PROPORTION (CLASS 6)

EXERCISE 8: PROPORTION

PROPORTION  MEANS THAT THE TWO RATIOS (OR FRACTION) ARE EQUAL.

  EXAMPLE ;

    1/3 =  2/6

So  1  out of 2 is equal to 2 out of 6

  1:3 =2:6

The ratios are same and they are in proportion

It is read as 1 is to 3 as 2 is to 6.

The  numbers 1,3,2,6 have their special names

1 is the -first term,  3 is the-second term,

2 is the-third term, 6 is the-fourth term

The symbol for representing proportion is ”  : :   “

The 1st  and the fourth terms  =extremes and  2^nd and the 3 rd terms= means

PRODUCT OF EXTREMES = PRODUCT OF MEANS

1 x 6  =2 x 3

6=6

Exercise 8 c

2. i.Find the value of x.

   x:4 =  6: 8

The numbers x, 4,  6 and 8 are in proportions

1^st       2nd             3^rd       4th

X     :     4        =      6      :    8

Product of extremes= product of means

1^st   x   4^th terms    = 2^nd   x 3^rd terms

x    x      8        =       4        x    6

8 x     =24  (divide both sides by 8)

 Therefore  x= 3  (to check put the value of x)              

8 x 3 = 4 x 6

24  =  24

ii   14:x = 7  : 9

The nos. 14, X , 7,and 9 are in proportions.

1^st        2^nd        3^rd          4^th

14    :     X          7         :    9

Product of extremes =product of means

1^st x 4^th       = 2^nd  x 3^rd terms

14 x 9        = X    x  7

126  =  7 X  (DIVIDE BOTH SIDES BY 7)

18 =X

USING THESE STEPS TRY THE GIVEN SUMS:

iii. 4:6=x:18   iv 8:10=x:25  v 5:15 =4:x

2. FIND THE VALUE OF x SO THAT THE GIVEN FOUR NOS ARE IN PROPORTION:

i.  x,  6 , 10 and 15

1^st     2^nd     =   3^rd     4^th

X      :  6      =   10   :   15

Product of extremes = product of means

1^st x  4^th  terms  =  2^nd  x   3^rd terms

X  x   15     =   6 x 10

15 X   =  60  (DIVIDING BOTH SIDES BY 15)

Therefore,  X= 4

PUTTING THE VALUE OF X

4 X 15  = 6 X 10

60=60

TRY OTHER SUMS

ii x,4,15 and 30               iii.2,x,10 and 25        iv.4 ,x,6 and 18

4. THE FIRST,SECOND AND THE FOURTH TERMS OF A PROPORTION ARE 6, 18  , AND 75 . FIND ITS THIRD TERM

    LET THE THIRD TERM BE X

1^st     2^nd   =    3^rd       4^th

6    :    18  =   X    :   75

PRODUCT OF EXTREMES=PRODUCT OF MEANS

  1^st x  4^th terms  =   2^nd  x  3^rd terms

   6  x  75    =      18    x       X

     450     =  18 X  (DIVIDING BOTH SIDES BY 18)

    25   =  X

5. FIND THE SECOND TERM OF THE PROPORTION WHOSE FIRST ,THIRD AND FOURTH TERMS ARE 9 , 8  ,AND 24.

Let the second term be X

     1^st     2^nd      3^rd       4^th

   9   :   X  =   8   :   24 

TRY THIS ON YOUR OWN USING THE ABOVE STEPS

6 .FIND THE FOURTH TERM OF THE PROPORTION  WHOSE FIRST SECOND AND THE THIRD TERMS ARE 18 , 27 AND 32?

7.THE RISE OF THE LENGTH TO THE WIDTH OF A SCHOOL GROUND IS 5:2  . FIND ITS LENGTH, IF WIDTH IS 40m

LET THE LENGTH BE X

                      1^st          2^nd                      3^rd                 4^th

GIVEN     length  :   width        =  LENGTH    :    WIDTH 

                5         :         2           = X                :     40

   PRODUCT OF EXTREMES = PRODUCT OF MEANS

       5 x 40                =    X   x    2

200      =  2 X  (DIVIDING BOTH SIDES BY 2)

Or, X=100

THE LENGTH OF THE GROUND IS 100 m

8.THE RATIO OF COPPER AND ZINC IN AN ALLOY IS 9:8. IF THE WEIGHT OF THE ZINC IN THE ALLOY IS 9.6 KG

FIND THE WEIGHT OF  COPPER IN TH ALLOY .

TRY THE REMAINING SUMS