Operations with Unlike Fractions Worksheets - 15 Worksheets Library - Free Printable

To solve these problems, we need to add fractions that have different bottom numbers (denominators).

The Golden Rule: You can only add fractions directly if they have the same bottom number.

The Strategy:
1. Find a Common Denominator: Look at the two bottom numbers. Find a number that both of them can divide into evenly. Usually, you can just multiply the two bottom numbers together to find a common one.
2. Adjust the Fractions: Change both fractions so they have that new common bottom number. To do this, whatever you multiply the bottom by, you must also multiply the top (numerator) by.
3. Add: Once the bottom numbers are the same, just add the top numbers together. Keep the bottom number the same.
4. Simplify: If the answer can be made smaller (like turning 2/4 into 1/2), do that.

Let's solve them one by one:

1) 2/5 + 5/10
* Common Denominator: 10 (since 5 goes into 10).
* Change 2/5: Multiply top and bottom by 2 -> 4/10.
* Add: 4/10 + 5/10 = 9/10

2) 4/9 + 3/12
* Common Denominator: 36 (9 x 4 = 36, 12 x 3 = 36).
* Change 4/9: Multiply top and bottom by 4 -> 16/36.
* Change 3/12: Multiply top and bottom by 3 -> 9/36.
* Add: 16/36 + 9/36 = 25/36. (Cannot be simplified).
* Answer: 25/36

3) 1/4 + 3/5
* Common Denominator: 20 (4 x 5).
* Change 1/4: Multiply top and bottom by 5 -> 5/20.
* Change 3/5: Multiply top and bottom by 4 -> 12/20.
* Add: 5/20 + 12/20 = 17/20

4) 2/5 + 1/3
* Common Denominator: 15 (5 x 3).
* Change 2/5: Multiply top and bottom by 3 -> 6/15.
* Change 1/3: Multiply top and bottom by 5 -> 5/15.
* Add: 6/15 + 5/15 = 11/15

5) 2/5 + 3/10
* Common Denominator: 10.
* Change 2/5: Multiply top and bottom by 2 -> 4/10.
* Add: 4/10 + 3/10 = 7/10.
* Answer: 7/10

6) 5/14 + 3/7
* Common Denominator: 14 (7 goes into 14).
* Change 3/7: Multiply top and bottom by 2 -> 6/14.
* Add: 5/14 + 6/14 = 11/14

7) 5/9 + 1/3
* Common Denominator: 9.
* Change 1/3: Multiply top and bottom by 3 -> 3/9.
* Add: 5/9 + 3/9 = 8/9.
* Answer: 8/9

8) 1/6 + 2/9
* Common Denominator: 18 (6 x 3, 9 x 2).
* Change 1/6: Multiply top and bottom by 3 -> 3/18.
* Change 2/9: Multiply top and bottom by 2 -> 4/18.
* Add: 3/18 + 4/18 = 7/18

9) 5/15 + 3/5
* *Tip: 5/15 simplifies to 1/3, but let's just find a common denominator first.*
* Common Denominator: 15.
* Change 3/5: Multiply top and bottom by 3 -> 9/15.
* Add: 5/15 + 9/15 = 14/15.
* Answer: 14/15

10) 3/9 + 1/5
* *Tip: 3/9 simplifies to 1/3, but let's use 45 as the common denominator (9 x 5).*
* Change 3/9: Multiply top and bottom by 5 -> 15/45.
* Change 1/5: Multiply top and bottom by 9 -> 9/45.
* Add: 15/45 + 9/45 = 24/45.
* Simplify: Both divide by 3 -> 8/15.
* Answer: 8/15

11) 4/10 + 7/20
* Common Denominator: 20.
* Change 4/10: Multiply top and bottom by 2 -> 8/20.
* Add: 8/20 + 7/20 = 15/20.
* Simplify: Both divide by 5 -> 3/4.
* Answer: 3/4

12) 3/10 + 2/15
* Common Denominator: 30 (10 x 3, 15 x 2).
* Change 3/10: Multiply top and bottom by 3 -> 9/30.
* Change 2/15: Multiply top and bottom by 2 -> 4/30.
* Add: 9/30 + 4/30 = 13/30

13) 6/15 + 3/20
* Common Denominator: 60 (15 x 4, 20 x 3).
* Change 6/15: Multiply top and bottom by 4 -> 24/60.
* Change 3/20: Multiply top and bottom by 3 -> 9/60.
* Add: 24/60 + 9/60 = 33/60.
* Simplify: Both divide by 3 -> 11/20.
* Answer: 11/20

14) 1/4 + 4/10
* Common Denominator: 20.
* Change 1/4: Multiply top and bottom by 5 -> 5/20.
* Change 4/10: Multiply top and bottom by 2 -> 8/20.
* Add: 5/20 + 8/20 = 13/20.
* Answer: 13/20

15) 3/15 + 7/12
* Common Denominator: 60 (15 x 4, 12 x 5).
* Change 3/15: Multiply top and bottom by 4 -> 12/60.
* Change 7/12: Multiply top and bottom by 5 -> 35/60.
* Add: 12/60 + 35/60 = 47/60.
* Answer: 47/60

16) 4/15 + 3/25
* Common Denominator: 75 (15 x 5, 25 x 3).
* Change 4/15: Multiply top and bottom by 5 -> 20/75.
* Change 3/25: Multiply top and bottom by 3 -> 9/75.
* Add: 20/75 + 9/75 = 29/75

17) 4/10 + 7/15
* Common Denominator: 30.
* Change 4/10: Multiply top and bottom by 3 -> 12/30.
* Change 7/15: Multiply top and bottom by 2 -> 14/30.
* Add: 12/30 + 14/30 = 26/30.
* Simplify: Both divide by 2 -> 13/15.
* Answer: 13/15

18) 3/10 + 2/15
* Common Denominator: 30.
* Change 3/10: Multiply top and bottom by 3 -> 9/30.
* Change 2/15: Multiply top and bottom by 2 -> 4/30.
* Add: 9/30 + 4/30 = 13/30.
* Answer: 13/30

Final Answer:
1) 9/10
2) 25/36
3) 17/20
4) 11/15
5) 7/10
6) 11/14
7) 8/9
8) 7/18
9) 14/15
10) 8/15
11) 3/4
12) 13/30
13) 11/20
14) 13/20
15) 47/60
16) 29/75
17) 13/15
18) 13/30