{"id":1327,"date":"2020-10-19T08:10:06","date_gmt":"2020-10-19T08:10:06","guid":{"rendered":"http:\/\/themindpalace.in\/?p=1327"},"modified":"2021-08-26T05:32:12","modified_gmt":"2021-08-26T05:32:12","slug":"integers","status":"publish","type":"post","link":"https:\/\/themindpalace.in\/index.php\/2020\/10\/19\/integers\/","title":{"rendered":"INTEGERS"},"content":{"rendered":"\n

summary of integers<\/a><\/p>\n\n\n\n

Solved exercise of integers<\/a><\/p>\n\n\n\n

<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

Summary<\/h1>\n\n\n\n

An integer is defined as the number that can be written without a fractional components ie,21, 4, 0, and \u22122048.A number which is not a fraction is a whole number that can be positive, negative , or zero.<\/p>\n\n\n\n

  • Z is a Subset of the set of all rational numbers<\/li>
  • Q, which in turn is a subset of the real numbers R.<\/li>
  • The symbol z can be to denote various sets <\/li>
  • Symbol z0+<\/sup> is denoted for the  positive integer<\/li>
  • Z0-<\/sup>is denoted for the negative integer.<\/li><\/ul>\n\n\n\n

    Example<\/span><\/strong><\/p>\n\n\n\n

    \"\"<\/figure><\/div>\n\n\n\n

    Natural numbers are positive integers                                                            <\/p>\n\n\n\n

    Natural numbers and “0” together termed as Whole numbers                   <\/p>\n\n\n\n

    Integers include whole numbers as well as negative integer.<\/p>\n\n\n\n

    Multiplication of Integers.<\/span><\/strong><\/p>\n\n\n\n

    Multiplication of a positive integer by a positive integer: If a sign is not attached to a number, it is considered to be positive.<\/p>\n\n\n\n

    Example<\/span><\/p>\n\n\n\n

    Bharath bought 3 pencil boxes from a shop. If each box contains 6 pencils, find the total number of pencils Bharatha has?<\/p>\n\n\n\n

    6+ 6 + 6 = 18 (addition).<\/p>\n\n\n\n

    Multiplication of a Positive integer by a Negative integer<\/span><\/strong><\/p>\n\n\n\n

    If we multiply two integers having unlike signs then, their product will be always negative.<\/p>\n\n\n\n

    Example<\/span><\/p>\n\n\n\n

    (-3)x(+4)=-12.<\/p>\n\n\n\n

    Multiplication of an integer by ‘0’<\/span><\/strong><\/p>\n\n\n\n

    When an integer is multiplied by zero we get zero.<\/p>\n\n\n\n

    Example:<\/span><\/p>\n\n\n\n

    5 \u00d7 0 = 0<\/strong><\/p>\n\n\n\n

    Multiplication of a Negative integer by a negative integer<\/strong>.<\/span><\/p>\n\n\n\n

    Here the product of two negative integers is a positive integer.<\/p>\n\n\n\n

    Example:<\/span><\/p>\n\n\n\n

    (-5)x-(6)=+30.<\/p>\n\n\n\n

    Division of Integer<\/span><\/strong><\/p>\n\n\n\n

    Division of whole numbers is an inverse process of multiplication.<\/p>\n\n\n\n

    Exercise 1.1<\/span><\/strong><\/p>\n\n\n\n

    Simplify the following<\/span><\/strong><\/p>\n\n\n\n

    1) 8 + 5      <\/p>\n\n\n\n

       = +13<\/span><\/strong><\/p>\n\n\n\n

    \n\n\n\n

    2) 2 + (\u20137)<\/p>\n\n\n\n

        +7 -2     <\/p>\n\n\n\n

          =  -5<\/span><\/strong><\/p>\n\n\n\n

    \n\n\n\n

    3) (\u20133) + (4)<\/p>\n\n\n\n

         4-3<\/p>\n\n\n\n

        = +1<\/span><\/strong><\/p>\n\n\n\n

    \n\n\n\n

    4) (\u2013 7) + (\u2013 2)<\/p>\n\n\n\n

         -7 + 2<\/p>\n\n\n\n

            =  -9<\/span><\/strong><\/p>\n\n\n\n

    \n\n\n\n

    Exercise 1.2<\/span><\/strong><\/h1>\n\n\n\n

    I.Multiply each number in the row by the numbers in the column and write the product as shown.<\/strong><\/p>\n\n\n\n

