**Adding fractions worksheets :**

Here we are going to see some practice questions on adding fractions.

"Adding two fractions with different denominators" is sometimes difficult job for some students who study math in school level.

(1) Add : 1 / 12 + 3 / 18

(2) Add : 3 / 20 + 7 / 30

(3) Add : 3 / 7 + 2 / 9

(4) Add : 1 / 2 + 7 / 3 + 4 / 5

(5) Add : 1 / 9 + 7 / 10 + 4 / 9

**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 L.C.M (Least common multiple) of 12 and 18.

L.C.M of (12 and 18) = 36

Now we have to 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 and for the second fraction by 2.

Then, we have

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

= (3 + 2) / 36

= 5 / 36

Hence, 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.

L.C.M 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

= (9 + 14) / 60

= 23 / 60

**Hence, 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-orime

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

= 41 / 63

**Hence, the sum of the two fractions is 41 / 63.**

**Problem 4 : **

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.

L.C.M 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

= (15+70+24) / 30

= (109) / 30

= 109 / 30

**Hence, the sum of the two fractions is 109/30.**

**Problem 5 : **

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 L.C.M method.

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

L.C.M 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

= (10+63+40) / 90

= (113) / 90

**Hence, the sum of the two fractions is 113/90**

After having gone through the stuff given above, we hope that the students would have understood "Adding fractions worksheets"

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