SUBTRACTION OF NUMBERS MADE EASY, WORD PROBLEMS, EXAMPLES, EXERCISES

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Please study the base-10 number system or
decimal number system,
if you have not already done so.

There, we have seen predecessor
numbers to a given number.

predecessor number is nothing but
the number obtained by subtracting
1 from the given number.

We have seen the base symbols or
characters or digits of the
decimal system as
0, 1, 2, 3, 4, 5, 6, 7, 8, 9.

You need to remember these digits
in order and their names.

In these digits, each digit is
1 less than the next digit or
1 subtracted from the next digit.

The symbol for subtracting is -.
So, we can say,
1 - 1 = 0; 2 - 1 = 1; 3 - 1 = 2;
4 - 1 = 3; 5 - 1 = 4; 6 - 1 = 5;
7 - 1 = 6; 8 - 1 = 7; 9 - 1 = 8.

Now suppose I ask you,
what is 3 - 2 ?

or find the values of
2 - 2; 4 - 2, 5 - 2, 6 - 2,
7 - 2, 8 - 2, 9 - 2.

Can you do that ?

















In stead of 1,
we are subtracting 2 here.

To find these differences,
you may use your fingers.

Close your fingers first.

Example 1 :

Find 3 - 2.

To subtract 2 from 3, open 3
(from which we are subtracting)
fingers from your closed fingers.

Start counting from 1,
and close one of your opened
fingers for every count.

so, you say one and close
one of the opened fingers.

Say two and close one more finger.

The process ends here, since two
(which is being subtracted )
is reached.

Now one finger is still open.
The number of fingers opened,
one, is the answer.

So 3 - 2 = 1.

The number from which another is
subtracted is called minuend.

The number that is subtracted from
another is called subtrahend.

Example 2 :

Similarly what is 8 - 2 ?

To subtract 2 from 8, open 8
( 8 is minuend )
fingers from your closed fingers.

Start counting from 1,
and close one of your opened
fingers for every count.

so, you say one and close one of
the opened fingers.

Say two and close one more finger.

The process ends here, since two
( 2 is subtrahend ) is reached.

Count the number of fingers opened.

The number of fingers opened is six.

The number of fingers opened, six,
is the answer.

So 8 - 2 = 6.

Similarly the other answers are,

2 - 2 = 0; 4 - 2 = 2, 5 - 2 = 3,
6 - 2 = 4, 7 - 2 = 5, 9 - 2 = 7.

Exercise 1A : single digit numbers

  1. Find 4 - 1
  2. Find 6 - 3
  3. Find 2 - 0
  4. Find 5 - 4
  5. Find 4 - 4
  6. Find 9 - 5
  7. Find 8 - 3
  8. Find 6 - 2
  9. Find 7 - 4
  10. Find 5 - 3

For Answers see at the end of the page.

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Problems : Fill in the Blank Type

Before going for Example 3 :

Observe that 4 - 1 = 3 and 4 - 3 = 1
i.e. 1 removed from 4 gives 3 and
this 3 removed from the same 4 gives 1.

Observe that 8 - 3 = 5 and 8 - 5 = 3
i.e. 3 removed from 8 gives 5 and
this 5 removed from the same 8 gives 3.

Observe that 7 - 4 = 3 and 7 - 3 = 4
i.e. 4 removed from 7 gives 3 and
this 3 removed from the same 7 gives 4.

If you remove a number from a given number,
you get the R.H.S. number.

If you remove the R.H.S. number
from the given number,
you will get the removed number.

To find the removed number
which is blank, remove the R.H.S.
number from the given number.

To summarise the above discussion,

We know minuend - subtrahend = result.
If subtrahend is blank, then
subtrahend = minuend - result



Example 3 :

Now I ask you how much subtracted
from 7 wiil give 3.

In other words,
fill in the blank 7 - --- = 3.

From the above observations,
we can say the blank number
= 7 - 3, which you can find by
opening 7 fingers and closing
3 fingers, and counting the
remaining open fingers which is 4.

So the answer is 4.

Let us see one more example.



Example 4 :

Fill in the blank 9 - --- = 2

From the above observations,
we can say the blank number
= 9 - 2, which you can find by
opening 9 fingers and closing
2 fingers and counting the
remaining open fingers which is 7.

So the answer is 7.

Before going for
Example 5 :

Observe that 4 - 1 = 3
and 4 = 3 + 1
i.e. 1 removed
from 4 gives 3 and
this 3 added to 1 gives 4.

Observe that 8 - 3 = 5
and 8 = 5 + 3
i.e. 3 removed
from 8 gives 5 and
this 5 added to 3 gives 8.

Observe that 7 - 4 = 3
and 7 = 3 + 4
i.e. 4 removed
from 7 gives 3 and
this 3 added to 4 gives 7.

If you remove a number
from a given number,
you get the R.H.S. number.

If you add the R.H.S. number
and the removed number,
you will get the given number.

To find the given number
which is blank, add the R.H.S.
number and the removed number.

To summarise the above discussion,

We know minuend - subtrahend = result.
If minuend is blank, then
minuend = subtrahend + result















Example 5 :

Fill in the blank --- - 4 = 2

From the above observations,
we can say the blank number
= 2 + 4, which you can find by
addition of 2 and 4 which is 6.

So the answer is 6.

Example 6 :

Fill in the blank --- - 3 = 6

From the above observations,
we can say the blank number
= 6 + 3 which you can find by
addition of 6 and 3 which is 9.

So the answer is 9.

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Exercise 1B : Fill in the Blanks

Fill in the Blanks.

  1. --- - 6 = 3
  2. 3 - --- = 1
  3. 8 - --- = 3
  4. --- - 9 = 0
  5. 8 - --- = 4
  6. --- - 4 = 5
  7. --- - 3 = 4
  8. 6 - ---- = 1
  9. --- - 1 = 7
  10. 7 - --- = 2

For Answers see at the end of the page.

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Further Topics :

The following Links take you to
different topics.

Subtraction of

Two Digit Numbers.

Three Digit Numbers.

Four Digit Numbers.

Any Digit Numbers.

Word problems.

Fractions.

Decimals.

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Answers to Exercises

Answers to Exercise 1A :
single digit numbers

  1. 3
  2. 3
  3. 2
  4. 1
  5. 0
  6. 4
  7. 5
  8. 4
  9. 3
  10. 2

Answers to Exercise 1B :
Fill in the Blanks

  1. 9
  2. 2
  3. 5
  4. 9
  5. 4
  6. 9
  7. 7
  8. 5
  9. 8
  10. 5