    x<\/span><\/strong><\/td>–3<\/span><\/strong><\/td>6<\/span><\/strong><\/td>11<\/span><\/strong><\/td>-5<\/span><\/strong><\/td><\/tr>
    7<\/span><\/td>-21<\/td>42<\/td>77<\/td>-35<\/td><\/tr>
    4<\/strong><\/span><\/td>-12<\/td>24<\/td>44<\/td>-20<\/td><\/tr>
    -8<\/span><\/strong><\/td>+24<\/td>-48<\/td>-88<\/td>+40<\/td><\/tr>
    -2<\/span><\/strong><\/td>+6<\/td>-12<\/td>-22<\/td>+10<\/td><\/tr>
    12<\/span><\/strong><\/td>-36<\/td>72<\/td>132<\/td>-60<\/td><\/tr>
    -9<\/span><\/strong><\/td>+27<\/td>-54<\/td>-99<\/td>+45<\/td><\/tr>
    -4<\/span><\/strong><\/td>+42<\/td>-84<\/td>-154<\/td>+70<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n

    II.Multiply the number in the outer circle by the number in the inner circle and fill in the appropriated boxes given outside the circle by their product.<\/strong><\/span><\/p>\n\n\n\n

    Now select any numbers from the 8 5 -5 -6 7 -2 1 wheel and multiply by other number.<\/p>\n\n\n\n

    \"\"<\/figure><\/div>\n\n\n\n

    Exercise 1.3<\/span><\/strong><\/p>\n\n\n\n

    I. Find the products of the following integers<\/strong>.<\/p>\n\n\n\n

    1)5, (\u2013 3)<\/p>\n\n\n\n

    +15 x -3<\/p>\n\n\n\n

      = -15<\/span><\/strong><\/p>\n\n\n\n

    \n\n\n\n

    <\/p>\n\n\n\n

      2)(\u2013 3), 8<\/p>\n\n\n\n

         -3 x 8<\/p>\n\n\n\n

       =-24<\/span><\/strong><\/p>\n\n\n\n

    \n\n\n\n

     3) 7, (\u2013 34)<\/p>\n\n\n\n

         7 x -34<\/p>\n\n\n\n

        =-238<\/span><\/strong><\/p>\n\n\n\n

    \n\n\n\n

    4) (\u20133), (\u2013 12)<\/p>\n\n\n\n

    -3 x -12<\/p>\n\n\n\n

     =+36<\/span><\/strong><\/p>\n\n\n\n

    \n\n\n\n

    5) (\u2013 21), 6<\/p>\n\n\n\n

        -21 x 6<\/p>\n\n\n\n

          =-126<\/span><\/strong><\/p>\n\n\n\n

    \n\n\n\n

    6) (\u20132), (3), \u2013(4)<\/p>\n\n\n\n

    -2 x3 x -4<\/p>\n\n\n\n

      =-6 x -4<\/p>\n\n\n\n

      =+24<\/span><\/strong><\/p>\n\n\n\n

    \n\n\n\n

    7) (\u20133), 4, (\u20135), (\u20131)<\/p>\n\n\n\n

        -3 x 4 (-5) (-1)<\/p>\n\n\n\n

       = -12 x-5 x -1                                                                                                         <\/p>\n\n\n\n

     -12 x +5  <\/p>\n\n\n\n

    =-60<\/span><\/strong><\/p>\n\n\n\n

    \n\n\n\n

    II. Fill in the blanks appropriately and write the product<\/span><\/strong><\/p>\n\n\n\n

    \"\"<\/figure><\/div>\n\n\n\n
    \n\n\n\n

    III. Tick the correct answer in the following situations.<\/span><\/strong><\/p>\n\n\n\n

    1.An open tank filled with water is on the terrace of a building. Evaporation causes the height of the water level to change by 2cm each day.<\/p>\n\n\n\n

    If the first day the water level is x cm, then after 6 days the level is<\/p>\n\n\n\n

     a) x cm + (2 \u00d7 6) cm                            b) x cm \u2013 (2 \u00d7 6) cm<\/p>\n\n\n\n

     c) x cm \u2013 (2 \u00d7 \u20136) cm                          d) 6 \u00d7 x cm \u2013 2 cm<\/p>\n\n\n\n

