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Question

# Replace each * by the correct digit in each of the following: (i) $876\phantom{\rule{0ex}{0ex}}-*3*\phantom{\rule{0ex}{0ex}}\overline{)\overline{)6*7}}$ (ii) $8989\phantom{\rule{0ex}{0ex}}-**34\phantom{\rule{0ex}{0ex}}\overline{)\overline{)34**}}$ (iii) $6000107\phantom{\rule{0ex}{0ex}}-**8978\phantom{\rule{0ex}{0ex}}\overline{)\overline{)506****}}$ (iv) $1000000\phantom{\rule{0ex}{0ex}}-****1\phantom{\rule{0ex}{0ex}}\overline{)\overline{)*7042*}}$ (v) $5001003\phantom{\rule{0ex}{0ex}}-**6987\phantom{\rule{0ex}{0ex}}\overline{)\overline{)484****}}$ (vi) $111111\phantom{\rule{0ex}{0ex}}-*6789\phantom{\rule{0ex}{0ex}}\overline{)\overline{)5432*}}$

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Solution

## (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

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