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.

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.

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.