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5 Minute Check

Complete in your notebook.

Estimate each product.

1. 9.7 x 3

2. 3.4 x 5

3. 17.5 x 8

Multiply.

4. 1.5 x 6

5. 3.1 x 13

6. 3.48 x 25

5 Minute Check

Complete in your notebook.

Multiply.

4. 1.5 x 6

1.5 1 decimal place

x 6

9.01 decimal place

5 Minute Check

Complete in your notebook.

Multiply.

5. 3.1 x 13

3.1 1 decimal place

x 1 3 Don’t forget the zero

93

+ 310

40.31 decimal place

5 Minute Check

Complete in your notebook.

Multiply.

6. 3.48 x 25

3.48 2 decimal places

x 25 Don’t forget the zero

1740

+ 6960

87.002 decimal places

Multiplying Decimals by Decimals

Objective: To understand how to estimate and multiply decimals by decimals.

Multiplying Decimals by Decimals

At the end of this lesson you should be able to answer the following questions.

How do you determine which place value to use when multiplying decimals by decimals?

Why is estimating not as helpful when multiplying very small numbers?

Multiplying Decimals by Decimals

To multiply decimals, multiply as normal and then place the decimal point.

Multiplying Decimals by Decimals

Find the product of 8.7 and 2.8.

First round the numbers to the nearest whole number to get an estimate.

What does 8.7 round to?

Digits from 0 to 4 round down and digits from 5-9 round up.

Multiplying Decimals by Decimals

Find the product of 8.7 and 2.8.

First round the numbers to the nearest whole number to get an estimate.

What does 8.7 round to? 9

What does 2.8 round to?

Multiplying Decimals by Decimals

Find the product of 8.7 and 2.8.

First round the numbers to the nearest whole number to get an estimate.

What does 8.7 round to? 9

What does 2.8 round to? 3

Multiplying Decimals by Decimals

Find the product of 8.7 and 2.8.

First round the numbers to the nearest whole number to get an estimate.

9 x 3 = 27, so

8.7 x 2.8 ≈ 27

Multiplying Decimals by Decimals

Find the product of 8.7 and 2.8.

To multiply decimals.

Step 1 – Stack the numbers with the number with the most digits on top.

8.7

x 2.8

(Since both numbers have 2 digits, either could be on top)

Multiplying Decimals by Decimals

Find the product of 8.7 and 2.8.

To multiply decimals.

Step 2 – Multiply the digits.

8.7

x 2.8

696 Don’t forget to add the zero.

+1740

2436

Multiplying Decimals by Decimals

Find the product of 8.7 and 2.8.

To multiply decimals.

Step 3 – Determine the number of decimal places in the factors to locate the decimal place in the product.

8.7 1 decimal place

x 2.8+ 1 decimal place

696

+1740

24.36 2 decimal places

Multiplying Decimals by Decimals

Find the product of 8.7 and 2.8.

8.7

x 2.8

696

+1740

24.36

Is this a reasonable answer?

Multiplying Decimals by Decimals

Find the product of 8.7 and 2.8.

Is this a reasonable answer?

24.35 ≈ 27

Multiplying Decimals by Decimals

Find the product of .98 and 7.3

Estimate?

1 x 7 = 7, so

.98 x 7.3 ≈ 7

Next?

Multiplying Decimals by Decimals

Find the product of .98 and 7.3

.98

x 7.3

294 Don’t forget to add a zero

+6860

7154

Next?

Multiplying Decimals by Decimals

Find the product of .98 and 7.3

.98 2 decimal places

x 7.3+1 decimal place

294

+6860

7.154 3 decimal places

Is this a reasonable answer?

Multiplying Decimals by Decimals

Find the product of .98 and 7.3

.98 2 decimal places

x 7.3+1 decimal place

294

+6860

7.154 3 decimal places

Is this a reasonable answer?

