imath - oefeninge i.v.m. omskakelings

WISKUNDIGE GELETTERDHEID
GRAAD 12
NOG OEFENINGE

Omskakeling.

MATHEMATICAL LITERACY
GRADE 12
MORE EXERCISES

Conversions.

        'n Wenk vir die omskakeling van nie-metriese

        hoeveelhede.

        Doen die nie-metriese omskakeling so:

        Verander die omskakelingsfaktor sodat

        daar 1 is van die eenheid wat omgeskakel

        moet word. Vermenigvuldig hierdie

        hoeveelheid met die hoeveelheid wat

        omgeskakel moet word.

        Van die tabel sien ons 1 km = 0,6214 myl.

        Skakel nou 10 km om na myl.

        Die faktor beweer dat 1 km = 0,6214 myl.

        Vermenigvuldig nou 1 km met 10 om

        10 km te kry en vermenigvuldig 0,6214 myl

        ook met 10 om 6,214 myl te kry.

        Dus, skryf dit so :

              1 km = 0,6214 myl.

        ∴  10 km = 0,6214  ×  10  myl.

                       = 6,214  myl.

        Nou, gegee dat 1 km = 0,6214 myl, skakel

        10 myl om na km.

        Verander die omskalelingsfaktor om te lees :

        1 myl  =  'n aantal km

        Doen dit so :

        0,6214 myl = 1 km

                                 1
        ∴  1 myl =  ──────  km
                            0,6214

        Vermenigvuldig die getal met 10

        om die omskakeling van 10 myl na

        km te kry.

        Skryf dit so neer :

             0,6214 myl = 1 km

                                 1
        ∴  1 myl =  ──────  km
                            0,6214

                                    1
        ∴  10 myl =  ──────  ×  10  km
                               0,6214

                          =  16,09269392...

                          =  16,093  km

                   (korrek tot 3 desilmale plekke)



        Gebruik die tabel hieronder om die

        omskakelingsfaktor te bereken.

        Die volgende afkortings geld:

          vt : voet ;   jrt : jaart ;    vk : vierkant

          kub. : kubieke ;        cc : kubieke cm

          gal : gallon ;    pt : pint; ;   lb : pond

        A tip for converting non-metric quantities.



        Do the non-metric conversions as follows:

        Change the conversion factor so that there

        is 1 of the unit that has to be converted.

        Then multiply this amount by the amount

        that has to be converted.

        The table shows that 1 km = 0,6214 miles.

        Now convert 10 km to miles.

        The factor states that 1 km = 0,6214 miles.

        Now multiply 1 km by 10 to find 10 km and

        also multiply 0,6214 miles by 10 to

        find 6,214 miles.



        Therefore, write it like this :

              1 km = 0,6214 miles.

        ∴  10 km = 0,6214  ×  10  miles.

                       = 6,214  miles.

        Now, given that 1 km = 0,6214 miles, convert

        10 miles to km.

        Change the conversion factor to read :

        1 mile  =  some number km

        Do it like this :

        0,6214 mile = 1 km

                                 1
        ∴  1 mile =  ──────  km
                            0,6214

        Now multiply this number by 10 to

        find the conversion of 10 miles to km.



        Write it like this :

             0,6214 mile = 1 km

                                 1
        ∴  1 mile =  ──────  km
                            0,6214

                                    1
        ∴  10 miles =  ──────  ×  10  km
                               0,6214

                          =  16,09269392...

                          =  16,093  kn

                         (correct to 3 decilmal places)



        Use the conversion table below to make

        the conversion factor.

        The following abbreviations apply:

        in : inch ;    ft : foot or feet ;    yd : yard

        sq or ² : square ;    cub. or ³ : cubic

        cc : cubcic cm ;    gal : gallon ;    pt : pint

        oz : ounce ;    lb : pound

          1 cm = 0,03937 duim / in             1 km = 0,6214 myl / mile             1 duim / in = 2,54 cm

           1 vt / ft = 12 duim / in                  1 jrt / yd = 3 vt / ft                         1 vt / ft = 0,3048 m

           1 jrt / yd = 0,9144 m                   1 myl / mile = 1700 jrt / yd           1 myl / mile = 1,6083 km

           1 gram = 0,0353 ons / oz           1 kg = 2,2048 lb                           1 lb = 16 onse / oz

           1 liter = 1,76 pt                           1 gal = 8 pt                                   1 gal = 4,5461 liter(ℓ)

Vraag / Question 1.

               Doen die volgende omskakelings:

        1.1  50 jaart na meter.                                  [ 1.1 ]

        1.2  31,35 myl na kilometer                          [ 1.2 ]

        1.3  18,42 lb na kg .                                      [ 1.3 ]

        1.4  75 meter na jaart.                                  [ 1.4 ]

        1.5  3,4 km na myl.                                      [ 1.5 ]

        1.6  25 kg na lb.                                           [ 1.6 ]

        1.7  6 pinte na liter.                                      [ 1.7 ]

        1.8  2,3 gallon na liter.                                 [ 1.8 ]

        1.9  234,6 liter na gallon                              [ 1.9 ]

        1.10  3,45 liter na pinte.                               [ 1.10 ]

        1.11  3,56 gallon na pinte.                           [ 1.11 ]

        1.12  210 liter na gallon.                              [ 1.12 ]

        1.13  5 onse na gram.                                 [ 1.13 ]

        1.14  7 lb na kilogram.                                [ 1.14 ]

        1.15  18,45 kg na lb.                                   [ 1.15 ]

        1.16  340 gram na onse.                            [ 1.16 ]

        1.17  3,3 duim na cm.                                [ 1.17 ]

        1.18  650 gram na lb.                                 [ 1.18 ]

               Do the following conversions:

        1.1  50 yards to meter.                            [ 1.1 ]

        1.2  31,35 miles to kilometer.                  [ 1.2 ]

        1.3  18,42 lb to kg.                                  [ 1.3 ]

        1.4  75 metres to yards.                          [ 1.4 ]

        1.5  3,4 km to miles.                                [ 1.5 ]

        1.6  25 kg to lb.                                        [ 1.6 ]

        1.7  6 pints to litre.                                   [ 1.7 ]

        1.8  2,3 gallons to litre.                            [ 1.8 ]

        1.9  234,6 litres to gallon.                        [ 1.9 ]

        1.10  3,45 litres to pints.                          [ 1.10 ]

        1.11  3,56 gallons to pints.                      [ 1.11 ]

        1.12  210 litres to gallons.                       [ 1.12 ]

        1.13  5 ounces to gram.                          [ 1.13 ]

        1.14  7 lb to kilogram.                              [ 1.14 ]

        1.15  18,45 kg to lb.                                 [ 1.15 ]

        1.16  340 gram to ounces.                      [ 1.16 ]

        1.17  3,3 in. to cm.                                  [ 1.17 ]

        1.18  650 gram to lb.                               [ 1.18 ]

Vraag / Question 2.

              Skakel

        2.1  8,5 duim om na mm.                                 [ 2.1 ]

        2.2  9,83 dm om na duim.                                [ 2.2 ]

       2.3  3 voet 6 duim om na meter.                       [ 2.3 ]

        2.4  4 gallon 7 pinte om na liter.                       [ 2.4 ]

        2.5  30,825 m om na jrt en vt.                          [ 2.5 ]

        2.6  1 487,5 jaart om na km.                            [ 2.6 ]

        2.7  6 lb 14 onse om na kg.                              [ 2.7 ]

        2.8  6 jrt 2 vt 7 duim om na m.                         [ 2.8 ]

              Convert

        2.1  8,5 inches to mm.                                   [ 2.1 ]

        2.2  9,83 dm to inches.                                  [ 2.2 ]

        2.3  3 feet 6 inches to metres.                       [ 2.3 ]

        2.4  4 gallon 7 pints to litres.                          [ 2.4 ]

        2.5  30,825 m to yd and ft.                             [ 2.5 ]

        2.6  1 487,5 yards to km.                               [ 2.6 ]

        2.7  6 lb 14 oz to kg.                                      [ 2.7 ]

        2.8  6 yd 2 ft 7 in. to m.                                  [ 2.8 ]

Vraag / Question   3.

            Let op die volgende afkortings :  /  Please take note of the following abreviations : >

             Australiese dollar  /  Australian dollar  :  AUD                          Emirati dirham    AED

             Indiese rupee  /  Indian rupee  :  INR                                       Israeli shekel    ILS

            Botswane pula    BWP

            Gegee dat    /    Given that

          € 1  = R16,3054                        £1  = R17,8927                        $1  = R14,9313                        $1  = £ 0,815906

          $ 1  = € 0,898820                     R 1  = AED 0,2498                   R 1  = AUD 0,1022

          R 1  = BWP 0,7917                  R 1  = INR 4,9514                    R 1  = ILS 0,2654

                                                                             Skakel  /  Convert

      3.1  R141  om na / to  $.                          [ 3.1 ]

      3.3  R325  om na / to  £.                          [ 3.3 ]

      3.5  AED 420  om na / to  R.                    [ 3.5 ]

      3.7  ILS 81,23  om na / to  R.                   [ 3.7 ]

      3.2  R872  om na / to  €.                         [ 3.2 ]

      3.4  R1 410  om na / to  AUD.                 [ 3.4 ]

      3.6  INR 8729  om na / to  R.                  [ 3.6 ]

      3.8  AUD 1 806  om na / to  R.                [ 3.8 ]

Vraag / Question 4.

         Ek kom van die VSA af terug en het nog

         $152,56 oor. Ek wil dit omskakel na £.

         Hoeveel Britse ponde kry ek daarvoor?        [ 4. ]

         I am returning from the USA and have a total of

         $152,56 left. I want to convert this to £.

         How many British pounds will I receive?           [ 4. ]

Vraag / Question 5.

     5.1  Die massa van 'n brood is 800 gram.

            Wat is die massa in onse en in ponde?

                                                                      [ 5.1 ]



     5.2  'n Maraton word oor 42 km beslis.

            Hoeveel myl is dit?                            [ 5.2 ]

         5.1  The mass of a loaf of bread is 800 gram.

                What is the mass in ounces and in pounds?

                                                                            [ 5.1 ]



         5.2  A marathon is run over 42 km. How many

                miles is that?                                      [ 5.2 ]