Subtraction

Subtract Across Zeros

Subtract 157 from 400. Both the ones and tens digits are 0, so borrowing must chain: first borrow from hundreds into tens, then from tens into ones.

borrow-across-zeros When the tens digit is 0, you cannot borrow directly into the ones column. First borrow from the hundreds: hundreds decreases by 1 and tens becomes 10. Then borrow from tens into ones: tens decreases by 1 (to 9) and ones increases by 10.

Example

Subtract 157 from 400 by borrowing across zero.

highlighted = computed this step

Step 1 — Set up

Line up the numbers by place value.

xxxxx400−157x□□□\begin{array}{rrrr}\phantom{x}&\phantom{x}&\phantom{x}&\phantom{x}\\\phantom{x}&4&0&0\\-&1&5&7\\\hline\\\phantom{x}&\square&\square&\square\end{array}
Line up hundreds, tens, and ones.hundredstensones441--005--007---Start with 400 - 157; the zeros mean regroup before subtracting ones.The value stays the same; only the place-value groups change.

Step 2 — Borrow from hundreds

Borrow from hundreds: 4 -> 3, tens 0 -> 10.

x310xx400−157x□□□\begin{array}{rrrr}\phantom{x}&\hl{3}&\hl{10}&\phantom{x}\\\phantom{x}&4&0&0\\-&1&5&7\\\hline\\\phantom{x}&\square&\square&\square\end{array}
Move 1 hundred into the tens column.hundredstensones341--1005--007---1 hundred = 10 tens4 hundreds -> 3 hundreds; 0 tens -> 10 tens.The value stays the same; only the place-value groups change.

Step 3 — Borrow for ones

Borrow from tens: 10 -> 9, ones become 10; 10 - 7 = 3.

x3910x400−157x□□3\begin{array}{rrrr}\phantom{x}&3&\hl{9}&\hl{10}\\\phantom{x}&4&0&0\\-&1&5&7\\\hline\\\phantom{x}&\square&\square&\hl{3}\end{array}
Move 1 of those tens into the ones column.hundredstensones341--905--10073-1 hundred = 10 tens1 ten = 10 ones10 tens -> 9 tens; 0 ones -> 10 ones, then 10 - 7 = 3.The value stays the same; only the place-value groups change.

Step 4 — Tens column

Tens: 9 - 5 = 4, write 4.

x3910x400−157x□43\begin{array}{rrrr}\phantom{x}&3&9&10\\\phantom{x}&4&0&0\\-&1&5&7\\\hline\\\phantom{x}&\square&\hl{4}&3\end{array}
Now the tens column has enough to subtract.hundredstensones341--905410073-1 hundred = 10 tens1 ten = 10 onesUse the regrouped tens: 9 - 5 = 4.The value stays the same; only the place-value groups change.

Step 5 — Hundreds column

Hundreds: 3 - 1 = 2, write 2.

x3910x400−157x243\begin{array}{rrrr}\phantom{x}&3&9&10\\\phantom{x}&4&0&0\\-&1&5&7\\\hline\\\phantom{x}&\hl{2}&4&3\end{array}
Finish with the hundreds column.hundredstensones3412905410073-1 hundred = 10 tens1 ten = 10 onesUse the regrouped hundreds: 3 - 1 = 2.The value stays the same; only the place-value groups change.

Step 6 — Result

Read the complete difference: 243.

x3910x400−157x243\begin{array}{rrrr}\phantom{x}&3&9&10\\\phantom{x}&4&0&0\\-&1&5&7\\\hline\\\phantom{x}&2&4&3\end{array}
Read the completed difference: 243.hundredstensones3412905410073-1 hundred = 10 tens1 ten = 10 onesResult: 400 - 157 = 243.The value stays the same; only the place-value groups change.