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.

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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

The sum of 40743 and 3214 using a vertical algorithm where the zero is a place holder.

2.01 Addition without regrouping

Ideas

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Examples

Example 1

Addition of large numbers without regrouping

Examples

Example 2

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