7.154 ≈ 7

Multiplying Decimals by Decimals

Find the product of 3.6 and 0.05.

4 x 0 = 4, so

3.6 x 0.05 ≈ 0

Actual product?

Multiplying Decimals by Decimals

Find the product of 3.6 and 0.05

0.05 2 decimal places

x 3.6+1 decimal place

0030

+ 0015

0.045 3 decimal places

Is this a reasonable answer?

Multiplying Decimals by Decimals

Find the product of 3.6 and 0.05

0.05 2 decimal places

x 3.6+1 decimal place

030

+0150

0.180 3 decimal places

Is this a reasonable answer?

0.180 ≈ 0

Multiplying Decimals by Decimals

Find the product of 0.112 and 7.2

Estimate?

0 x 7 = 0, so

0.112 x 7.2 ≈ 0

Actual product?

Multiplying Decimals by Decimals

Find the product of 0.112 and 7.2

0.112 3 decimal places

x 7.2+1 decimal place

0224

+07840

.8064 4 decimal places

Is this a reasonable answer?

Multiplying Decimals by Decimals

Find the product of 0.112 and 7.2

0.112 3 decimal places

x 7.2+1 decimal place

0224

+07840

.8064 4 decimal places

Is this a reasonable answer?

0.8064 ≈ 0

Multiplying Decimals by Decimals

Find the product of 1.4 and 0.067

Estimate?

1 x 0 = 0

1.4 x 0.067 ≈ 0

Actual product?

Multiplying Decimals by Decimals

Find the product of 1.4 and 0.067

0.067 3 decimal places

x 1.4+1 decimal place

0268

+00670

0.0938 4 decimal places

Is this a reasonable answer?

Multiplying Decimals by Decimals

Find the product of 1.4 and 0.067

0.067 3 decimal places

x 1.4+1 decimal place

0268

+00670

0.0938 4 decimal places

Is this a reasonable answer?

0.0938 ≈ 0

Multiplying Decimals by Decimals

Mr. Avery’s car can travel 28.45 miles on one gallon of gas. If his gas tank holds 11.5 gallons, how far can he travel on one tank?

Estimate?

Multiplying Decimals by Decimals

Mr. Avery’s car can travel 28.45 miles on one gallon of gas. If his gas tank holds 11.5 gallons, how far can he travel on one tank?

Estimate?

28 x 12 = 336

Keep in mind

28 x 12 = 28 x 10 + 28 x 2

= 280 + 56 = 336

Actual product?

Multiplying Decimals by Decimals

Mr. Avery’s car can travel 28.45 miles on one gallon of gas. If his gas tank holds 11.5 gallons, how far can he travel on one tank?

28.45 2 decimal places

x 11.5+1 decimal place

14225

28450

+284500

327.175 3 decimal places

Is this a reasonable answer?

Multiplying Decimals by Decimals Mr. Avery’s car can travel 28.45 miles on one gallon of gas. If his gas tank holds 11.5 gallons, how far can he travel on one tank?

28.45 2 decimal places

x 11.5+1 decimal place

14225

28450

+284500

327.175 3 decimal places

Is this a reasonable answer? 327.175 ≈ 336

Multiplying Decimals by Decimals

Determine whether the following statement is always, sometimes or never true.

The product of two decimals less than 1 is less than either of the factors.

Give examples to support your answer.

Multiplying Decimals by Decimals

Determine whether the following statement is always, sometimes or never true.

The product of two decimals less than 1 is less than either of the factors.

Always.

0.3 x 0.5 = .15, which is less than 0.3 and 0.5

0.75 x 0.6 = 0.45

Multiplying Decimals by Decimals

Complete the Mid-Chapter Check on page 214. When complete bring to the desk and show Mr. Avery.

Agenda Notes

Homework –Homework Practice 3-2/3-4

Due Thursday, Oct 10

Mid-Chapter 3 Quiz –Thursday, Oct 10

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