Find the equivalent fraction in the group: 3 4 , 5 7 , 15 21

Given, The fractions are 3 4 , 5 7 , 15 21 . Equivalent fractions are different fractions that equal the same number. The numerator and the denominator of a fraction must be multiplied or divided by the same non-zero whole number in order to have equivalent fractions. Let us consider the first two fractions 3 4 and 5 7 . The above fractions are not equivalent as the respective numerators and denominators are co-prime to each other. Let us now consider the fractions 5 7 and 15 21 . The above fractions are equivalent as, 5 7 = 5 × 3 7 × 3 = 15 21 Now, let us consider 3 4 and 15 21 . If we take the numerators, 15 is a multiple of 3 but 21 is not a multiple of 4 . Hence, the required group is 5 7 and 15 21 .

Find the equivalent fractions in each group: 6 32 , 4 16 , 3 16 , 15 80

Given fractions are 6 32 , 4 16 , 3 16 , 15 80 . We know that, equivalent fractions are different fractions that are equal to the same number. The numerator and the denominator of a fraction must be multiplied or divided by the same non-zero whole number in order to have equivalent fractions. Let us consider the first three fractions 6 32 , 4 16 and 3 16 . The above group of fractions are not equivalent as 16 × 2 = 32 but 4 × 2 ≠ 6 . Also, 4 16 and 3 16 are like fractions as their denominators are same. Thus, 6 32 , 4 16 and 3 16 are not equivalent fractions. Now, let us consider 4 16 , 3 16 and 15 80 . The above group of fractions are not equivalent as, 4 16 and 3 16 are like fractions. Let us now consider the fractions 3 16 , 15 80 and 6 32 . The above fractions are equivalent as, 3 16 = 3 × 2 16 × 2 = 6 32 3 16 = 3 × 5 16 × 5 = 15 80 Thus, the required group is 3 16 , 6 32 and 15 80 .

Arrange in ascending order: 14 15 , 27 30 , 37 40

Given fractions are 14 15 , 27 30 and 37 40 . We now arrange the given fractions in ascending order which means smaller fraction to greater fraction. But the given fractions are unlike fractions where the denominators are different. We now make the denominators same by taking the LCM of the denominators. LCM of 15 , 30 and 40 is 120 . Now, 14 15 = 14 × 8 15 × 8 = 112 120 27 30 = 27 × 4 30 × 4 = 108 120 37 40 = 37 × 3 40 × 3 = 111 120 We now arrange the above like fractions in ascending order. For this, we compare the numerators. 108 < 111 < 112 Hence, the ascending order is as follows: 27 30 < 37 40 < 14 15

Arrange in ascending order: 6 13 , 1 3 , 10 26

Given fractions are 6 13 , 1 3 and 10 26 We now arrange the given fractions in ascending order, which means smaller fraction to greater fraction. But the given fractions are unlike fractions where the denominators are different. We now make the denominators same by taking the LCM of the denominators. LCM of 13 , 3 and 36 is 468 . Now, 6 13 = 6 × 36 13 × 36 = 216 468 1 3 = 1 × 156 3 × 156 = 156 468 10 26 = 10 × 18 26 × 18 = 180 468 We now arrange the above like fractions in ascending order. For this, we compare the numerators. 156 < 180 < 216 Hence, the ascending order is as follows: 1 3 < 10 26 < 6 13