Chapter 8Add & Subtract Decimals

Chapter 8 Vocabulary

Associative Property of Addition – the property that states that when the grouping of addends is changed, the sum is the same.

Example: (1 + 2) + 3 = 1 + (2 + 3)

Benchmark – a familiar number used as a point of reference

Example: 0, 0.25, 0.5, 0.75, 1

Vocabulary continued

Commutative Property of Addition – the property that states when the order of two addends is changed the sum is the same.

Example: 1 + 2 = 2 + 1

Estimate – to find a number that is close to an exact number

Vocabulary continued

Hundredth – one of one hundred equal parts (example: pennies)

Round – to replace a number with one that is simpler and is approximately the same size as the original number

Tenth – one of ten equal parts (example: dimes)

8.1 Decimal Addition

Draw Conclusions

What if you combine the tenths first and then the hundredths? Explain how you would regroup.

Synthesize If you add two decimals that are each greater than 0.5, will the sum be less than or greater than 1.0?

Investigate (materials: base-ten blocks)

Connect – use a quick pictureStep 1: use a quick picture to model 2.5 + 2.8.

Step 2: Add the tenths.

(Are the there more than 10 tenths? ~ If there are more than 10 tenths, regroup.)

Add the ones.

Step 3: Draw a quick picture of your answer then record.

Problem Solving pg. 338

8.1 math journal question

How can you use base-ten blocks to model addition of decimals?

8.2 Decimal Subtraction

Draw Conclusions

What if you remove the tenths first and then the hundredths? Explain how you would regroup.

Synthesize If two decimals are both less than 1.0, what do you know about the difference between them?

Investigate (materials: base-ten blocks)

Connect – use a quick picture to subtract decimals

Problem Solving pg. 342

8.2 Math Journal Question

How can you use base-ten blocks to model subtraction of decimals?

8.3 Estimate Decimals Sums & Differences

Remember

To round a number, determine the place to which you want to round.

•If the digit to the right is less than 5, the digit in the rounding place stays the same.

•If the digit to the right is 5 or higher, the digit in the rounding place increases by 1.

A singer is recording a CD. The lengths of the three songs are 3.4 minutes, 2.78 minutes and 4.19 minutes. About how much total recording time will be on the CD?

Round to the nearest whole number. Then add.

3.4 ____2.78 ____

+ 4.19 +____

Try This! Pg. 343

Do you want an overestimate or an underestimate when you estimate the total cost of items you want to buy? Explain

Use benchmark numbers

Use the benchmark numbers 0, 0.25, 0.50, 0.75, 1

Try This! Use benchmark numbers to estimate

0.76 – 0.22

Problem Solving pg. 346

Connect to Science pg. 346

8.3 Math Journal Question

How can you estimate decimal sums and differences?

8.4 Add Decimals

Draw a quick picture to check your work.

So, ____ centimeters of rain fell.

Since, ____ is close to the estimate, 4. Henry’s answer is reasonable.

Equivalent decimals

Sometimes you need to use equivalent decimals in addition to keep the numbers aligned in each place.

Add zeros to the right as needed, so that the addends have the same number of decimals places.

Is your answer reasonable?

Unlock the Problem & multiple choice pg. 350

8.4 Math Journal Question

How can place value help you add decimals?

8.5 Subtract DecimalsDraw a quick picture to check your work.

So, Hannah has ___ more kilograms of apple than oranges.

Since ___ is close to 1. Hannah’s answer is reasonable.

Unlock the Problem

Try This! Equivalent Decimals

Step 2:

Subtract the hundredths first.

Then subtract the tenths, ones and tens. Regroup as needed.

Step 1:Estimate the difference

14.2 - 8.63

Estimate: ___ - ___ = ___

Unlock the Problem & multiple choice pg. 354

8.5 Math Journal Question

How can understanding place value help you subtract decimals?

Mid-Chapter Review

8.6 Make ChangeAnother Way – subtraction

Subtract the amount spent from the amount of money given to the cashier.

$10.00- 3.39

So, Tamara should receive ____ in change.

Step 1: Start with the price of the item. Count on to the next dollar using the fewest coins. Draw the coins. Count to $10 using the fewest bills. Draw the bills.

Step 2: Count the change.

One Way – use a model

Try This!

A customer paid for a fruit cup with a $5 bill.

Draw coins and bills to count on to find the change.

Change: _______

Problem Solving pg. 359

17. Amelia bought goggles and a beach ball. She paid with a $10 bill. How much change should she receive?

18. Arturo bought one of each of the 5 items on the shelf for his trip to the beach. When he got to the cash register, he found that the sand pail was on sale for $0.50 less than the price on the tag. He gave the cashier $25. How much change should Arturo receive?

