Adding and Subtracting Within 100

Add tens and ones

To add $47 + 38$, add the tens and the ones on their own.

• Tens: $40 + 30 = 70$
• Ones: $7 + 8 = 15$

Then put them back together: $70 + 15 = 85$.

Written in columns, the $15$ ones are $1$ ten and $5$ ones. The new ten goes on top of the tens column:

$$\begin{array}{r} \rlap{\scriptsize 1}\phantom{0}\phantom{0} \\ 47 \\ +\; 38 \\ \hline 85 \end{array}$$

Make a ten

Another way: move part of one number to fill a ten.

$47$ needs $3$ to reach $50$. Take $3$ from the $38$, which leaves $35$.

$$47 + 38 = 50 + 35 = 85$$

Subtract tens and ones

For $72 - 35$, there are only $2$ ones, and $5$ ones must go. So break one ten into ten ones: $72$ is $6$ tens and $12$ ones.

• Ones: $12 - 5 = 7$
• Tens: $6 - 3 = 3$

The answer is $37$.

You can also count up from $35$ to $72$: $5$ gets to $40$, then $32$ more gets to $72$. $5 + 32 = 37$.

Why these ways work

Each way changes how the numbers are split up. None of them changes how much there is.

• A ten is ten ones. Trading one ten for ten ones, or ten ones for a ten, keeps the amount the same. That is why regrouping is allowed.
• A sum can be added in any order. $47 + 38$ can be split into tens and ones and added back in any order, and the total stays $85$.
• Adding and subtracting undo each other. $35 + 37 = 72$, so $72 - 35 = 37$. That is why counting up finds a difference.

Add three or four numbers

A sum can be added in any order. So look for pairs whose ones make ten.

$$26 + 14 + 35 + 25 = (26 + 14) + (35 + 25) = 40 + 60 = 100$$

Worked examples

Common mistakes

Practice problems