Section 2.5 Addition and Subtraction with Mixed Numbers 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. 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. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 1: Adding Mixed Numbers 2 5 Find the sum: 5 8 9 9 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. 2 5 2 5 2 5 5 8 5 8 5 8 9 9 9 9 9 9 7 7 13 13 9 9 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, 2 5 9 5 8 9 7 13 9 HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 2: Adding Mixed Numbers 1 7 Find the sum: 35 22 6 18 Solution In this case, the fractions do not have the same denominator. 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.) 1 7 1 7 35 22 35 22 6 18 6 18 1 3 7 35 22 6 3 18 3 7 57 18 18 10 57 18 5 57 9 HAWKES LEARNING SYSTEMS Students Matter. Success Counts. LCD 18 Reduce the fraction part. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 3: Adding Mixed Numbers 3 3 Find the sum: 5 9 2 4 10 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. 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.) 3 3 5 15 5 5 5 4 4 5 20 LCD 20 3 2 6 3 9 9 9 10 2 20 10 2 2 2 1 1 21 16 1 17 16 20 20 20 Fraction is greater than 1. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Change to a mixed number. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 4: Application of Adding with Mixed Numbers 1 4 A triangle has sides measuring 3 meters, 6 meters, 5 3 14 and 6 meters. Find the perimeter (total distance 15 around) of the triangle. Solution We find the perimeter by adding the lengths of the three sides. 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 (cont.) 1 5 5 1 3 3 3 3 5 15 3 4 3 4 12 6 6 6 LCD 15 5 3 5 15 14 14 14 6 6 6 15 15 15 31 1 1 15 15 2 17 meters 15 15 15 1 The perimeter is 17 meters. 15 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. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 5: Subtracting Mixed Numbers 3 2 Find the difference: 10 6 7 7 Solution Or, we can subtract vertically. 3 2 3 2 10 6 10 6 7 7 7 7 1 4 7 1 4 7 HAWKES LEARNING SYSTEMS Students Matter. Success Counts. 3 10 7 2 6 7 1 4 7 Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 6: Subtracting Mixed Numbers 4 1 Find the difference: 13 7 5 3 Solution 4 4 3 12 13 13 13 5 5 3 15 LCD 15 1 5 1 5 7 7 7 3 5 3 15 7 6 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 1 Find the difference: 6 2 3 Solution 3 Borrow 1 from 6 in the form of as follows: 3 3 6 5 3 1 1 2 2 3 3 2 3 3 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 5 13 Find the difference: 76 29 12 20 Solution First, find the LCD and then borrow 1 if necessary. 12 2 2 3 LCD 2 2 3 5 60 20 2 2 5 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.) 5 76 12 5 5 76 12 5 25 76 60 85 75 60 Borrow 1 60 . 60 13 13 3 39 39 29 29 29 29 20 20 3 60 60 46 23 46 46 60 30 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 2 5 Find the difference: 4 1 9 9 Solution 2 4 9 5 1 9 HAWKES LEARNING SYSTEMS Students Matter. Success Counts. 5 2 is larger than , so "borrow" 1 from 4. 9 9 Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 9: Subtracting Mixed Numbers with Borrowing (cont.) 2 2 2 11 Rewrite 4 as 3 1 3 1 3 . 9 9 9 9 2 2 11 4 31 3 9 9 9 5 5 5 1 1 1 9 9 9 6 2 2 2 9 3 HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Practice Problems Find the following sums. 1 7 1. 11 2. 9 8 2 3 9 1 9 5 1 7 3 HAWKES LEARNING SYSTEMS Students Matter. Success Counts. 2 3. 1 7 1 8 2 3 2 5 Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Practice Problems (cont.) Find the following differences. 3 4. 3 4 2 1 5. 6 3 1 4 2 HAWKES LEARNING SYSTEMS Students Matter. Success Counts. 2 6. 5 5 7 3 10 Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Practice Problem Answers 1 1. 20 3 97 2. 9 120 27 3. 12 70 3 4. 1 4 5 5. 1 6 7 6. 1 10 HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved.