Lesson

## Ideas

Can you recall how to use a  vertical algorithm  with smaller numbers?

### Examples

#### Example 1

Find the value of 4400 + 403.

Worked Solution
Create a strategy

Use the vertical algorithm method.

Apply the idea

Write it in a vertical algorithm.\begin{array}{c} & &4 &4 &0 &0 \\ &+ & &4 &0 &3 \\ \hline \\ \hline \end{array}

Add the units column first: 0 + 3 = 3.

\begin{array}{c} & &4 &4 &0 &0 \\ &+ & &4 &0 &3 \\ \hline & & & & &3\\ \hline \end{array}

Add the tens column: 0 + 0 = 0

\begin{array}{c} & &4 &4 &0 &0 \\ &+ & &4 &0 &3 \\ \hline & & & &0 &3\\ \hline \end{array}

Add the hundreds column: 4 + 4 = 8

\begin{array}{c} & &4 &4 &0 &0 \\ &+ & &4 &0 &3 \\ \hline & & &8 &0 &3\\ \hline \end{array}

Add the thousands column: 4 + 0 = 4

\begin{array}{c} & &4 &4&0 &0 \\ &+ & &4 &0 &3 \\ \hline & &4 &8 &0 &3\\ \hline \end{array}

4400 + 403 = 4803

Idea summary

We can use a vertical algorithm to add numbers, starting with the units column.

## Addition of large numbers without regrouping

If our numbers have more digits, the vertical algorithm is an ideal way to solve a subtraction problem. It's important to line our numbers up by place value, as this video shows.

### Examples

#### Example 2

Find the value of 34\,246+3213.

Worked Solution
Create a strategy

Use the standard algorithm method.

Apply the idea

Write it in a vertical algorithm.\begin{array}{c} & &3 &4 &2 &4 &6 \\ &+ & &3 &2 &1 &3 \\ \hline & \\ \hline \end{array}

Add the units column first: 6 + 3 = 9.

\begin{array}{c} & &3 &4 &2 &4 &6 \\ &+ & &3 &2 &1 &3 \\ \hline & & & & & &9 \\ \hline \end{array}

Add the tens column: 4 + 1 = 5

\begin{array}{c} & &3 &4 &2 &4 &6 \\ &+ & &3 &2 &1 &3 \\ \hline & & & & &5 &9 \\ \hline \end{array}

Add the hundreds column: 2 + 2 = 4

\begin{array}{c} & &3 &4 &2 &4 &6 \\ &+ & &3 &2 &1 &3 \\ \hline & & & &4 &5 &9 \\ \hline \end{array}

Add the thousands column: 4 + 3 = 7

\begin{array}{c} & &3 &4 &2 &4 &6 \\ &+ & &3 &2 &1 &3 \\ \hline & & &7 &4 &5 &9 \\ \hline \end{array}

Add the ten thousands column: 3 + 0 = 3

\begin{array}{c} & &3 &4 &2 &4 &6 \\ &+ & &3 &2 &1 &3 \\ \hline & & 3 &7 &4 &5 &9 \\ \hline \end{array}

So, we have: 34\,246 + 3213 = 37\,459

Idea summary
• You can add numbers in any order, but we often add them with the largest number on the top row.

• Zero placeholders are important when we write our digits in a vertical algorithm. In the number below, 40\,743 would be written as 4743 if we didn't include a zero placeholder