2.07 Applications of subtraction

Use the subtraction algorithm with regrouping.

Write the subtraction in a vertical algorithm.\begin{array}{c} & &5 &8 \\ &- &2 &9 \\ \hline & \\ \hline \end{array}

Begin with the ones column. Since we don't have enough ones to subtract 9 from 8, we need to trade 1 ten from the tens place. \begin{array}{c} & &4 & \text{}^1 8 \\ &- &2 &9 \\ \hline & & \\ \hline \end{array}

Now we can subtract 9 from 18 in the ones column and 5 tens becomes 4 tens.\begin{array}{c} & &4 & \text{}^1 8 \\ &- &2 &9 \\ \hline & & & 9 \\ \hline \end{array}

Then subtract the numbers in the tens column, 4- 2 = 2.\begin{array}{c} & &4 & \text{}^1 8 \\ &- &2 &9 \\ \hline & &2 & 9 \\ \hline \end{array}

So, 58 - 29=29.

Find the difference of the first and second numbers and subtract the third number from it.

Write the first two numbers in a vertical algorithm.\begin{array}{c} & &3 &0 \\ &- &1 &8 \\ \hline & \\ \hline \end{array}

Subtract the numbers starting with the units column. We can see that 0 is less than 8, so we need to trade 1 ten from the tens column.\begin{array}{c} & &2 &\text{}^1 0 \\ &- &1 &8 \\ \hline & &1 &2 \\ \hline \end{array}

Subtract 7 from the result using a vertical algorithm.\begin{array}{c} & &1 &2 \\ &- & &7 \\ \hline & \\ \hline \end{array}

In the units column, we can see that 2 is less than 7, so we need to trade 1 ten from the tens column. This gives us 12 - 7 = 5 in the units column and 1 ten becomes 0 ten in the first row. \begin{array}{c} & &0 &\text{}^1 2 \\ &- & &7 \\ \hline & & &5 \\ \hline \end{array}

30 - 18 - 7 = 5

Use the subtraction algorithm method.

Write it in a vertical algorithm.\begin{array}{c} & &4 &2 &3 &7 &3 \\ &- &2 &5 &2 &1 &5 \\ \hline & \\ \hline \end{array}

Begin with the units column. We can see that 3 is less than 5, so we need to trade 1 ten from the tens column. This gives us 13 - 5 = 8 in the units column and 7 tens becomes 6 tens in the first row. \begin{array}{c} & &4 &2 &3 &6 &\text{}^13 \\ &- &2 &5 &2 &1 &5 \\ \hline & & & & & &8 \\ \hline \end{array}

For the tens place: 6 - 1 = 5.\begin{array}{c} & &4 &2 &3 &6 &\text{}^13 \\ &- &2 &5 &2 &1 &5 \\ \hline & & & & &5 &8 \\ \hline \end{array}

For the hundreds place: 3 - 2 = 1.\begin{array}{c} & &4 &2 &3 &6 &\text{}^13 \\ &- &2 &5 &2 &1 &5 \\ \hline & & & &1 &5 &8 \\ \hline \end{array}

In the thousands column, we can see that 2 is less than 5, so we need to trade 1 ten thousand from the ten thousands column. This gives us 12 - 5 = 7 in the thousands column and 4 ten thousands becomes 3 ten thousands in the first row. \begin{array}{c} & &3 &\text{}^1 2 &3 &6 &\text{}^13 \\ &- &2 &5 &2 &1 &5 \\ \hline & & &7 &1 &5 &8 \\ \hline \end{array}

For the ten thousands place: 3 - 2 = 1.\begin{array}{c} & &3 &\text{}^1 2 &3 &6 &\text{}^13 \\ &- &2 &5 &2 &1 &5 \\ \hline & &1 &7 &1 &5 &8 \\ \hline \end{array}

42\,373 - 25\,215 = 17\,158

The words "taken away" mean subtraction while the words "get into" mean addition.

We have 83 sheeps in total, 9 of them were taken away and 2 got in. So the number sentence for this is:\text{Number of sheep} = 83 - 9 + 2

From the number sentence above, write the first number and the second number in a vertical algorithm to find their difference. \begin{array}{c} & &8 &3 \\ &- & &9 \\ \hline \\ \hline \end{array}

Begin with the units column. We can see that 3 is less than 9, so we need to trade 1 ten from the tens column. This gives us 13 - 9 = 4 in the units column and 8 tens becomes 7 tens in the first row. \begin{array}{c} & &7 &\text{}^1 3 \\ &- & &9 \\ \hline & & &4 \\ \hline \end{array}

For the tens place: 7 - 0 = 7.\begin{array}{c} & &7 &\text{}^1 3 \\ &- & &9 \\ \hline & &7 &4 \\ \hline \end{array}

Add 2 to the result. Write it in a vertical algorithm. \begin{array}{c} & &7 &4 \\ &+ & &2\\ \hline \\ \hline \end{array}

For the units place: 4 + 2 = 6. \begin{array}{c} & &7 &4 \\ &+ & &2 \\ \hline & & &6 \\ \hline \end{array}

For the tens place: 7 + 0 = 7. \begin{array}{c} & &7 &4 \\ &+ & &2 \\ \hline & &7 &6 \\ \hline \end{array}

So there are 76 sheep in the paddock now.