Which is greater? 2 3 of 2 2 3 or 2 7 of 7 9 .

We shall find the value of 2 3 of 2 2 3 and 2 7 of 7 9 and compare the two results (fractions). Thus, we have, 2 3 of 2 2 3 = 2 3 × 2 2 3 [Replace "of" by × sign] = 2 3 × 8 3 [Convert the mixed fraction into improper fraction] = 2 × 8 3 × 3 [Multiply the numerators together and the denominators together for multiplication of fractions] = 16 9 . And, 2 7 of 7 9 = 2 7 × 7 9 [Replace "of" by × sign] = 2 7 × 7 9 [Cancel the common factor from the numerator and the denominator] = 2 1 × 1 9 = 2 × 1 1 × 9 [Multiply the numerators together and the denominators together for multiplication of fractions] = 2 9 . Now, between the two fractions, 16 9 and 2 9 , we observe that their denominators are the same and 16 > 2 . Hence, 16 9 > 2 9 . [If denominators are the same, then the fraction having the greater numerator is greater] Therefore, 2 3 of 2 2 3 is greater than 2 7 of 7 9 .

Which is greater? 2 3 of 3 1 2 or 6 2 by 15 6 .

We shall find the value of 2 3 of 3 1 2 and 6 2 by 15 6 and compare the two results (fractions). Thus, we have, 2 3 of 3 1 2 = 2 3 × 3 1 2 [Replace "of" by × sign] = 2 3 × 7 2 [Convert the mixed fraction into improper fraction] = 2 3 × 7 2 [Cancel the common factor from the numerator and the denominator] = 1 × 7 3 × 1 [Multiply the numerators together and the denominators together for multiplication of fractions] = 7 3 . And, 6 2 by 15 6 = 6 2 ÷ 15 6 [Replace "by" by ÷ sign] = 6 2 × 6 15 [For division, multiply the dividend by the reciprocal of the divisor] = 6 2 × 2 × 3 3 × 5 [Cancel the common factor from the numerator and the denominator] = 6 × 1 1 × 5 [Multiply the numerators together and the denominators together for multiplication of fractions] = 6 5 . Now, the factors are 7 3 and 6 5 . We shall convert these two factors into factors with the same denominators. Thus, we have, 7 3 = 7 × 5 3 × 5 = 35 15 and 6 5 = 6 × 3 5 × 3 = 18 15 . Now, between the two fractions, 35 15 and 18 15 , we observe that their denominators are the same and 35 > 18 . Hence, 35 15 > 18 15 . [If denominators are the same, then the fraction having the greater numerator is greater] Thus, we have, 7 3 > 6 5 . Therefore, 2 3 of 3 1 2 is greater than 6 2 by 15 6 .

Which is greater? 4 5 - 2 3 of 4 6 or 6 2 by 4 3 of 2 5

We shall find the value of 4 5 - 2 3 of 4 6 and 6 2 by 4 3 of 2 5 and compare the two results (fractions). In the expression 4 5 - 2 3 of 4 6 , there are no brackets and "of" stands for multiplication. Hence, according to BODMAS rule, while solving this expression we shall perform the "of" operation ahead of " - " operation. Thus, we obtain, 4 5 - 2 3 of 4 6 = 4 5 - 2 3 × 4 6 [Replace "of" by × sign] = 4 5 - 2 3 × 2 × 2 2 × 3 [Cancel the common factors from the numerator and the denominator] = 4 5 - 2 × 2 3 × 3 = 4 5 - 4 9 [Multiply the numerators together and the denominators together for multiplication of fractions] = 36 - 20 45 [Now, perform the subtraction operation by finding LCM of the denominators] = 16 45 . In the expression 6 2 by 4 3 of 2 5 , there are no brackets and "of" stands for multiplication and "by" stands for division. Hence, according to BODMAS rule, while solving this expression we shall perform the "of" operation ahead of "by" operation. Thus, we obtain, 6 2 by 4 3 of 2 5 = 6 2 by 4 3 × 2 5 [Replace "of" by × sign] = 6 2 by 4 × 2 3 × 5 [Multiply the numerators together and the denominators together for multiplication of fractions] = 6 2 by 8 15 = 6 2 ÷ 8 15 [Replace "by" with ÷ sign] = 6 2 × 15 8 [For division, multiply the dividend by the reciprocal of the divisor] = 2 × 3 × 15 2 × 8 [Cancel the common factors from both the numerator and the denominator] = 45 8 [Multiply the remaining factors in the numerators together and the remaining factors in the denominators together] Now, the factors are 16 45 and 45 8 . We shall convert these two factors into factors with the same denominators. Thus, we have, 16 45 = 16 × 8 45 × 8 = 128 360 and 45 8 = 45 × 45 8 × 45 = 2025 360 . Now, between the two fractions, 128 360 and 2025 360 , we observe that their denominators are the same and 2025 > 128 . Hence, 2025 360 > 128 360 . [If denominators are the same, then the fraction having the greater numerator is greater] Thus, we have, 45 8 > 16 45 . Therefore, 6 2 by 4 3 of 2 5 is greater than 4 5 - 2 3 of 4 6 .