Question

Replace each * by the correct digit in each of the following:

(i) $$\begin{gathered} 876 \\ -*3* \\ \overline{\underline{6*7}} \end{gathered}$$

(ii) $$\begin{gathered} 8989 \\ -**34 \\ \overline{\underline{34**}} \end{gathered}$$

(iii) $$\begin{gathered} 6000107 \\ -**8978 \\ \overline{\underline{506****}} \end{gathered}$$

(iv) $$\begin{gathered} 1000000 \\ -****1 \\ \overline{\underline{*7042*}} \end{gathered}$$

(v) $$\begin{gathered} 5001003 \\ -**6987 \\ \overline{\underline{484****}} \end{gathered}$$

(vi) $$\begin{gathered} 111111 \\ -*6789 \\ \overline{\underline{5432*}} \end{gathered}$$

Answer 1

(i)

Here, we can we see that in the units digit, 6 $-$ * = 7, which means that the value of * is 9, as 1 gets carried from 7 at tens place to 6 at unit place and 6 at unit digit becomes 16 then 16 $-$ 9 = 7.
Now, when 7 gives 1 to 6, it becomes 6, so 6 $-$ 3 = 3.
Also, it can be easily deduced that in ( 8 $-$ * = 6 ), the value of * is 2.

8 7 6
$-$ 2 3 9
6 3 7

(ii)

Here, it is clear that in the units place, 9 $-$ 4 = 5; and in the tens place, 8 $-$ 3 = 5.
We can now easily find out the other missing blanks by subtracting 3455 from 8989.

8 9 8 9
$-$ 3 4 5 5
5 5 3 4

Addend (difference) = 3455

Thus, the correct answer is :
8 9 8 9
$-$ 5 5 3 4
3 4 5 5


(iii)

Here, in the units digit, 17 $-$ 8 = 9; in the tens digit, 9 $-$ 7 = 2; in the hundreds place, 10 $-$ 9 = 1; and in the thousands place, 9 $-$ 8 = 1.
Addend difference = 5061129
So, in order to get the addend, we will subtract 5061129 from 6000107.
6 0 0 0 1 0 7
$-$ 5 0 6 1 1 2 9
0 9 3 8 9 7 8

Thus, the correct answer is:
6 0 0 0 1 0 7
$-$ 0 9 3 8 9 7 8
5 0 6 1 1 2 9


(iv)

In the units place, 10 $-$ 1 = 9. Also, in the lakhs place, 9 $-$ 0 = 9. So, clearly the addend (difference) is 970429.
To find out the other addend, we will subtract 970429 from 1000000.

1 0 0 0 0 0 0
$-$ 0 9 7 0 4 2 9
0 0 2 9 5 7 1

Thus, the correct answer is:
1 0 0 0 0 0 0
$-$ 0 0 2 9 5 7 1
0 9 7 0 4 2 9

(v)

Here, in the units digit, 13 $-$ 7 = 6; in the tens digit, 9 $-$ 8 = 1; in the hundreds place, 9 $-$ 9 = 0; and in the thousands place, 10 $-$ 6 = 4.
Addend (difference ) = 4844016
So, to get the other addend, we will subtract 4844016 from 5001003.
5 0 0 1 0 0 3
$-$ 4 8 4 4 0 1 6
0 1 5 6 9 8 7

Thus, the other addend is 156987.
The correct answer is:

5 0 0 1 0 0 3
$-$ 0 1 5 6 9 8 7
4 8 4 4 0 1 6

(vi)

It is clear from the units place that 11 $-$ 9 = 2. So, the addend (difference) is 54322.
So, to get the other addend, we will subtract 54322 from 111111.
1 1 1 1 1 1
$-$ 5 4 3 2 2
5 6 7 8 9

Thus, the other addend is 56789.
The correct answer is:
1 1 1 1 1 1
$-$ 5 6 7 8 9
5 4 3 2 2