Note on Ratio

  • Note
  • Things to remember
  • Exercise
  • Quiz

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The ratio is the method to show the relationship between two numbers or two quantities which indicate the number of times the first number contains the second. The ratio between two quantities is obtained by dividing the first quantity by the second. For example: the ratio between Rs 15 and Rs 30 = \(\frac{15}{30}\) = \(\frac{1}{2}\) = 1:2

There are three ways to write a ratio:

  • As fraction = \(\frac{1}{2}\) ( 1 upon 2 )
  • With a colon ( : ), 2 : 5 ( 2 is to 5)
  • With the word " to", ( 2 to 5)

 

Things to remember

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  • A ratio doesn't contain any unit as it is pure number.
  • While finding the ratio between two quantities, both quantities should be of the same unit. For example, the ratio between 20 cm and 3 m = ratio between 20 cm and 300 cm = \(\frac{20}{300}\) = \(\frac{1}{15}\) = 1:15.
  • A ratio remains unchanged if both of its terms be multiplied or divided by the same number.
    For example:
    \(\frac{1}{3}\) = \(\frac{1}{3}\) x \(\frac{4}{4}\) = \(\frac{4}{12}\) = \(\frac{1}{3}\)
  • A ratio should always be expressed in its lowest terms.
    For example;
    \(\frac{20}{32}\) = \(\frac{20}{32}\) ÷ \(\frac{4}{4}\) = \(\frac{5}{8}\)

To divide a given quantity in a given ratio

Let's divide Rs 450 among three persons in the ratio 2 : 3: 4

Since 2 + 3 + 4 =9

  • Renu's share = \(\frac{2}{9}\) x Rs 450 = Rs 100
  • Barsha's share = \(\frac{3}{9}\) x Rs 450 =Rs 150
  • Sabina's share = \(\frac{4}{9}\) x Rs 450 =Rs 200

  • We can use ratios to scale drawings up or down (by multiplying or dividing).
  • The trick with ratios is to always multiply or divide the numbers by the same value.
  • A ratio says how much of one thing there is compared to another thing.
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Very Short Questions

Solution:

Since 3 : 5 = 8

Rita's share = \(\frac{3}{8}\) \(\times\)Rs 240 = Rs 90

Renu"s share = \(\frac{5}{8}\)\(\times\) Rs 240 = Rs 150

Solution:

Here, Rs 3 = 300 paisa

Ratio of 75 paisa to Rs 3 = \(\frac{75}{300}\) = \(\frac{1}{4}\) = 1 : 4

Solution:

Given information,

5 hrs and 10 hrs.

First quantity = 5 hrs

Second quantity = 10 hrs

Ratio = \(\frac{5hrs}{10hrs}\)

= \(\frac{ 1}{2}\)

= 1 : 2

Solution:

Given information:

20 cm and 25 cm.

First quantity = 20 cm

Second quantity = 25 cm

Two quantities are of same units.

Ratio = \(\frac{20cm}{25cm}\)

= \(\frac{4}{5}\)

= 4 : 5

Solution:

Given information:

Rs 75 and 750 paisa.

First quantity = Rs 75

Second quantity = 750 paisa

Since two quantities are not of same unit. So, convert Rs 75 into paisa. = Rs 75\(\times\)100

= 7500 paisa

Now, both quantities are of same units.

Ratio = \(\frac{7500 paisa}{750 paisa}\)

= \(\frac{10}{1}\)

= 10 : 1

Solution:

First quantity = 750 grams

Second quantity = 1.5 kg

Sine both quantities are not of same units. So, 1.5 kg = 1.5\(\times\) 1000 = 1500 grams

Now,

Ratio = \(\frac{750 grams}{1500 grams}\)

= \(\frac{1}{2}\)

= 1 : 2

Solution:

Given information:

3 ft and 9 ft.

First quantity = 3 ft

Second quantity = 9 ft

Since, both quantities are of same units.

Ratio = \(\frac{3 ft}{9ft}\)

= \(\frac{1}{3}\)

= 1 : 3

Solution:

Since, 5 + 3 = 8

Saroj's share = \(\frac{3}{8}\)\(\times\) Rs 500 = Rs 187.5

Renu's share = \(\frac{5}{8}\)\(\times\)Rs 500 = Rs 312.5

Solution:

Since, 3 + 5 = 8

First's person = \(\frac{3}{8}\)\(\times\) Rs 296 = Rs 111

Second's person = \(\frac{5}{8}\)\(\times\) Rs 296 = Rs 185

Solution:

Here, Rs 9 = 900 paisa

Ratio of 90 paisa to Rs 9

Rs 9 = 9 \(\times\) 100 paisa = 900

= \(\frac{90}{900}\)

= \(\frac{1}{10}\) = 1 : 10

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  • Express each ratios in the  simplest form:

    22: 66

     

    1:3
    2:3
    1:1
    2:2
  • Find the Ratio of the following:
    5 hrs and 10 hrs.

    3:1
    2:1
    1:3
    1:2
  • Express  ratios in the  simplest form:

    16:36

    (frac{4}{9})
    (frac{4}{4})
    (frac{3}{9})
    (frac{2}{4})
  • Express  ratios in the  simplest form:

     7 : 49

    1 : 1
    1 : 5
    2 : 7
    1 : 8
  • Express  ratios in the  simplest form:

     

    4 : 6

    2 : 1
    2 : 2
    2 : 3
    1: 3
  • Express  ratios in the  simplest form:

    6 : 15

     

    3 : 4
    2 : 2
    1 : 5
    2 : 5
  • Express  ratios in the  simplest form:

     14 : 20

    8: 1
    9 :9
    7 : 10
    7 : 11
  • Express percent as a ratio:

    12 %  

    3 : 25
    1 : 2
    3 : 30
    2 : 2
  • Express percent as a ratio:

     6.5 % 

     

    13 :125
    15 : 200
    13 : 200
    14 : 150
  • What is the ratio of 65 paisa to Rs 3.

    2 : 2
    1 : 4
    1 : 3
    2 : 3
  • A class of 32 students has 12 girls.What is the ratio of girls to boys?

    5:3
    3:4
    3:5
    3:3
  • A real horse is 1.8 m high.A statue of the horse is 3 n high. What is the ratio of the real horse to the height of the statue?

    3:8
    1:1
    3:3
    3:5
  • Two numbers are in ratio 2:7. If the second numbers is 378, find the first number.

    120
    88
    108
    96
  • Two numbers are in the ratio 2 : 7. If the  first number is 24, find the second number.

    40
    35
    30
    25
  • Two numbers are in the ratio 4: 5. If the difference between these number is 24, then find the numbers.

    125, 95
    121, 97
    130, 88
    120, 96
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DISCUSSIONS ABOUT THIS NOTE

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Forum Time Replies Report
hritu kiran sharma

can we do directly without changing values ? like rs 3 and 75 paisa


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What is the ratio of a gross and 6 scores

What is the ratio of a gross and 6 scores


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two numbers are in ratio 3:4if 3 is added then the ratio becomes 2:3 find these numbers


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