Use the picture to solve 17 – 18.

Problem Solving pg. 360

So, the clerk gave Jess _____, but the correct change is ____.

Describe the clerk’s error?

How could Jess have known the clerk gave her the incorrect change?

8.6 Math Journal Question

Tyrone bought a sandwich that cost $3.58. He handed the cashier $4.08. Explain why Tyrone handed the cashier $4.08 instead of $4.00?

8.7 Make a Table – add and subtract money (checkbook)

At the end of May. Mrs. Freeman had a balance of $442.37. Since then, she has written a check for $63.92 and made a deposit of $350.00. Mrs. Freeman says she has $729.45 in her account. Make a table to find Mrs. Freeman’s balance.

Try Another Problem

Nick is buying juice for himself and 5 friends. Each bottle of juice costs $1.25. Make table to find the cost of 6 bottles of juice.

What is the total cost of 6 bottles of juice?

If Nick had $10, how many bottles of juice could he buy?

On Your Ownpg. 364

Use the poster to solve 4-7.

4. Aiden paid the admission for himself and two friends at Open Skate Night. Aiden had a membership card, but his friends did not. Aidan paid with a $20 bill. How much change should Aiden receive?

5. The Moores and Cotters were at Open Skate Night. The Moores paid $6 more for skate rentals than the Cotters. Together the two families paid $30 for skate rentals. How many pairs of skates did the Moores rent?

6. Jennie and 5 of her friends are going to Open Skate Night. Jennie does not have a membership card. Some of her friends have membership cards, but not all. What is the total amount that Jennie and her friends might pay for admission?

8.7 Math Journal Question

How can making a table help you organize and keep track of your bank balance?

8.8 Add & Subtract Decimals Through Thousandths

•Line up numbers in each place.

•First, add the thousandths.

•Then, add the hundredths, tenths, ones and tens. Regroup as needed.

•Place the decimal point in the sum.

At the 2006 Winter Olympics, Armin Zoeggeler won the gold medal in the men’s luge event. He completed the first interval in 23.835 seconds. It took him another 27.883 seconds to reach the finish line. What was Zoeggeler’s finish time?

Try This!

Use Subtraction to check your work. Subtract one of your addends from the sum.

Addition & subtraction are inverse operations. You can use subtraction to check your answer to an addition problem & addition to check a subtraction problem.

***The difference should equal the other addend.***

SubtractionStep 1: Line up the place values. Subtract the thousandths.

Step 2: Subtract the hundredths. Subtract the tenths. Regroup as needed.

Step 3: Subtract the ones and tens. Place the decimal point in the difference.

Problem Solving pg. 368

19. Apollo Ohno won the men’s 500-meter speed skating final at the 2006 Winter Olympics. His time for the race was 41.935 seconds. Francois-Louis Tremblay came in second, finishing 0.067 second behind Ohno. What was Tremblay’s time?

20. Jon Eley came in fifth in the men’s speed skating final. How many seconds after Apollo Ohno did Eley finish?

Use the table to solve 19 & 20.

Problem Solving pg. 368

21. Ricardo had a batting average of .279 last year. This year his batting average is .304. What is the difference between Ricardo’s two batting averages?

22. Reasoning The sum of two numbers is 4.004. One number has a 4 in the tenths place and a 3 in the thousandths place. The other number has a 1 in the ones place and an 8 in the hundredths place. What are the two numbers?

8.8 Math Journal Question

How can you record addition and subtraction of decimals through thousandths?

8.9 Choose a Method

One Way – Use the properties

Another Way – Use paper & pencil

At a track meet, Steven entered the long jump. His jumps were 2.25 meters, 1.81 meters & 3.75 meters. What was the total distance Steven jumped?

Try This!

In 1924, William DeHart Hubbard won a gold medal with a long jump of 7.44 meters. In 2000, Roman Schurenko won the bronze medal with a jump of 8.31 meters. How much longer was Schurenko’s jump than Hubbards?

Explain why you cannot use the Commutative Property or the Associative Property to find the difference between two decimals.

Problem Solving pg. 372

26. How much farther did the gold medal winner jump than the silver medal winner?

28. In the 2008 Olympics, the gold medalist for the men’s long jump had a jump of 8.34 meters. How much farther did the 2004 gold medalist jump compared to the 2008 gold medalist?

29. Jake cuts a length of 1.12 meters from a 3-meter board. How long is the board now?

Use the table to solve 26-28.

8.9 Math Journal Question

The fourth-place competitor’s jump measured 8.31 meters. If his jump had been 0.25 meter greater, what medal would he have received? Explain how you solved the problem.

Use the table to solve.

Chapter Review

Chapter Review continued