044. Multiplying Decimals

Learning Intentions

• multiply decimals
• To understand that it is helpful to estimate to Check the position of the decimal point in the final answer

Pre-requisite Summary

• Understand place value in decimal numbers, including tenths, hundredths and thousandths
• Be able to multiply whole numbers Use written or mental methods
• Know that digits in a decimal still follow place value rules
• Be able to estimate products using rounding
• Understand that an answer should be reasonable in size compared with the numbers being multiplied

Worked Examples

Worked Example 1

a) Calculate

b) Estimate the product first

c) Explain how the estimate helps check the decimal point

Worked Example 2

a) Calculate

b) Estimate the product first

c) Check whether the final answer is reasonable

Worked Example 3

a) Calculate

b) Estimate the product first

c) Explain why the answer must be less than

Worked Example 4

a) Calculate

b) Estimate the product by rounding

c) Use the estimate to check the position of the decimal point

Worked Example 5

a) Calculate

b) Estimate the product first

c) Explain why an answer of would be unreasonable

Worked Example 6

a) Calculate

b) Estimate the product first

c) Use the estimate to justify the final decimal placement

Problems

Problem 1

a) Calculate

b) Estimate the product first

c) Explain how the estimate helps check the decimal point

Problem 2

a) Calculate

b) Estimate the product first

c) Check whether the final answer is reasonable

Problem 3

a) Calculate

b) Estimate the product first

c) Explain why the answer must be less than

Problem 4

a) Calculate

b) Estimate the product by rounding

c) Use the estimate to check the position of the decimal point

Problem 5

a) Calculate

b) Estimate the product first

c) Explain why an answer of would be unreasonable

Problem 6

a) Calculate

b) Estimate the product first

c) Use the estimate to justify the final decimal placement

Exercises

Understanding and Fluency

Exercise 1.

Multiply each decimal:

a)

b)

c)

Exercise 2.

Multiply each decimal:

a)

b)

c)

Exercise 3.

Multiply each decimal:

a)

b)

c)

Exercise 4.

Multiply each decimal:

a)

b)

c)

Exercise 5.

Multiply each decimal:

a)

b)

c)

Exercise 6.

Multiply each decimal:

a)

b)

c)

Exercise 7.

Estimate first, then multiply:

a)

b)

c)

Exercise 8.

Estimate first, then multiply:

a)

b)

c)

Reasoning

Exercise 9.

Explain why estimating as about helps check the final answer.

Exercise 10.

A student says . Explain the mistake.

Exercise 11.

Explain why multiplying by a decimal less than makes the product smaller than the starting number.

Exercise 12.

A student calculates . Explain why the estimate shows this cannot be correct.

Problem-solving

Exercise 13.

A ribbon is m long. Four equal pieces are cut from the same type of ribbon. Solve the total length of ribbon needed.

Exercise 14.

A bottle holds L of juice. How much juice is in bottles?

Exercise 15.

A runner completes km per lap. How far does the runner travel in laps?

Exercise 16.

A shop sells fabric for $3.4 per metre. What is the cost of m of fabric?

Exercise 17.

A tank is filled at a rate of L per minute for minutes. How much water is added?

Exercise 18.

A packet weighs kg. What is the total mass of packets?

Potential Misunderstandings

• Students may ignore place value and multiply decimals as though they were whole numbers without adjusting the final answer
• Students may place the decimal point incorrectly in the product
• Students may think the total number of decimal places rule works without checking whether the answer is reasonable
• Students may forget to estimate before calculating, so they miss an unreasonable answer
• Students may think multiplying by a decimal less than should make the answer larger
• Students may confuse multiplication by or with general decimal multiplication
• Students may line up decimal points in a multiplication algorithm as if they were adding
• Students may not recognise that an estimate can be used to reject an answer with the decimal point in the wrong place

Next: 045. Dividing Decimals