Presented by members of lovely brats.

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Presented by members of lovely brats.
.

• RATIO ,PROPORTION AND UNITARY METHOD.

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INTRODUCING RATIO

• When we compare two numbers or quantities by
  dividing one by the other, we say we have formed
  the ratio of the two numbers or have followed the
  method of division.

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Ratio in ALGEBRAIC form

• The ratio of any number a to number b can be
  written as a upon b or a divided by b or ab and
  is read as a is to b.

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Example-If in a class 20 boys are selected for
football team and 10 girls are selected for
tennis team, then how shall we find the ratio of
no of boys in football team to the girls in the
tennis team?

• We may say that boys in the football team are
  twice than the girls in the tennis team. Here we
  divide 20 by10 and we call this RATIO OR METHOD
  OF COMPARISON BY DIVISION

• Thus a ratio of 20 and 10 is 20 divided by 10. A
  ratio is therefore, a fraction,and all rules that
  are applicable to fraction are applicable to
  ratio also.

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Some things to remember!

• It should be noted that a RATIO IS A NUMBER.It
  has NO UNITS. The ratio sould always be EXPRESED
  IN ITS SIMPLEST FORM, that is in the form in
  which its terms have no factors in common other
  than 1.WE SHOULD THERFORE ,WRITE A RATIO OF, SAY
  3224 AS 43 AND EXPRESS A RATIO AS 1/2 INSTEAD
  OF 5/10 OR 14/28.

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• Note that only measures of like quantities can be
  compared. For example we cannot compare Rs2 and
  2Kg. However we can compare Rs2 and 50paise.
  Since we express Rs2 in paiseRs2 200p. The
  ratio thus becomes 20050, which in simplest form
  is 41. Since, 20050 or 200/50 4/1 or 41

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Comparing Ratios

• In order to compare two or more ratios, we reduce
  them to the same denominator.
• Whenever two fractions are in a ratio, multiply
  them by the LOWEST COMMON MULTIPLE L.C.M. of
  their denominators, and whenever two whole
  numbers are in a ratio, divide both numerator and
  denominator by their HIGEST COMMON FACTOR
  H.C.F. in order to simplify the ratios.

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EXAMPLE-COMPARE THE RATIOS 25 AND 49

• TO SOLVE SUCH QUESTIONS WE FIRST FIND THE EQUAL
  DENOMINATORS OF ANY TWO OR MORE RATIOS AND SO
  25 2/5 BOTH NUMERATOR AND DENOMINATOR OF THE
  FRACTION ARE MULTIPLIED BY 9AND THE ANSWER WHICH
  WE GAIN IS 18/45.WE DO THE SAME WITH OTHER RATIO
  THAT IS 49 WHICH IS EQUALS TO 4/9. THEN WE
  MULTIPLY 4/9 BY 5 AND ANSWER WHICH WE GET IS
  20/45.
• SINCE 20/45 gt18/45
• THAT IS WHY 4/9gt 2/5 OR 49gt 25.

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INTRODUCING PROPORTION

• Whe two ratios are found to be equal they are
  said to be in proportion.
• e.g.- 23 46
• Proportion in algebric form ab cd
• NOTE-symbol is used for or equals to .
• So 2336 means 23 36 and abcd means
  ab cd. And it is read as 2 is to b as 3 is to
  6 and a is to b as c is to d.

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If I go to a shop to buy some milk, which costs
Rs 8 per litre. If we buy 5 litres of milk we pay
Rs 40. If we buy 8 litres of milk, we pay Rs 64.
Now what is the ratio of 5 litre to 8 litres of a
milk ?

• The ratio of 5litres to 8litres of milk is 58.
• what is the ratio of Rs 40 toRs 64 ?
• It is 4064 and we express this number in the
  lowest form it is 58 . Thus we can say that
• 584064
• Such a quantity of two ratios is known as a
  proportion.
• We say that the numbers 5 ,8 ,40 and 64 are in
  proportion.

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5, 8, 40 and 64 are called the terms of the
proportion. They are respectively first, second,
third and fourth terms. The first and fourth
terms are called extremes and second and the
third terms are called the middle or the mean
terms.

• If the product of the first and the fourth term
  are equal to product of the second and third term
  then we say that the number are in proportion.
  And if it is not so then the numbers not in
  propotion.

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Are these ratios in proportion?

• Find if the numbers10,20 30 and 40 are in
  proportion?
• We follow the same rule as shown in the prievous
  example.
• So10 multiplied by 40 is not equal to 20
  multiplied by 30
• And 400 is not equal to 600
• That is why 10, 20 , 30 and 40 are not in
  proportion.

• Find if the numbers 15,25,30 and 50 are in the
  ratios?
• product of the extreme terms equals to product
  of the mean terms.
• That is why 15 multiplied by 50 25multiplied by
  30 Which is equal to 750750
• And so 15, 90 ,30 and 5 are in proportion.

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UNITARY METHOD

• The problems which were solved by ratio and
  proportion method can also be solved by method
  popularly known as unitary method.
• In this method , we first find the value of one
  (unit) quantity from the value of the given
  quantities and then find the value of the
  required number of quantities.

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The monthly consuption of cereals of a hostel
with 500 students is 6500 Kg . Find the
consuption if the number of students is only 75.

• Consuption of cereals by 500 students6500Kg
• Consuption by 1 student6500 divided by 50013Kg
• Consuption by 75 students13multipied by 75
  975Kg

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