How do you Evaluate each expression of 681 subtracted by 265?

Answer 1

416

Answer 2

I guess you are asking about subtracting when a digit in the second number is larger than the same place value digit in the first number.

I'll explain the two methods of subtraction with an example before using them on your numbers.

There are two methods of subtraction: "borrowing" and "payback". They both have the effect of taking 10 of the place value column to the left and putting it in the current place value column being worked on, but with different mechanisms.

When subtracting, align the decimal points (which for while numbers are hiding after the last (ones) digit, so align them to the right) and then do the subtraction digit-by-digit from the rightmost place value column.

Where the digit being subtracted is less than or equal to the one being subtracted from the subtraction can be done, eg 8 - 5 = 3

If the digit being subtracted is greater, then you need to add 10 to it before the subtraction is done, eg 5 - 8; in this case 8 > 5, so need to add 10 to the 5 to get 15 and it becomes 15 - 8 = 7. Where the 10 comes from is the next place value column to the left (as each digit there represents 10 of the place value column to its right). The method of accounting for the 10 that is used is different between the two subtraction methods:

• Borrowing method

In this case, the 10 is found in the place value column to the left. One is subtracted from this column and 10 are added to the column being worked on.

However, if the column to the left contains a 0, 1 cannot be subtracted, so 10 must be "borrowed" for the column to its left, making the column 0 + 10 = 10; 1 can now be subtracted from this column making it 10 - 1 = 9 and 10 added to the working column.

If there are multiple columns of 0s next to each other, the borrowing meth0d is repeatedly applied until the 10 can be "borrowed", with each 0 becoming a 9 and 10 being added to the working column.

Example: 200348 - 19356

Aligning right gives:

_____2__0__0__3__4__8

________1__9__9__5__6 -

8 - 6 = 2, so last digit of result is 2:

_____2__0__0__3__4__8

________1__9__9__5__6 -

-----------------------------

_____________________2

4 - 5 cannot be done since 4 > 3, so need to "borrow" 10, subtracting 1 from the 3; then we have 10 + 4 - 5 = 14 - 5 = 9 for the next digit of the answer:

_____2__0__0__2_14__8

_________1__9__9__5__6 -

-----------------------------

___________________9__2

2 - 9 cannot be done, so need to borrow 10, but as the next column is 0, we need to keep going left to find a non-zero column and borrowing all the way back: the 2 is the column we can use, so it becomes 1, the 0s becomes 9s and we can now add the 10 to the 2 to get: 2 + 10 - 3 = 9 in the answer:

_____1__9__9_12_14__8

_________1__9__9__5__6 -

-----------------------------

_______________3___9__2

9 - 9 = 0:

_____1__9__9_12_14__8

_________1__9__9__5__6 -

-----------------------------

____________0__3___9__2

9 - 1 = 8:

_____1__9__9_12_14__8

_________1__9__9__5__6 -

-----------------------------

_________8__0__3___9__2

1 - nothing = 1:

_____1__9__9_12_14__8

_________1__9__9__5__6 -

-----------------------------

______1__8__0__3__9__2

Done all the digits, so the result is: 199348 - 19956 = 180392

• Payback method

In this case, the 10 is found by increasing the number to subtract from the next column to the left by 1; in other words, the "borrowing" method of subtracting 1 is done by adding the 1 subtracted to the next digit to subtract.

Should the next digit to subtract be a 9, when 1 is added it becomes 10, so like normal addition, the 1 is carried to the next column left to leave 0 to be subtracted.

Example: 200348 - 19356

Aligning right gives:

_____2__0__0__3__4__8

________1__9__9__5__6 -

8 - 6 = 2, so last digit of result is 2:

_____2__0__0__3__4__8

________1__9__9__5__6 -

-----------------------------

_____________________2

4 - 5 cannot be done since 4 > 3, so need to get 10, by adding 1 to the 9 in the next column left of the bottom number; then we have 10 + 4 - 5 = 14 - 5 = 9 for the next digit of the answer:

_____2__0__0__3_14__8

_________1__9_10__5__6 -

-----------------------------

___________________9__2

As 10 is more than a column can hold, the 1 is carried to the next column left (to be added on to 9 to get 10) leaving 0, making the subtraction 3 - 0 = 3:

_____2__0__0__3_14__8

________1_10__0__5__6 -

-----------------------------

________________3__9__2

Again as 10 is more than a column can hold, the 1 is carried to the next column left (to be added on to 1 to get 2) leaving 0, making the subtraction 0 - 0 = 0:

_____2__0__0__3_14__8

________2__0__0__5__6 -

-----------------------------

____________0__3__9__2

0 - 2 cannot be done since 2 > 0, so need to get 10, by adding 1 to the empty next column left of the bottom number, which is the same as 0; then we have 10 + 0 - 2 = 10 - 2 = 8 for the next digit of the answer:

_____2_10__0__3_14__8

_____1__2__0__0__5__6 -

-----------------------------

_________8__0__3__9__2

2 - 1 = 1:

_____2_10__0__3_14__8

_____1__2__0__0__5__6 -

-----------------------------

______1__8__0__3__9__2

All digits done, so: 199348 - 19956 = 180392

With 681 - 265 we have:

• Borrowing method

_____6__8__1

_____2__6__5 -

------------------

"Borrow" 10 from the 8 and subtract:

_____6__7_11

_____2__6__5 -

------------------

____________6

Subtract next column:

_____6__7_11

_____2__6__5 -

------------------

_________1__6

Subtract next column:

_____6__7_11

_____2__6__5 -

------------------

______4__1__6

Result: 681 - 265 = 416

• Payback method

_____6__8__1

_____2__6__5 -

------------------

"Payback" 10 to the 6:

_____6__8_11

_____2__7__5 -

------------------

____________6

Subtract next column:

_____6__8_11

_____2__7__5 -

------------------

_________1__6

Subtract next column:

_____6__8_11

_____2__7__5 -

------------------

______4__1__6

Result: 681 - 265 = 416

Answer 3

681 - 265 = 416