ADDING FRACTIONS WITH UNLIKE DENOMINATORS WORKSHEET

Problem 1 :

Add :

1/12 + 3/18

Problem 2 :

Add :

3/20 + 7/30

Problem 3 :

Add :

3/7 + 2/9

Problem 4 :

Add :

1/12 + 1/16

Problem 5 :

Add :

1/2 + 7/3 + 4/5

Problem 6 :

Add :

1/9 + 7/10 + 4/9

Detailed Answer Key

Problem 1 :

Add :

1/12 + 3/18

Solution :

The given two fractions are unlike fractions. Because, they have different denominators.

For 12 and 18, we have the following common divisors other than 1.

2, 3 and 6

So 12 and 18 are not co-prime.

In the next step, we have to find the LCM (Least common multiple) of 12 and 18.

LCM of (12 and 18) = 36

Now, make the denominators of both the fractions to be 36.

To make the denominator to be 36, we have to multiply the numerator and denominator of the first fraction by 3 and the second one by 2.

Then, we have

1/12 + 3/18 = 3/36 + 2/36

1/12 + 3/18 = (3 + 2) / 36

1/12 + 3/18 = 5 / 36

So, the sum of the two fractions is 5/36.

Problem 2 :

Add :

3/20 + 7/30

Solution :

The given two fractions are unlike fractions. Because, they have different denominators.

For 20 and 30, we have the following common divisors other than 1.

2, 5 and 10

So 20 and 30 are not co-prime.

In the next step, we have to find the L.C.M (Least common multiple) of 20 and 30.

LCM of (20 and 30) = 60

Now we have to make the denominators of both the fractions to be 60.

To make the denominator to be 60, we have to multiply the numerator and denominator of the first fraction by 3 and and for the second fraction by 2.

Then, we have

3/20 + 7/30 = 9/60 + 14/60

3/20 + 7/30 = (9 + 14) / 60

3/20 + 7/30 = 23 / 60

So, the sum of the two fractions is 23/60.

Problem 3 :

Add :

3/7 + 2/9

Solution :

The given two fractions are unlike fractions. Because, they have different denominators.

For 7 and 9, there is no common divisor other than 1.

So 7 and 9 are co-prime

Here, we have to apply cross multiplication method to add the two fractions.

To add the two fractions, we have to do the following three steps.

Step 1 :

Multiply the numerator of the first fraction by denominator of the second fraction.

Step 2 :

Multiply the numerator of the second fraction by denominator of the first fraction.

Step 3 :

Multiply the denominators of the two fractions.

When we do the above three steps, we will have

3/7 + 2/9 = (27 + 14) / 63

3/7 + 2/9 = 41 / 63

So, the sum of the two fractions is 41 / 63.

Problem 4 :

Add :

1/12 + 1/16

Solution :

The given two fractions are unlike fractions. Because, they have different denominators.

For 12 and 16, we have the following common divisors other than 1.

2 and 4

So 12 and 16 are not co-prime.

In the next step, we have to find the LCM (Least common multiple) of 12 and 16.

LCM of (12 and 16) = 48

Now, make the denominators of both the fractions as 48.

To make the denominator of both the fractions as 48 , we have to multiply the numerator and denominator of the first fraction by 4 and the second one by 3.

Then, we have

1/12 + 1/16 = 4/48 + 3/48

1/12 + 1/16 = (4 + 3) / 48

1/12 + 1/16 = 7 / 48

So, the sum of the two fractions is 7/48.

Problem 5 :

Add :

1/2 + 7/3 + 4/5

Solution :

The denominators of all the fractions are not same.

In this problem, we have more than two fractions.

If we have more than two fractions, we can use only L.C.M method.

In the next step, we have to find the L.C.M (Least common multiple) of 2, 3 and 5.

LCM of (2, 3 and 5) = 30

Now we have to make the denominators of all the three fractions to be 30.

To make the denominator to be 30, we have to multiply the numerator and denominator of the first fraction by 15, for the second fraction by 10 and for the third fraction by 6.

Then, we have

1/2 + 7/3 + 4/5 = 15/30 + 70/30 + 24/30

1/2 + 7/3 + 4/5 = (15 + 70 + 24) / 30

1/2 + 7/3 + 4/5 = 109 / 30

So, the sum of the two fractions is 109/30.

Problem 6 :

Add :

1/9 + 7/10 + 4/9

Solution :

The denominators of all the fractions are not same.

In this problem, we have more than two fractions.

If we have more than two fractions, we can use only LCM method.

In the next step, we have to find the LCM (Least common multiple) of 9, 10 and 9.

LCM of (9, 10 and 9) = 90

Now we have to make the denominators of all the three fractions to be 90.

To make the denominator to be 90, we have to multiply the numerator and denominator of the first fraction by 10, for the second fraction by 9 and for the third fraction by 10.

Then, we have

1/9 + 7/10 + 4/9 = 10/90 + 63/90 + 40/90

1/9 + 7/40 + 4/9 = (10 + 63 + 40) / 90

1/9 + 7/40 + 4/9 = 113 / 90

So, the sum of the two fractions is 113/90.