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Year 7 Interactive Maths - Second Edition


Subtraction

Subtracting one number from another number is to find the difference between them.
The symbol used for subtraction is ''.  This is known as the minus sign.

For example, 14 6 = 8

This is read as fourteen take away six is equal to eight (or fourteen take away six is eight).  Also, we can say that 14 minus 6 is 8.


Example 6

Subtract 8 from 17.

Solution:

17 8 = 9


Subtraction of Large Numbers

To subtract large numbers, list them in columns and then subtract only those digits that have the same place value, as illustrated below.

Example 7

Find the difference between 8053 and 397.

Solution:

When subtracting large numbers, remember to write the numbers so that the same place values are in the same column.


Note:
  • We could calculate the above subtraction using the equals addition method.  This method adds the same number (10, 100, 1000 etc.) to both the top number and the bottom number but in different columns whenever the top number's place value cannot be subtracted from the bottom number's place value.  This is shown for Example 7 in the following three steps.

Step 1:  Equals addition method Step 2:  Equals addition methodStep 3:  Equals addition method

  • As 7 cannot be subtracted from 3, add 10 units to 3 in the top number to form 13 and add 10 units to 90 in the bottom number which adds up to 100 as shown above.  The answer remains the same because we have added 10 to the both the top number and bottom number.  We can now subtract 7 from 13 to obtain 6 in the units column.
  • Continuing on, 5 tens (in the tens column) is smaller than 10 tens (9 + 1 tens).  So, we need to add 10 to 5 in the tens column and add 1 to 3 in the hundreds column.  The answer remains the same because we have just added 100 to the both the top number and bottom number.  We can now subtract 10 from 15 to obtain 5 as shown above. 
  • Finally, 0 hundreds (in the hundreds column) is smaller than 4 hundreds (3 + 1 hundreds).  So, we need to add 10 to 0 in the hundreds column and add 1 to the thousands column of the bottom number.  The answer remains the same because we have just added 1000 to both the top number and bottom number.  We can now subtract 4 from 10 in the hundreds column and then 1 from 8 in the thousands column as shown above.

  • We could also calculate the subtraction using the decomposition method.  This method involves borrowing an amount from a higher place value and giving it to a lower place value in the top number and re-writing the top number so that its value does not change as shown in the following two steps.

The decomposition method is used with the two steps shown.

  • As 7 cannot be subtracted from 3, borrow ten from the tens column and add it to 3 and at the same time, reduce the number of tens from 5 to 4 as shown above.  Now subtract 7 from 13 to obtain 6 in the units column.

  • We cannot subtract 9 from 4 in the tens column.  So we must borrow 100 from the thousands column and add it to the tens column (i.e. add 10 to 4 to obtain 14) as shown above.  You can also see that we have reduced 8000 to 7900.  Now subtract 9 from 14, 3 from 9 and 0 from 7 to complete the subtraction.

Key Terms

subtraction, subtracting, difference, minus sign, equals addition method, decomposition method


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