    Ans:<\/span>b) x cm \u2013 (2 \u00d7 6) cm<\/p>\n\n\n\n

    \n\n\n\n

    2) During the past 8 weeks Mr. Girish has deposited  7500 each week to his bank account. He has a bank balance of  62000 now. So his bank balance 8 weeks ago if no interest is added up in this period was,<\/p>\n\n\n\n

     a)  (62000 \u2013 8 \u00d7 7 \u00d7 7500)                  b)  (62000 \u2013 8 \u00d7 7500)<\/p>\n\n\n\n

     c) (62000 + 8 \u00d7 7500)                         d)   (8 \u00d7 7500 \u2013 62000)<\/p>\n\n\n\n

    Ans:<\/span>b)  (62000 \u2013 8 \u00d7 7500)<\/p>\n\n\n\n

    Exercise 1.4<\/span><\/strong><\/p>\n\n\n\n

    I. Simplify the following<\/strong>.<\/span><\/p>\n\n\n\n

    1)(\u2013 40) \u00f7 (\u2013 10)<\/p>\n\n\n\n

    -40 \u00f7 -10<\/p>\n\n\n\n

    =+4<\/span><\/strong><\/p>\n\n\n\n

    \n\n\n\n

    2) 34 \u00f7 (\u2013 2)<\/p>\n\n\n\n

     34\u00f7 -2<\/p>\n\n\n\n

    =-2<\/span><\/strong><\/p>\n\n\n\n

    \n\n\n\n

    3) (-44) \u00f7 4<\/p>\n\n\n\n

     -44\u00f74<\/p>\n\n\n\n

    =  -11<\/span><\/strong><\/p>\n\n\n\n

    \n\n\n\n

    4) (-28) \u00f7 (-7)<\/p>\n\n\n\n

        -28 \u00f7 -7<\/p>\n\n\n\n

        = +4<\/span><\/strong><\/p>\n\n\n\n

    \n\n\n\n

    5)0 \u00f7 (-8)<\/p>\n\n\n\n

        0\u00f7 -8<\/p>\n\n\n\n

       =-0<\/span><\/strong><\/p>\n\n\n\n

    \n\n\n\n

    II. Fill in the blanks<\/span><\/strong><\/p>\n\n\n\n

    1.(\u2013 45) \u00f71<\/span><\/span><\/strong> = -45<\/p>\n\n\n\n

    2)(\u2013 27) \u00f7 (\u2013 27) =  1<\/span><\/span><\/strong><\/p>\n\n\n\n

    3)30 \u00f7   -2 <\/span><\/span><\/strong>=    -15<\/p>\n\n\n\n

    4)-12<\/span><\/span><\/strong>\u00f7 4 = -3<\/p>\n\n\n\n

    5)-30<\/span><\/span><\/strong>\u00f7 (-3) =10<\/p>\n\n\n\n

    II. Fill this table.<\/span><\/strong><\/p>\n\n\n\n

    Division of Integers<\/span><\/strong><\/td>Quotient<\/strong><\/span><\/td><\/tr>
    24 \u00f7 12<\/td>+2<\/td><\/tr>
    24 \u00f7 (\u201312)<\/td>-2<\/td><\/tr>
    (\u201324) \u00f7 12<\/td>-2<\/td><\/tr>
    (\u201324) \u00f7 (\u201312)<\/td>+2<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n

    Commutative Property<\/span><\/strong><\/p>\n\n\n\n

    For any two Integers a and b, if a+ b = b +a then, this property is called commutative property.<\/p>\n\n\n\n

