Adding and Subtracting Fractions with like Denominators

1. Adding and Subtracting Fractions with like Denominators You know that the bottom number of a fraction tells how may parts each whole is divided into. In this picture each circle is divided into 4 parts so the bottom number for this fractions is 4. 4 We use or shade 5 parts so the top number of this fraction is 5. The picture shows the fraction 5 . 4 In a fraction the bottom number has a special name. The bottom number in a fraction is called the denominator. The denominator or the bottom number in a fraction tells how many parts each whole is divided into.

2. 1 2 4 6 7 8 7 5 2 3 What are the denominators in these fractions? Two Six Eight Five Three Remember the bottom number in a fraction is called the denominator.

3. You have learned to add fractions using pictures. + = 1 4 5 3 3 3 Fractions can be added and subtracted without using pictures. Here’s a problem. 5 3 4 4 When you add and subtract fractions you do not work on the top and the bottom the same way. + = = +

4. + = When you add and subtract fractions you COPY the denominator, then you work on the top. Remember, you copy the denominator and then you work on the top. 5 3 4 4 Look at this problem. What is the denominator? Yes, it’s 4. What do you do with the denominator? Right, you copy it in the answer so the denominator in the answer is 4. Now we can add the numbers on the top. What do we get when we add 5 + 3? Correct, 5 + 3 = 8. We put the 8 on top in the answer so 5 + 3 = 8 . 4 4 4 4

5. - = 7 2 • 5 Here’s a different problem. First look at the sign. We are subtracting in this problem. Next look at the denominators. What do we do with the denominator? Yes, we copy it in the answer. On the top the sign tells us to subtract. 7 – 2, what’s the answer? Right, 7 – 2 = 5. We put the 5 on top. 5 5 7 2 5 5 5 5 5 - =

6. Let’s try another problem. - = 4 3 • 2 First you copy the denominator then you work the top. What is the denominator? Yes, it’s 2. Now work on the top. What is 4 – 3? Right, it’s 1. So 4 3 1 2 2 2 2 - =

7. Here’s a new problem. + = 2 3 • 4 What do we do with the denominator? Yes, we copy the 4. 4 What do we get on top? Good Job! 2 + 3 = 5. 2 3 5 4 4 4 + =

8. 6 5 7 3 4 6 7 4 5 4 Your Turn - = Copy these problems on your paper and write the answer. 1. 8 2 5 5 2. 5 2 3 3 3. 8 4 6 6 4. 10 3 4 4 5. 3 2 4 4 = + Check your work - = - = = +

9. If the fraction you are working does not have the same denominator you cannot work the problem the way it is written. You can’t work this problem the way it is written because the denominators are not the same. 6 1 4 3 - =

10. Some of these problems can be worked the way they are written but some cannot. Look at the denominators to decide, then write the numbers of the problems that can be worked the way they are written. 1. 7 2 4. 4 4 3 4 5 6 2. 8 2 5. 8 2 3 5 5 5 3. 6 1 6. 2 5 2 2 3 4 - = = + - - = = = + + =

11. Check your work. You can work problems 3 and 5 the way they are written. Remember, if you can’t copy the denominator of the fraction you are adding or subtracting you cannot work the problem the way it is written. 1. 7 2 4. 4 4 3 4 5 6 2. 8 2 5. 3 5 3.6. 2 5 3 4 - = + = 8 5 2 5 - - = = 6 2 1 2 = + = +

12. Look at these new problems. Write the numbers of the problems that can be worked the way they are written. 1. 6 5 4. 2 1 8 8 3 3 2. 7 2 5. 6 3 6 4 4 2 3. 1 4 6. 4 3 2 3 6 6 - - = = - = + = = + + =

13. Check your work. You can work problems 1, 4, and 6. Now on your paper work the problems that can be worked the way they are written. 1. 6 5 1 8 8 8 4. 2 1 1 3 3 3 6. 4 3 7 6 6 6 - - = = • 6 5 8 8 • 2 1 3 3 • 4 3 6 6 - = - = + = + =

14. Let’s try one more. + = • 1 • 3 What do you do in the denominator? Yes, you copy the denominator. 3 What do you get on top? That’s right, 2. 1+1=2. 1 1 2 • 3 3 + =

15. - = New problem. 1 1 3 3 • Do we work in the denominator? • No. What do we do in the denominator? • Correct, we copy the denominator. 3 • Do we work on top? • Yes. • What do we get on top? • Yes, 0.

16. Think about the picture of this problem when you work it. 1 1 3 3 - = You have 1 and you take away 1 . How many thirds do you have left? 3 3 That’s Correct. You have 0 thirds left. You have no thirds or 0 . 3 1 1 0 3 3 3 When you see a problem that is addition or subtraction first look at the denominators. If they are the same you can work the problem the way it is written. If the denominators are not the same you cannot work the problem the way it is written. - =

17. You have learned to work problems this way. - = + = 3 1 4 or 7 5 2 4 4 4 8 8 8 You can also work fraction addition and subtraction problems when they are written this way. 5 8 8 3 2 2 8 3 7 6 8 3 Just like before check to see if you can work the problem the way it is written, copy the denominator, then add or subtract. - +

18. Your Turn Copy each problem you can work the way it is written, then work the problem. 1. 2. 3. 4. 5. 6 8 4 5 2 8 4 5 3 6 + 1 - 3 + 2 - 6 - 1 8 4 6 3 2

19. 7 8 3 3 5 4 Check your work. Problems 3 and 5 cannot be worked the way they are written.Work problems 1, 2, and 4. 1. 2. 3. 4. 5. 6 8 4 5 2 8 4 5 3 6 + 1 - 3 + 2 - 2 - 1 8 4 6 3 2 Remember which ever way the problem is written to check the denominators. If the denominators are the same copy the denominator in the answer and add or subtract the top.