2. Adding and Subtracting Decimals

3. Today’s Learning Goals  We will continue to use estimation as a way to determine the reasonableness of our exact answers with problems involving decimals.  We will think about how to solve addition and subtraction problems involving decimals with fractions.  We will think about how to solve addition and subtraction problems involving decimals using our knowledge of how to add and subtract whole numbers.

4. Decimal Addition Consider the following problem: A jogger ran for 2.84 miles and then stopped to get a drink of water. She started up again and ran for 3.69 more miles. How many miles did she run altogether? What would you do to solve this problem? Exactly…add 2.84 and 3.69 together. What would be a good estimate to the answer? Great…6.5 is a good estimate if you said that 2.84  3 and 3.69  3.5. So the problem becomes close to 3 + 3.5 = 6.5!

5. Decimal Addition How would you add 2.84 and 3.69 using single fractions for each number? Yes… Notice how the exact answer of 6.53 is close to our estimate of 6.5!

6. Decimal Addition Correct…line up the decimal points and add as if they were whole numbers. So, we have 2.84 +3.69 3 1 5 1 6. So, the jogger ran 6.53 miles total. This is close to our estimate of 6.5 miles! How would you add 2.84 and 3.69 using decimals? Notice how we added as if they were whole numbers because the single fractions numerators are those whole numbers!

7. Decimal Subtraction Consider the following problem: What would you do to solve this problem? Exactly…subtract 6.78 from 15.34. A science lab had 15.34 grams of sulfuric acid. A scientist used 6.78 grams of sulfuric acid for a chemistry experiment. How many grams of sulfuric acid was left in the science lab? What would be a good estimate to the answer? Great…8 is a good estimate if you said that 6.78  7 and 15.34  15. So the problem becomes close to 15 – 7 = 8!

8. Decimal Subtraction How would you subtract 6.78 from 15.34 using single fractions for each number? Yes… Notice how the exact answer of 8.56 is close to our estimate of 8! You should always use your estimate as a way to check the reasonableness of your exact answer!

9. Decimal Subtraction How would you subtract 6.78 from 15.34 using decimals? Correct…line up the decimal points and subtract as if they were whole numbers. So, we have 15.34 – 6.78 6 2 5 4 8. So, the science lab has 8.56 grams of sulfuric acid left. Again, this is close to our estimate of 8! 1 1 1 Notice how we subtracted as if they were whole numbers because the single fractions numerators are those whole numbers!

10. Partner Work You have 20 minutes to work on the following problems with your partner.

11. For those that finish early Samuel buys the following at the grocery store: 2 dozen eggs at $0.75 per dozen 1 pound of butter at $1.39 1 5-pound bag of sugar for $1.79 2 5-pound bags of flour at $1.19 each 1 8-ounce package of unsweetened chocolate for $1.64 1. What was the total bill for his groceries? 2. Suppose he didn’t have enough money to pay for everything. So, he decided to buy just 1 bag of sugar and 1 bag of flour. How much would his total bill be then?

12. Big Idea from Today’s Lesson We can change decimals to single fractions and then add and subtract the fractions because we already know how to do that. When we add and subtract decimals, we want to add and subtract things of the same-sized pieces (just like we did with fractions). This is why we line up decimal points. We can add and subtract decimals just like they were whole numbers because these are the whole numbers in the numerators for the single fractions.

13. Homework Complete Homework Worksheet. Pgs. 118 – 119 (8, 9, 11, 14 – 19)