Question

Which of the following pairs is equivalent? -20/12,5/3 16/-30,-8/15. -18/36,-20/44. 7/-5,-5/7

Answer 1

Step-by-step explanation:

(ii) 15 : 16 or 24 : 25

(iii) 4 : 7 or 5 : 8

(iv) 9 : 20 or 8 : 13

(v) 1 : 2 or 13 : 27

ANSWER:

(i) Writing the ratios as fractions, we have

3 : 4 = 34 and 9 : 16 = 916

Now, LCM of 4 and 16 = 16.

Making the denominator of each fraction = 16, we have

34 = 3 × 44 × 4 = 1216 and the other fraction = 916

Of 1216 and 916, clearly 1216>916.

Therefore, 34>916.

(ii) Writing the ratios as fractions, we have

15 : 16 = 1516 and 24 : 25 = 2425

Now, LCM of 16 and 25 = 400.

Making the denominator of each fraction = 400, we have

1516 = 15 × 2516 × 25= 375400 and the other fraction = 24 × 1625 × 16= 384400

Clearly, 384 > 375. So, 384400 > 375400.

Therefore, 2425>1516.

(iii) Writing the ratios as fractions, we have

4 : 7 = 47 and 5 : 8 = 58

Now, LCM of 7 and 8 = 56.

Making the denominator of each fraction = 56, we have

4× 87 × 8= 3256 and the other fraction = 5 × 78 × 7= 3556

Clearly, 36 > 32. So, 3556 > 3256.

Therefore, 58>47.

(iv) Writing the ratios as fractions, we have

9 : 20 = 920 and 8 : 13 = 813

Now, LCM of 20 and 13 = 260.

Making the denominator of each fraction = 260, we have

9× 1320 × 13= 117260 and the other fraction = 8 × 2013 × 20= 160260

Clearly, 160 > 117. So, 160260 > 117260.

Therefore, 813>920.

(v) Writing the ratios as fractions, we have

1 : 2 = 12 and 13 : 27 = 1327

Now, LCM of 2 and 27 = 54.

Making the denominator of each fraction = 54, we have

1× 272 × 27= 2754 and the other fraction = 13 × 227 × 2= 2654

Clearly, 27 > 26. So, 2754 > 2654.

Therefore, 12>1327.