1. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Section 2.5 Addition and Subtraction with Mixed Numbers

2. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Objectives o Add mixed numbers. o Subtract mixed numbers. o Subtract mixed numbers with borrowing.

3. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Addition with Mixed Numbers To Add Mixed Numbers 1.Add the fraction parts. 2.Add the whole numbers. 3.Write the answer as a mixed number with the fraction part less than 1.

4. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 1: Adding Mixed Numbers Find the sum: Solution We can write each number as a sum and then use the commutative and associative properties of addition to treat the whole numbers and fraction parts separately.

5. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 1: Adding Mixed Numbers (cont.) Or, vertically,

6. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 2: Adding Mixed Numbers Find the sum: Solution In this case, the fractions do not have the same denominator.

7. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 2: Adding Mixed Numbers (cont.)

8. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 3: Adding Mixed Numbers Find the sum: Solution Since the whole number 2 has no fraction part, we must be careful to align the whole numbers if we write the numbers vertically.

9. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 3: Adding Mixed Numbers (cont.)

10. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 4: Application of Adding with Mixed Numbers A triangle has sides measuring meters, meters, and meters. Find the perimeter (total distance around) of the triangle. Solution We find the perimeter by adding the lengths of the three sides.

11. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. The perimeter is meters. Example 4: Application of Adding with Mixed Numbers (cont.)

12. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Subtraction with Mixed Numbers To Subtract Mixed Numbers 1. Subtract the fraction parts. 2. Subtract the whole numbers.

13. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 5: Subtracting Mixed Numbers Find the difference: Solution Or, we can subtract vertically.

14. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 6: Subtracting Mixed Numbers Find the difference: Solution

15. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 7: Subtracting Mixed Numbers with Borrowing Find the difference: Solution Borrow 1 from 6 in the form of as follows:

16. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 8: Subtracting Mixed Numbers with Borrowing Find the difference: Solution First, find the LCD and then borrow 1 if necessary.

17. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 8: Subtracting Mixed Numbers with Borrowing (cont.)

18. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 9: Subtracting Mixed Numbers with Borrowing Find the difference: Solution

19. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 9: Subtracting Mixed Numbers with Borrowing (cont.) Rewrite

20. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Find the following sums. 1.2.3. Practice Problems

21. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Find the following differences. 4.5.6. Practice Problems (cont.)

22. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. 1.2.3. 4.5.6. Practice Problem Answers