2.08 Vertical algorithms

Use the vertical algorithm method.

Write it in a vertical algorithm.\begin{array}{c} & &4 &1 \\ &+ &5 &6 \\ \hline \\ \hline \end{array}

Add the numbers down each column starting from the ones column, then the tens column to get:\begin{array}{c} & &4 &1 \\ &+ &5 &6 \\ \hline & &9 &7 \\ \hline \end{array}So 41 + 56 = 97.

Use the subtraction algorithm method.

Write it in a vertical algorithm.\begin{array}{c} & & &9 &9 &7 \\ &- & &6 &4 &8 \\ \hline & \\ \hline \end{array}

Begin with the units column. We can see that 7 is less than 8, so we need to trade 1 ten from the tens place.

So we get 17 - 8 = 9 in the units column and 9 tens becomes 8 tens in the first row.\begin{array}{c} & & &9 &8 &\text{ }^1 7 \\ &- & &6 &4 &8 \\ \hline & & & & &9 \\ \hline \end{array}

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

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

So 997 - 648 = 349.

Use the vertical algorithm method.

Write it in a vertical algorithm.\begin{array}{c} & & &2 &1 &2 &4 \\ &+ & &3 &3 &5 &1 \\ \hline & \\ \hline \end{array}

Add the ones column first. So 4 + 1 = 5:

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

Then add the tens column, 2 + 5 = 7:\begin{array}{c} & & &2 &1 &2 &4 \\ &+ & &3 &3 &5 &1 \\ \hline & & & & &7 &5\\ \hline \end{array}

Then add the hundreds column, 1 + 3 = 4:\begin{array}{c} & & &2 &1 &2 &4 \\ &+ & &3 &3 &5 &1 \\ \hline & & & &4 &7 &5\\ \hline \end{array}

Then add the thousands column, 2 + 3 = 5

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

So 2124 + 3351 = 5475.

Use the vertical algorithm method.

Write it in a vertical algorithm.\begin{array}{c} & & &7 &2 &6 &3 \\ &- & &2 &4 &1 &8 \\ \hline & \\ \hline \end{array}

Subtract the ones column first. In the ones column we can see that 3 is less than 8, so we need to trade 1 ten from the tens place.

So we get 13-8=5 in the ones column and 6 tens becomes 5 tens in the first row.\begin{array}{c} & & &7 &2 &5 &\text{}^1 3 \\ &- & &2 &4 &1 &8 \\ \hline & & & & & &5\\ \hline \end{array}

So for the tens column we have 5 - 1 = 4:\begin{array}{c} & & &7 &2 &5 &\text{}^1 3 \\ &- & &2 &4 &1 &8 \\ \hline & & & & &4 &5\\ \hline \end{array}

In the hundreds column, we can see that 2 is less than 4, so we need to trade 1 thousand from the thousands place.

So we get 12-4=8 in the hundreds column and 7 thousands becomes 6 thousands in the first row.\begin{array}{c} & & &6 &\text{}^1 2 &5 &\text{}^1 3 \\ &- & &2 &4 &1 &8 \\ \hline & & & &8 &4 &5\\ \hline \end{array}

And for the thousands place 6 - 2 = 4:\begin{array}{c} & & &6 &\text{}^1 2 &5 &\text{}^1 3 \\ &- & &2 &4 &1 &8 \\ \hline & & &4 &8 &4 &5\\ \hline \end{array}

So 7263 - 2418 = 4845.