Subtraction

Subtract Three-Digit Numbers With Borrowing

Subtract 284 from 731 with borrowing in both the ones column and the tens column to get 447.

Example

Subtract 284 from 731 with two regrouping steps.

highlighted = computed this step

Step 1 — Set up

Line up the numbers by place value.

xxxxx731−284x□□□\begin{array}{rrrr}\phantom{x}&\phantom{x}&\phantom{x}&\phantom{x}\\\phantom{x}&7&3&1\\-&2&8&4\\\hline\\\phantom{x}&\square&\square&\square\end{array}
Line up 731 and 284 by placehundreds72tens38ones14-731 - 284Start in the ones column and move left.

Step 2 — Borrow for ones

Ones: 1 < 4, borrow 1 ten: 11 - 4 = 7.

xx211x731−284x□□7\begin{array}{rrrr}\phantom{x}&\phantom{x}&\hl{2}&\hl{11}\\\phantom{x}&7&3&1\\-&2&8&4\\\hline\\\phantom{x}&\square&\square&\hl{7}\end{array}
Ones: 1 is less than 4, borrow 1 tenhundreds72tens238ones11147-1 ten = 10 ones11 - 4 = 7 ones1 ten becomes 10 ones, so 1 ones become 11 ones.

Step 3 — Borrow for tens

Borrow for tens: hundreds become 6, tens become 12; 12 - 8 = 4.

x61211x731−284x□47\begin{array}{rrrr}\phantom{x}&\hl{6}&\hl{12}&11\\\phantom{x}&7&3&1\\-&2&8&4\\\hline\\\phantom{x}&\square&\hl{4}&7\end{array}
Tens: 2 is less than 8, borrow 1 hundredhundreds672tens12384ones11147-1 ten = 10 ones1 hundred = 10 tens12 - 8 = 4 tens1 hundred becomes 10 tens, so 2 tens become 12 tens.

Step 4 — Hundreds column

Hundreds: 6 - 2 = 4, write 4.

x61211x731−284x447\begin{array}{rrrr}\phantom{x}&6&12&11\\\phantom{x}&7&3&1\\-&2&8&4\\\hline\\\phantom{x}&\hl{4}&4&7\end{array}
Hundreds: 6 - 2 = 4hundreds6724tens12384ones11147-1 ten = 10 ones1 hundred = 10 tens6 - 2 = 4 hundredsThe hundreds column is now 6 - 2.

Step 5 — Result

Read the complete difference: 447.

x61211x731−284x447\begin{array}{rrrr}\phantom{x}&6&12&11\\\phantom{x}&7&3&1\\-&2&8&4\\\hline\\\phantom{x}&4&4&7\end{array}
731 - 284 = 447hundreds6724tens12384ones11147-1 ten = 10 ones1 hundred = 10 tens4 hundreds, 4 tens, 7 ones make 447Read the hundreds, tens, and ones digits together.
chained-borrowing A subtraction problem may require borrowing in more than one column. Each borrow reduces the column to the left by 1 and adds 10 to the current column. Handle borrows from right to left, one column at a time.