042. Adding and Subtracting Decimals

Learning Intentions

• To understand that to add or subtract decimals, additional zeros might need to be entered for some decimal places
• add decimals
• subtract decimals

Pre-requisite Summary

• Understand the meaning of the decimal point
• Know the place value of tenths, hundredths and thousandths
• Be able to align numbers by place value in vertical calculations
• Understand that adding trailing zeros does not change the value of a decimal, for example
• Recall basic addition and subtraction facts with whole numbers
• Understand regrouping in addition and subtraction

Worked Examples

Worked Example 1

a) Explain why can be written as .

b) Rewrite so the decimal places line up.

c) Solve the sum.

Worked Example 2

Add the decimals:

a)

b)

Worked Example 3

Add the decimals:

a)

b)

Worked Example 4

Subtract the decimals:

a)

b)

Worked Example 5

Subtract the decimals:

a)

b)

Worked Example 6

a) Calculate .

b) Show how adding zeros helps line up the decimals.

c) State the final answer.

Problems

Problem 1

a) Explain why can be written as .

b) Rewrite so the decimal places line up.

c) Find the sum.

Problem 2

Add the decimals:

a)

b)

Problem 3

Add the decimals:

a)

b)

Problem 4

Subtract the decimals:

a)

b)

Problem 5

Subtract the decimals:

a)

b)

Problem 6

a) Calculate .

b) Show how adding zeros helps line up the decimals.

c) State the final answer.

Exercises

Understanding and Fluency

Exercise 1.

Rewrite each decimal with extra zeros so both numbers have the same number of decimal places:

a) and

b) and

c) and

Exercise 2.

Add the decimals:

a)

b)

c)

Exercise 3.

Add the decimals:

a)

b)

c)

Exercise 4.

Subtract the decimals:

a)

b)

c)

Exercise 5.

Subtract the decimals:

a)

b)

c)

Exercise 6.

Add or subtract as required:

a)

b)

c)

Exercise 7.

Add or subtract as required:

a)

b)

c)

Exercise 8.

Calculate:

a)

b)

c)

Reasoning

Exercise 9.

Explain why and have the same value.

Exercise 10.

A student writes

Explain the mistake.

Exercise 11.

Explain why decimal points must line up when adding or subtracting decimals.

Exercise 12.

A student says . Explain the error.

Problem-solving

Exercise 13.

A bottle contains L of juice and another contains L. How much juice is there altogether?

Exercise 14.

A runner completes km in the morning and km in the afternoon. What total distance does the runner complete?

Exercise 15.

A rope is m long. A piece of length m is cut off. How much rope remains?

Exercise 16.

A tank contains L of water. If L is used, how much water remains?

Exercise 17.

A shop sale totals $14.75, and a customer returns an item costing $2.80. What is the new total?

Exercise 18.

A packet weighs kg and another weighs kg. What is the combined mass?

Potential Misunderstandings

• Students may line up digits instead of lining up decimal points
• Students may think adding zeros to the end of a decimal changes its value
• Students may ignore place value and add tenths to hundredths incorrectly
• Students may forget to regroup when adding or subtracting decimals
• Students may drop the decimal point in the answer
• Students may subtract the smaller digit from the larger digit in each column instead of regrouping correctly
• Students may think the answer must have the same number of decimal places as the first number only
• Students may make errors when one decimal has fewer decimal places and needs trailing zeros added

Next: 043. Multiplying and Dividing Decimals by Powers of Ten