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**Q.1. Divide and check your answer by the corresponding multiplication in each of the following :****(i) 1936/16****(ii) 19881/47****(iii) 257796/341****(iv) 612846/582****(v) 34419/149****(vi) 39039/1001****Ans.** **(i)** By actual division, we have

Check : 121 × 16 = 1936.**(ii)** By actual division, we have

Check :**(iii)** By actual division, we have

Check :

**(iv)** By actual division, we have

Check :

**(v)** By actual division, we have

Check :

**(vi)** By actual division, we have

Check :**Q.2. Divide and find out the quotient and ****remainder. Check your answer :**

**(i) 6971/47****(ii) 4178/35****(iii) 36195/153****(iv) 93575/400****(v) 23025/1000****(vi) 16135/875****Ans. ****(i) **By actual division, we have

∴ Quotient = 148, Remainder = 15

Check : Dividend = Divisor × Quotient + Remainder

= 47 × 148 + 15

= 6956 + 15

= 6971**(ii) **By actual division, we have

∴ Quotient = 119, Remainder = 13

Check : Dividend = Divisor × Quotient + Remainder

= 35 × 119 + 13

= 4165 + 13

= 4178**(iii) **By actual division, we have

∴ Quotient = 236, Remainder = 87

Check : Dividend = Divisor × Quotient + Remainder

= 153 × 236 + 87

= 36108 × 87

= 36195**(iv)** By actual division, we have

∴ Quotient = 233, Remainder = 375

Check : Dividend = Divisor × Quotient + Remainder

= 400 × 233 + 375

= 93200 × 375

= 93575

(v) By actual division, we have

∴ Quotient = 23, Remainder = 25

Check : Dividend = Divisor × Quotient + Remainder

= 1000 × 23 + 25

= 23000 × 25

= 23025**(vi)** By actual division, we have

∴ Quotient = 18, Remainder = 385

Check : Dividend = Divisor × Quotient + Remainder

= 875 × 18 + 385

= 15750 × 385

= 16135**Q.3. Find the value of :****(i) 65007/1****(ii) 0/879****(iii) 981 + 5720/10****(iv) 1507 – 625/25****(v) 32277/(648 – 39)****(vi) 1573/1573 – 1573/1573****Ans.****(i) **We know that any number (non-zero)

divided by 1 gives the number itself

∴ 65007/1 = 65007**(ii) **We know that 0 divided by any natural

number gives 0

∴ 0/879 = 0**(iii) **981 + 5720/10 = 981 + (5720/10)

= 981 + 572

= 1553**(iv)** 1507 – 625 25 = 1507 – (625 25)

= 1507 – 25

= 1482**(v)** 32277/(648 – 39)

= 32277/609

∴ 32277/(648 – 39) = 53**(vi)** 1573/1573 – 1573/1573

= (1573/1573) – (1573/1573)

= 1 – 1 = 0**Q.4. Find a whole number n such that n/n = n.**

**Ans.** We have n/n = n

let n = 1, 1/1 = 1

1 = 1

which is true

Hence 1 is the required whole number.**Q.5. The product of two numbers is 504347. If one of the numbers is 317, find the**

**other.****Ans. **Product of two numbers = 504347

One number = 317

∴ Other number = 504347/317

∴ Other number = 1591**Q.6. On dividing 59761 by a certain number, the quotient is 189 and the remainder is 37. Find the divisor.****Ans.**

Here Dividend = 59761, Quotient = 189

Remainder = 37

We know that Dividend = Divisor × Quotient + Remainder

∴ 59761 = Divisor × 189 + 37

59761 – 37 = Divisor × 189

59724 = Divisor × 189

Divisor × 189 = 59724

Divisor = 59724/189

∴ Divisor = 59724/189 = 316**Q.7. On dividing 55390 by 299, the remainder is 75. Find the quotient, using the division algorithm.**

**Ans.**

Here dividend = 55390,

Divisor = 299 and Remainder = 75

By division algorithm, we have

Dividend = Quotient × Divisor + Remainder

∴ 55390 = Quotient × 299 + 75

55390 – 75 = Quotient × 299

55315 = Quotient × 299

Quotient × 299 = 55315

∴ Quotient = 55315/299

∴ Required quotient = 185**Q.8. What least number must be subtracted from 13601 to get a number exactly divisible by 87 ?****Ans.**

On dividing 13601 by 87, we have

It is clear that if we subtract 29 from 13601, the resulting number will be exactly divisible by 87.

∴ The required least number = 29.**Q.9. What least number must be added to 1056 to get a number exactly divisible by 23 ?****Ans.**

Here dividend = 1056, Divisor = 23

By actual divison, we have

It is clear that if we add 2 to 21, it will become 23 which is divisible by 23.

∴ Required least number = 2.**Q.10. Find the largest 4-digit number divisible by 16.****Ans.**

Greatest 4-digit number = 9999

On, dividing by 16, we get remainder as 15

∴ The required largest 4-digit number

= 9999 – 15 = 9984**Q.11. Divide the largest 5-digit number by 653. Check your answer by the division algorithm.****Ans. **Largest number of 5-digits = 99999

On dividing 99999 by 653, we have

∴ Quotient = 153, Remainder = 90

Check : By division algorithm

Dividend = Divisor × Quotient + Remainder

= 653 × 153 + 90

= 99909 + 90

= 99999**Q.12. Find the least 6-digit number exactly divisible by 83.****Ans.** The least 6-digit number = 100000

On dividing 100000 by 83, we have

It is clear that if we add 15 to 68, it will become 83 which is divisible by 83.

∴ Required least 6-digit number

= 100000 + 15 = 100015**Q.13. 1 dozen bananas cost Rs. 29. How many dozens can be purchased for Rs. 1392 ?****Ans.** Cost of 1 dozen bananas = Rs. 29

∴ Bananas can be purchase in Rs. 1392

= 1392/29 = 48 dozens**Q.14. 19625 trees have been equally planted in 157 rows. Find the number of trees in each row.****Ans.** Total number of trees = 19625

Total number of rows = 157

∴ Number of trees in each row

= 19625/157

∴ Number of trees in each row = 125**Q.15. The population of a town is 517530. If one out of every 15 is reported to be**

**literate, find how many literate persons are there in the town.****Ans. **Total population of the town = 517530 Since there is one educated person out

of 15.

∴ Total number of educated persons in the town = 517530/15

∴ Total number of educated persons in the town = 34502.**Q.16. The cost price of 23 colour television sets is Rs. 570055. Determine the cost price of each TV set if each costs the same.****Ans.**

Cost of 23 colour TV sets = Rs. 570055

Cost of 1 colour TV set

∴ Cost of 1 colour TV set

= Rs. 570055/23 = Rs. 24785

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