113r. Review Operations with Decimals

Learning Intentions

• add and subtract decimals
• multiply decimals
• divide decimals
• To understand that multiplying and dividing by powers of can be done by moving the digits left or right of the decimal point

Pre-requisite Summary

• Know the place value of digits in decimals, including tenths, hundredths and thousandths
• Be able to line up decimal points when writing decimals in columns
• Understand that decimals represent parts of a whole
• Recall multiplication and division facts with whole numbers
• Know that powers of include
• Understand that multiplying makes groups larger and dividing shares into smaller groups
• Be able to compare decimals and Recognise which is greater
• Know that trailing zeros do not change the value of a decimal, for example

Worked Examples

Worked Example 1

Add or subtract the decimals:

a)

b)

Worked Example 2

Add or subtract the decimals:

a)

b)

Worked Example 3

Multiply the decimals:

a)

b)

Worked Example 4

Multiply the decimals:

a)

b)

Worked Example 5

Divide the decimals:

a)

b)

Worked Example 6

Use powers of :

a)

b)

c)

Problems

Problem 1

Add or subtract the decimals:

a)

b)

Problem 2

Add or subtract the decimals:

a)

b)

Problem 3

Multiply the decimals:

a)

b)

Problem 4

Multiply the decimals:

a)

b)

Problem 5

Divide the decimals:

a)

b)

Problem 6

Use powers of :

a)

b)

c)

Exercises

Understanding and Fluency

Exercise 1.

Add the decimals:

a)

b)

c)

Exercise 2.

Subtract the decimals:

a)

b)

c)

Exercise 3.

Add or subtract the decimals:

a)

b)

c)

d)

Exercise 4.

Multiply the decimals:

a)

b)

c)

Exercise 5.

Multiply the decimals:

a)

b)

c)

Exercise 6.

Divide the decimals:

a)

b)

c)

Exercise 7.

Multiply or divide by powers of :

a)

b)

c)

d)

Exercise 8.

Multiply or divide by powers of :

a)

b)

c)

d)

Reasoning

Exercise 9.

Explain why the decimal points must be lined up when adding or subtracting decimals.

Exercise 10.

A student says that because . Explain the mistake.

Exercise 11.

Noah says that multiplying by means “add a zero”. Is he correct? Explain your answer Use a decimal example.

Exercise 12.

Explain why .

Exercise 13.

A student says that because . Describe the error.

Problem-solving

Exercise 14.

A runner completed one lap in min and another lap in min. What was the total time?

Exercise 15.

A water tank held L and L was used. How much water was left?

Exercise 16.

A ribbon costs $ per metre. What is the cost of m?

Exercise 17.

A machine packs kg of rice into each bag. What is the total mass of bags?

Exercise 18.

A m rope is cut equally into pieces. How long is each piece?

Exercise 19.

A number is . What number is times as large, and what number is of it?

Potential Misunderstandings

• Students may forget to line up decimal points when adding or subtracting
• Students may treat decimals as whole numbers and ignore place value
• Students may think a longer decimal is always greater or more precise in a calculation
• Students may make regrouping errors when subtracting decimals
• Students may multiply the digits correctly but place the decimal point incorrectly in the answer
• Students may think multiplying by always means writing an extra zero at the end
• Students may think dividing by only changes the last digit
• Students may move the decimal point in the wrong direction when multiplying or dividing by powers of
• Students may forget that multiplying by powers of changes place value, not the digits themselves
• Students may confuse dividing a decimal by a whole number with moving the decimal point automatically
• Students may not check whether their answer is reasonable compared with the original numbers

Next: 114. Recurring Decimals and Rounding