Lesson

## Practice

Before you practice the work from this chapter, take some time to go over some of the  addition  and  subtraction  strategies and problems we've looked at. These include:

• using a number line

• modelling with place value (base ten) blocks

• partitioning numbers by place value

• using a vertical algorithm

We also looked at how to use a vertical algorithm to solve  addition  or  subtraction.  This strategy is useful if we need to trade, or regroup. For addition, we  regroup to the higher place value,  but for subtraction, we  regroup down to a lower place value.

### Examples

#### Example 1

Find the value of 796 - 429.

Worked Solution
Create a strategy

Use the subtraction algorithm method.

Apply the idea

Write it in a vertical algorithm.\begin{array}{c} & &7 &9 &6 \\ &- &4 &2 &9 \\ \hline \\ \hline \end{array}

Begin with the units column. We can see that 6 is less than 9, so we need to trade 1 ten from the tens column. This gives us 16 - 9 = 7 in the units column and 9 tens becomes 8 tens in the first row. \begin{array}{c} & &7 &8 &\text{}^1 6 \\ &- &4 &2 &9 \\ \hline & & & &7 \\ \hline \end{array}

For the tens place: 8 - 2 = 6. \begin{array}{c} & &7 &8 &\text{}^1 6 \\ &- &4 &2 &9 \\ \hline & & &6 &7 \\ \hline \end{array}

For the hundreds place: 7 - 4 = 3. \begin{array}{c} & &7 &8 &\text{}^1 6 \\ &- &4 &2 &9 \\ \hline & &3 &6 &7 \\ \hline \end{array}

So 796 - 429 = 367.

#### Example 2

Find the value of 7681 + 9273.

Worked Solution
Create a strategy

Use the vertical algorithm method.

Apply the idea

Write it in a vertical algorithm.\begin{array}{c} & & &7 &6 &8 &1 \\ &+ & &9 &2 &7 &3 \\ \hline \\ \hline \end{array}

Add the units column. \begin{array}{c} & & &7 &6 &8 &1 \\ &+ & &9 &2 &7 &3 \\ \hline & & & & & &4\\ \hline \end{array}

Add the tens column: 8 + 7 = 15, so we bring down the 5 in the tens column and carry the 1 to the hundreds column:\begin{array}{c} & & &7 &\text{}^1 6 &8 &1 \\ &+ & &9 &2 &7 &3 \\ \hline & & & & &5 &4\\ \hline \end{array}

Add the hundreds column. \begin{array}{c} & & &7 &\text{}^1 6 &8 &1 \\ &+ & &9 &2 &7 &3 \\ \hline & & & &9 &5 &4\\ \hline \end{array}

Add the thousands column: 7 +9 = 16, so we bring down the 6 in the thousands column and carry the 1 to the ten thousands column:\begin{array}{c} & &\text{}^1 &7 &\text{}^1 6 &8 &1 \\ &+ & &9 &2 &7 &3 \\ \hline & & &6 &9 &5 &4\\ \hline \end{array}

Add the ten thousands column. \begin{array}{c} & &\text{}^1 &7 &\text{}^1 6 &8 &1 \\ &+ & &9 &2 &7 &3 \\ \hline & &1 &6 &9 &5 &4\\ \hline \end{array}

So 7681 + 9273 = 16\, 954.

#### Example 3

Find the value of 55\,872-2619.

Worked Solution
Create a strategy

Use the standard algorithm method.

Apply the idea

Write it in a vertical algorithm.\begin{array}{c} & & &5 &5 &8 &7 &2 \\ &- & & &2 &6 &1 &9 \\ \hline & \\ \hline \end{array}

In the ones column we can see that 2 is less than 9, so we need to trade 1 ten from the tens place.

So we get 12-9=3 in the ones column and 7 tens becomes 6 tens in the first row.\begin{array}{c} & && 5&5 &8 &6 &\text{}^1 2 \\ &- && &2 &6 &1 &9 \\ \hline & && & & & &3\\ \hline \end{array}

In the tens column, we have 6-1=5:\begin{array}{c} & && 5&5 &8 &6 &\text{}^1 2 \\ &- && &2 &6 &1 &9 \\ \hline & && & & & 5 &3\\ \hline \end{array}

In the hundreds column, we have 8-6=2:\begin{array}{c} & && 5&5 &8 &6 &\text{}^1 2 \\ &- && &2 &6 &1 &9 \\ \hline & && & & 2& 5 &3\\ \hline \end{array}

In the thousands column, we have 5-2=3:\begin{array}{c} & && 5& 5 &8 &6 &\text{}^1 2 \\ &- && &2 &6 &1 &9 \\ \hline & && & 3& 2& 5 &3\\ \hline \end{array}

And for the ten thousands place 5-0=5:\begin{array}{c} & && 5& 5 &8 &6 &\text{}^1 2 \\ &- && &2 &6 &1 &9 \\ \hline & && 5& 3& 2& 5 &3\\ \hline \end{array}

So the answer is:55\,872 - 2619 = 53\,253

Idea summary

There are different strategies we can use to solve addition or subtraction questions. Even if our numbers get bigger, we can still use the same strategies, just with more steps.

### 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