    Exercise1.5<\/span><\/strong><\/p>\n\n\n\n

    I. Simplify the following using appropriate property.<\/span><\/strong><\/p>\n\n\n\n

    1)5  \u00d7  [(\u20134) + 2]<\/span><\/p>\n\n\n\n

    5 x (-4) + 2<\/p>\n\n\n\n

    5x -4 +2<\/p>\n\n\n\n

    5x-2<\/p>\n\n\n\n

    Ans:=-10<\/span><\/strong><\/p>\n\n\n\n

    \n\n\n\n

    2) (-3) x (8-5)<\/span><\/strong><\/p>\n\n\n\n

     -3 x 8-5<\/p>\n\n\n\n

    -3 x +3<\/p>\n\n\n\n

    Ans:=-9<\/span><\/strong><\/p>\n\n\n\n

    \n\n\n\n

    3)(4 x (-2)  )          +         (5 x (-2 ) <\/strong> <\/span>   <\/p>\n\n\n\n

       (4 x (-2 )         +    (5 x (2)<\/p>\n\n\n\n

        4 x -2        + 5×2<\/p>\n\n\n\n

            -8 +10<\/p>\n\n\n\n

             Ans:=-18<\/span><\/strong><\/p>\n\n\n\n

    \n\n\n\n

    4)(5 + (-3 ) )     -2<\/span><\/strong><\/p>\n\n\n\n

                5+ (-3 ) -2<\/p>\n\n\n\n

                5 + -3 -3<\/p>\n\n\n\n

                   2 \u2013 2<\/p>\n\n\n\n

              Ans:=0<\/span><\/strong><\/p>\n\n\n\n

    \n\n\n\n

    5) (-7 )   +  (8-3)<\/span><\/strong><\/p>\n\n\n\n

                 -7  +  5<\/p>\n\n\n\n

                   Ans: =-2<\/span><\/strong><\/p>\n\n\n\n

    \n\n\n\n

    6)(7 x ( 2 ) )   + (4  –  7 )   -6 (2 x (-3)<\/span><\/strong><\/p>\n\n\n\n

         14   +   4  – 7   –  12  x  3<\/p>\n\n\n\n

         14 +  3  –  36<\/p>\n\n\n\n

            17  –  36<\/p>\n\n\n\n

            Ans:=19<\/span><\/strong><\/p>\n\n\n\n

    \n\n\n\n

    Exercise 1.6<\/span><\/strong><\/p>\n\n\n\n

    Solve the following Verbal Problems<\/strong><\/p>\n\n\n\n

    1.Monika had 5 boxes of chocolates<\/p>\n\n\n\n

    Each  box contains 25 chocolates<\/p>\n\n\n\n

    There fore the total number of chocolates is  25 x 5<\/p>\n\n\n\n

                                                                                    =Ans:125<\/span><\/strong><\/p>\n\n\n\n

    \n\n\n\n

    3.Rashmi had 12350 in her bank account. If she withdrew 200 from her account 3 times, What is the balance amount in her account?  <\/strong><\/p>\n\n\n\n

     <\/strong>The amount Rashmi had in the bank account          = 12,350<\/p>\n\n\n\n

     Rashmi withdrew 200 from her account 3 times<\/p>\n\n\n\n

                                                                            200 x3        = 600<\/p>\n\n\n\n

      Her balance in account is                                           =11,750     <\/span><\/strong>           <\/p>\n\n\n\n

    \n\n\n\n

    4.The cost of a pen is `8 and the cost of a pencil is 5. Find the cost of a dozen pens and half a dozen pencils.<\/p>\n\n\n\n

    The cost of a pen is    8 x 12   = 96<\/p>\n\n\n\n

    The cost of a pencil is 5 x 6     =30                                    <\/p>\n\n\n\n

    Therefore the cost of pen and pencil is  96 + 30                          <\/p>\n\n\n\n

                                                                                 Ans:126  <\/span><\/strong><\/p>\n\n\n\n

    \n\n\n\n

    5.There are 38 students in a class. The cost of a set of books for one student is 1235. Find the cost of books for 38 sets.<\/p>\n\n\n\n

    No of students in a classis    38<\/p>\n\n\n\n

    cost of a set of books forone student is 1235<\/p>\n\n\n\n

    The cost of books for 38 sets is     1235×38      <\/p>\n\n\n\n

    =Ans:46,930<\/span><\/strong><\/p>\n\n\n\n

    \n","protected":false},"excerpt":{"rendered":"

    summary of integers Solved exercise of integers Summary An integer is defined as the number that can be written without a fractional components ie,21, 4, 0, and \u22122048.A number which is not a fraction...<\/p>\n","protected":false},"author":3,"featured_media":1328,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[116,475,14],"tags":[162,163,164],"cp_meta_data":{"_edit_lock":["1629955932:2"],"_edit_last":["2"],"_layout":["inherit"],"_thumbnail_id":["1328"],"_oembed_95287caaddeb112cd4edfcbd8e525566":["