/5

=  3 : 4

So, they are equal ratios.

10. Solution :

4 : 6, 20 : 30 

Product of extremes  =  4(30)  ==> 120

Product of means  =  6(20)  ==> 120

So, the given ratios are equal ratios.

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