Lesson

## Ideas

Now that we are ready to add large numbers with regrouping, it's worth checking back to make sure we are able to  add large numbers where we don't need to regroup  .

### Examples

#### Example 1

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, the answer is: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. For example, 40\,743 would be written as 4743 if we didn't include a zero placeholder

## Addition of large numbers with regrouping

It's time to see how to add large numbers when we do need to do some regrouping. This means we end up with a number more than 9 in one (or more) of our places.

### Examples

#### Example 2

Find the value of 19\,292 + 34\,131.

Worked Solution
Create a strategy

Use the standard algorithm method.

Apply the idea

Write it in a vertical algorithm.\begin{array}{c} & & &1 &9 &2 &9 &2 \\ &+ & &3 &4 &1 &3 &1 \\ \hline & \\ \hline \end{array}

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

In the tens column we get 9+3=12. So we bring down 2 and carry the 1 to the hundreds place.\begin{array}{c} & & &1 &9 &\text{}^ 1 2 &9 &2 \\ &+ & &3 &4 &1 &3 &1 \\ \hline & & & & & &2 &3\\ \hline \end{array}

In the hundreds column we get 1+2+1=4.\begin{array}{c} & & &1 &9 &\text{}^ 1 2 &9 &2 \\ &+ & &3 &4 &1 &3 &1 \\ \hline & & & & &4 &2 &3\\ \hline \end{array}

In the thousands column we get 9 + 4 = 13. So we bring down 3 and carry the 1 to the ten thousands place.\begin{array}{c} & & &\text{}^1 1 &9 &\text{}^ 1 2 &9 &2 \\ &+ & &3 &4 &1 &3 &1 \\ \hline & & & & 3&4 &2 &3\\ \hline \end{array}

For the ten thousands place we get 1+1+3=5.\begin{array}{c} & & &\text{}^1 1 &9 &\text{}^ 1 2 &9 &2 \\ &+ & &3 &4 &1 &3 &1 \\ \hline & & & 5& 3&4 &2 &3\\ \hline \end{array}

So the answer is:19\,292 + 34\,131 = 53\,423

Idea summary

When we add, we always start from the digit furthest to the right, and work left. Any time we have more than 9 in any place, we regroup to the place to the left.