Subtracting Integers

Subtraction is a basic algebraic operation where we take one number away from another. If we had $9$ chocolates, and someone took $3$ chocolates away, we would have $6$ chocolates left. This is expressed as

$9 - 3 = 6.$

Note that when we subtract a large number from a small number, we will have a negative number. So $8 - 10 = -2$.

When subtracting numbers with more than one digit, it is sometimes necessary to decompose the larger unit. For example, in $35-9$ we want to subtract $9$ units, but there are only $5$ units available in $35$. To solve this, we take one of the tens and break it into units which gives us $20$ in tens and $15$ units. $15-9 = 6$ so the result is $26$.

What is $23 - 9$?

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We have $\begin{array} { r r r } & \not 2 ^ 1 & ^1 3 \\ - & & 9 \\ \hline & 1 & 4 \\ \end{array}$

Thus $23 - 9 = 14$. $_\square$

What is $37-4 ?$

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We have $\begin{array} { r r r } & 3 & 7 \\ - & & 4 \\ \hline & 3 & 3 \\ \end{array}$

Thus $37 - 4 = 33 .$ $_\square$

What is $121 - 17 ?$

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We have $\begin{array} { r r r } & 1 & \not 2 ^1 & ^1 1 \\ - & & 1 & 7 \\ \hline & 1 & 0 & 4 \\ \end{array}$

Thus $121 - 17 = 104 .$ $_\square$

What is $2-17 ?$

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When we subtract a large number from a small number, we have a negative number. Since $17-2$ is

$\begin{array} { r r r } & 1 & 7 \\ - & & 2 \\ \hline & 1 & 5 \end{array}$

thus $2 - 17 = -15 .$ $_\square$

What is $27 - 35?$

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When we subtract a large number from a small number, we have a negative number. Since $35-27$ is

$\begin{array} { r r r } & \not 3^2 & ^1 5 \\ - & 2 & 7 \\ \hline & & 8 \end{array}$

thus $27 - 35 = -8 .$ $_\square$