OPERATIONS ON INTEGERS

Positive and Negative Integers with Operations

Adding Rules:

·        Positive + Positive = Positive       e.g  5 + 4 = 9 

·        Negative + Negative = Negative  e.g (- 7) + (- 2) = - 9 

·        Sum of a negative and a positive number :-Use the sign of the larger number and subtract e.g

            (- 7) + 4 = -3

                  6 + (-9) = - 3 

                 (- 3) + 7 = 4

                 5 + ( -3) = 2.

Subtracting Rules:

·        Negative - Positive = Negative  e.g(- 5) - 3 = -5 + (-3) = -8

·        Positive - Negative = Positive + Positive = Positive   e.g 5 - (-3) = 5 + 3 = 8 

·        Negative - Negative = Negative + Positive = Use the sign of the larger number and subtract

          (Change double negatives to a positive.)

          (-5) - (-3) = ( -5) + 3 = -2

          (-3) - ( -5) = (-3) + 5 = 2

Multiplying Rules

·        Positive x Positive = Positive           e.g 3 x 2 = 6

·        Negative x Negative = Positive        e.g (-2) x (-8) = 16 

·        Negative x Positive = Negative       e.g(-3) x 4 = -12

·        Positive x Negative = Negative       e.g 3 x (-4) = -12

Dividing Rules

·        Positive ÷ Positive = Positive          e.g 12 ÷ 3 = 4 

·        Negative ÷ Negative = Positive   e.g(-12) ÷ (-3) = 4 

·        Negative ÷ Positive = Negative   e.g (-12) ÷ 3 = -4

·        Positive ÷ Negative = Negative   e.g 12 ÷ (-3) = -4

INTEGERS WORKSHEET (ADDITION )

1.)  −10 +−7 +−14                         2.)  −7 +−4 +12

3.)  −13 +4 +3                               4.)  −5 +−9 +−16

5.)  −13 +7 +4                               6.)  16 +−16 +3

7.)  −14 +−13 +10                         8.)  13 +−12 +10

9.) 16 +−1 +5                               10)  −2 +7 +1

11.)  15 +−16 + 1                          12.)  3 +4 +−12

13.)   12 +−8 +3                            14.) −14 +1 +−2

15.) −1 +−15 +−1                          16)  −7 +−3 +−1

17.)  −4 +−16 +−15                        18)  13 +14 +−11

19.)   −16 +12 +5                           20.)   −15 +−4 +−15

21.)  −16 + 12 +5                           2 2.)  10 +12 +−9

23.)  2 +−2 +−2                              24.)   −5 +−7 +16

25.)  −6 +−15 +−7                          26.)   −15 +−6 +5

27.)  −7 +−10 +−5                          28.)   −15 +−5 +10

29.)  −1 +−3 +10                             30.)  1 +1 +−16

31.)  7 +8 +−2                                 32.)   −1 +14 +2

33.) −14 +−14 +−9                          34.)   −6 +−6 +−7

35.)  10 +−2 +14                             36.)   −11 +−11 +5

37.)   14 +−6 +5                              38.)   −13 +−2 +1

39.)   8 +−15 +8                              40.)  14 +−14 +13

PRACTICE Assignment for class 6

Q1. Write down the mobile number of your parents in Indian and international System of     

numeration.

Q2. Using the digits  8,0,5 make

a) Smallest 4-digit number.

b) Greatest 6-digit number.

c) Smallest 5-digit number.

Q3. Estimate the following.

a) 1729+235+46

b) 4962+6239-23

c) 8956x23

Q4. Write Roman numerals for following.

1) 690         2) 1846       3) 2090         4) 999

Q5. Write Hindu-Arabic numerals for following.

1) MDCLVI     2) MCDXII      3) CLXII     4) CDLXII

Q6.What should be subtracted from 1lakh to get 77335?

Q7.A machine on an average , produces 3370 screws a day .how many screws did it  produce in

the month of February 2000?

Q8.Replace* by the smallest digit so that 2*345 is divisible by 11.

Q9.Define prime Triplets. Give two examples of prime Triplets.

Q10. Represent the following on number line.

1) 9+4-3

2) 8-5

3) 2x7

4) 5+6

Q11. Solve the following by using properties of whole numbers.

a) 661x93+7x661

b) 569x17+569x13+569x70

c) 631x10x465-367x6310

d) 7265x7265-7265x265

Q12. Test the divisibility of 4295629 by 30.

Q13. Check the divisibility of 23596 by 11.

Q14.Find the least 3-digit number which when divided by 18,24 &34 leaves a remainder 7 in    

each case.

Q15. Determine the greatest number which divides 280 and 1245 leaving remainder 4 and 3

respectively.

Q16. Express 49 &31 as the sum of three odd primes.

Q17.H.C.F. of two numbers is 6 and their L.C.M. is 36. If one of the number is 12 then find

another number.

Q18. Find the difference between place value and face value of 6 in 23654.

Q19 Write all the Prime numbers between 1 and 100.

Q20.The number of sheets of paper available for making notebooks is 75,000. Each sheet makes 8 pages of notebook. Each notebook contains 120 pages. How many books can be made from the paper available

Factors and Mutiples for class 6

Assignment no.-1

Playing with numbers

1. Which of the following is divisible by 3?

a) 24357806   b) 35796812  c) 34679345

2. Which of the following are multiple of 6?

a) 8790432  b) 63458924     c) 85492014

3. Which of the following are divisible by 11?

a) 14322341    b) 222222222    c) 1111111

4. Which of the following is a prime number?

a) 81               b) 87          c) 91       d)   97

5.Which of the following are co-primes?

a)  8,11      b)   9 ,10      c)  6,8      d)   15 ,18

2. The  numbers13 and 31 are prime numbers . Both of these numbers have same digits 1 and 3 . Find such pairs of prime numbers up to 100.

3. Write seven consecutive composite numbers less than 100 so that there is no prime number between them.

4.A number is divisible by 3 and 8 both . By which other number will that number is always divisible?

5.The product of 3 consecutive numbers is always divisible by 6? verify this statement with help of some examples.

6. In each of the following numbers , replace * by the smallest number to make it divisible by 9

a) 2*135       b)   6678*1         c) 385*356

7. In which of the following numbers,replace * by the smallest number to make it divisible by 11

a) 467*91         b)   1723*4           c)   9*8071         d) 39*43

8. Express the greatest 5-digit number as product of primes.

9. What do you mean by perfect numbers ? write any 3 perfect numbers with proper verification.

10. write as many as as possible pairs of prime numbers less than 50 but more than 20 whose sum is divisible by 5.

11. verify that sum any two odd numbers is always multiple of 4.

12.Which of the following are prime numbers?

a) 193                            b)  497       c)  253        d)    323

13. find the greatest 5- digit number which when divided by 20 ,24 , 45 leaves remainder 18 in each case.

14. find the smallest number which is when divided by 20,25,35 and 40 leaves a remainder of 14,19,29,34 respectively.

REFER DIFFERENT MATHEMATICS BOOKS AND DO MORE QUESTIONS BASED ON THIS CHAPTER.