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2.02 Applications of addition

Lesson

Are you ready?

Do you remember some of the methods, or strategies, we've used to  add numbers together? 

Examples

Example 1

765 + 104 = 869. Use this to fill in the gaps in the number sentences.

a

665+ ⬚ = 869

Worked Solution
Create a strategy

Use the given number sentence to find the pattern.

Apply the idea

Comparing the number sentences: 765 +104 = 869 and 665 + ⬚ = 869, we notice that they have the same sum of 869. The first numbers 765 and 665 differ by 100. So we need to add 1 hundred to 104.

Add the digits in each place value column.

HundredsTensUnits
104
+100
204

665+204=689

b

565+ ⬚ = 869

Worked Solution
Create a strategy

Use the number sentence from the previous part to find a pattern.

Apply the idea

Comparing the number sentences: 665 +204 = 869 and 565 + ⬚ = 869, in the first number of each statement the number of hundreds differ by 1, so we need to add 1 hundred to 204.

Add the digits in each place value column.

HundredsTensUnits
204
+100
304

565+304=869

Idea summary

We can use patterns to add two numbers. If we are given one number sentence, and need to complete another, then we can compare the number sentences to find a pattern to help.

Addition of more than two numbers

What happens when we have more than two numbers to add together? Let's see how we might approach a problem like this, in the following video.

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Examples

Example 2

Find the value of 540 + 44 +5.

Worked Solution
Create a strategy

Use a place value table.

Apply the idea

Write the numbers in the place value table.

HundredsTensUnits
540
44
+ 5
=

Add the digits in each place value column.

HundredsTensUnits
540
44
+ 5
=589

540 + 44 + 5 = 589

Idea summary

We can use a place value table when adding more than two numbers. We add the numbers in each column starting from the units place value.

Addition with word clues

If we have a written problem, it helps to know which words relate to addition. Looking for clues helps us find out what we need to add, as we can see in this video.

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Examples

Example 3

In a family, the grandmother is 73 years old, the mother is 32 years old, and the daughter is 4 years old. What is the combined age of the family?

Worked Solution
Create a strategy

The word "combined" means addition. So we need to add the ages.

Apply the idea
\displaystyle \text{Combined age}\displaystyle =\displaystyle 73 + 32 + 4Add the ages
\displaystyle =\displaystyle 70 + 3 + 30 + 2 + 4Partition the numbers
\displaystyle =\displaystyle 70 + 30 + 3 + 2 + 4Group the tens and units
\displaystyle =\displaystyle 100 + 9Add the tens and units
\displaystyle =\displaystyle 109Add the final numbers

The combined age of the family is 109 years.

Idea summary

There are some words we might come across that mean we will be using addition whereas other words may suggest subtraction. This is not a complete list, so we need to understand the context of the question, to work out whether to add or subtract.

These words suggest additionThese words suggest subtraction
moreless
longershorter
laterearlier
boughtsold
joinedleft

Outcomes

VCMNA209

Select and apply efficient mental and written strategies and appropriate digital technologies to solve problems involving all four operations with whole numbers and make estimates for these computations

VCMNA219

Continue and create sequences involving whole numbers, fractions and decimals. Describe the rule used to create the sequence

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