Change 2 3 , 1 6 and 4 9 into like fractions with common denominator.

We find the common denominator by finding the LCM of denominators. Given fractions are 2 3 , 1 6 and 4 9 . 3 3 , 6 , 9 1 , 2 , 3 LCM = 3 × 2 × 3 = 18 Now, writing the fractions with denominator 18 , 2 3 = 2 × 6 3 × 6 = 12 18 1 6 = 1 × 3 6 × 3 = 3 18 4 9 = 4 × 2 9 × 2 = 8 18 Hence, the like fractions are 12 18 , 3 18 and 8 18 .

Change 2 3 , 1 6 and 4 9 into like fractions with common denominator.

We find the common denominator by finding the LCM of denominators. Given fractions are 2 3 , 1 6 and 4 9 . 3 3 , 6 , 9 1 , 2 , 3 LCM = 3 × 2 × 3 = 18 Now, writing the fractions with denominator 18 , 2 3 = 2 × 6 3 × 6 = 12 18 1 6 = 1 × 3 6 × 3 = 3 18 4 9 = 4 × 2 9 × 2 = 8 18 Hence, the like fractions are 12 18 , 3 18 and 8 18 .

Change 2 5 , 3 10 , 4 15 and 7 20 into like fractions with common denominator.

We find the common denominator by finding the LCM of denominators. Given fractions are 2 5 , 3 10 , 4 15 and 7 20 . 5 5 , 10 , 15 , 20 1 , 2 , 3 , 4 LCM = 5 × 4 × 3 = 60 Now, writing the fractions with denominator 60 , 2 5 = 2 × 12 5 × 12 = 24 60 3 10 = 3 × 6 10 × 6 = 18 60 4 15 = 4 × 4 15 × 4 = 16 60 7 20 = 7 × 3 20 × 3 = 21 60 Hence, the like fractions are 24 60 , 18 60 , 16 60 and 21 60 .

Arrange the fractions 1 4 , 1 8 , 3 16 in ascending order.

To arrange the given fractions in ascending order, we have to express the fractions as like fractions, i.e, fractions with same denominators. We find the common denominator by finding the LCM of denominators. Given fractions are 1 4 , 1 8 and 3 16 , 4 4 , 8 , 16 1 , 2 , 4 LCM = 4 × 2 × 4 = 32 Now, writing the fractions with denominator 32 , 1 4 = 1 × 8 4 × 8 = 8 32 1 8 = 1 × 4 8 × 4 = 4 32 3 16 = 3 × 2 16 × 2 = 6 32 . By inspecting the numerators we can write the like fractions in ascending order. The fractions in the ascending order are 4 32 , 6 32 , 8 32 . Hence, the ascending order of the given fractions are 1 8 , 3 16 , 1 4 .

Arrange the fractions 4 7 , 3 14 , 2 21 and 9 28 in ascending order.

To arrange the given fractions in ascending order, we have to express the fractions as like fractions, i.e, fractions with same denominators. We find the common denominator by finding the LCM of denominators. Given fractions are 4 7 , 3 14 , 2 21 and 9 28 , 7 7 , 14 , 21 , 28 2 1 , 2 , 3 , 4 1 , 1 , 3 , 2 LCM = 7 × 2 × 3 × 2 = 84 Now, writing the fractions with denominator 32 , 4 7 = 4 × 12 7 × 12 = 48 84 , 3 14 = 3 × 6 14 × 6 = 18 84 , 2 21 = 2 × 4 21 × 4 = 8 84 , 9 28 = 9 × 3 28 × 3 = 27 84 . By inspecting the numerators we can write the like fractions in ascending order. The fractions in the ascending order are 8 84 , 18 84 , 27 84 , 48 84 . Hence, the ascending order of the given fractions are 2 21 , 3 14 , 9 28 , 4 7 .

Insert a fraction between 3 7 and 2 13 .

Given fractions 3 7 and 2 13 , We get a fraction which lies between two given fractions by adding the numerator and denominator and making a new fraction with these two sums. Sum of the numerators = 3 + 2 = 5 , Sum of the denominators = 7 + 13 = 20 . Hence, the required fraction is 5 20 or 1 4 .

Insert a fraction between 7 25 and 3 5 .

Given fractions 7 25 and 3 5 , We get a fraction which lies between two given fractions by adding the numerator and denominator and making a new fraction with these two sums. Sum of the numerators = 7 + 3 = 10 , Sum of the denominators = 25 + 5 = 30 . Hence, the required fraction is 10 30 or 1 3 .