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    Ratio and Proportion

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    preeti
    The document defines ratio, proportion, and continued proportion. It provides examples of finding a third proportional and using properties of proportion like invertendo, alternando, componendo, and dividendo. It then gives a classwork and homework assignment involving word problems on ratios, proportions, finding missing terms, and using properties of proportion.

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    Ratio and Proportion

    Uploaded by

    preeti
    33 views3 pages
    The document defines ratio, proportion, and continued proportion. It provides examples of finding a third proportional and using properties of proportion like invertendo, alternando, componendo, and dividendo. It then gives a classwork and homework assignment involving word problems on ratios, proportions, finding missing terms, and using properties of proportion.

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    PF-L9

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    The document defines ratio, proportion, and continued proportion. It provides examples of finding a third proportional and using properties of proportion like invertendo, alternando, componendo, and dividendo. It then gives a classwork and homework assignment involving word problems on ratios, proportions, finding missing terms, and using properties of proportion.

    Copyright:

    © All Rights Reserved
    Download as PDF, TXT or read online from Scribd
    Download as pdf or txt
    33 views3 pages

    Ratio and Proportion

    Uploaded by

    preeti
    The document defines ratio, proportion, and continued proportion. It provides examples of finding a third proportional and using properties of proportion like invertendo, alternando, componendo, and dividendo. It then gives a classwork and homework assignment involving word problems on ratios, proportions, finding missing terms, and using properties of proportion.

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    of 3

    M Prakash Institute STD VII

    Pre Foundation Lecture 9

    RATIO AND PROPORTION


    What is Proportion?
    When two ratios are equal, the four quantities composing them are said to be
    a c
    proportional. Hence, if = , then a, b, c, d are proportional and are written as
    b d
    a : b :: c : d. The terms a and d are also called extremes while the terms b and c are
    called the means.
    a c
    a : b : c : d ⇒ = ⇒ ad = bc
    b d
    Hence Product of extremes = Product of means

    Continued Proportion
    a b
    (i) If = , then a, b, c, are said to be in continued proportion and vice-versa.
    b c
    If A : B and B : C, is given, how to find A : B : C ?
    Eg: If A : B = 2 : 3, and B : C is 7 : 9, find A : B : C
    A B: : C
    2 :
    3
    7 : 9
    2×7 : 3×7 : 3×9
    14 : 21 : 27

    Properties of Proportion
    a c b d
    (i) Invertendo: If = , then =
    b d a c
    a c a b
    (ii) Alternando: If = , then =
    b d c d
    a c a+b c+d
    (iii) Componendo: If = , then =
    b d b d
    a c a−b c−d
    (iv) Dividendo: If = , then =
    b d b d
    a c a+b c+d
    (v) Componendo and Dividendo: If = , then =
    b d a−b c−d

    Classwork:

    1. Find the third proportional to 36, 12

    2. Check whether the following numbers are in proportion


    1 1 1 1
    (a) 20, 18, 5, 6 (b) 3.6, 0.4, 4.5, 0.5 (c) , , ,
    5 8 4 10
    3. If a : b = 3 : 2 and b : c is 4 : 5, find a : c

    4. The car that I own can go 150 Km with 25 litres of petrol. How far can it go with 30
    litres of petrol?
    (5a + 7b) (5c + 7d)
    5. If a : b = c : d, prove that =
    (5a − 7b) (5c − 7d)
    (4x + 3y) 7 x
    6. If = , use properties of proportion to find
    (4x − 3y) 4 y
    7. Do the two ratios 100 : 225 and 32 : 56 form a proportion?

    8. What least number should be subtracted from 7, 17, 47 so that the remainders are in
    continued proportion?

    Homework:

    1. Find the third proportional to each of the following sets of numbers.


    3 7 2 3
    (a) 2,8 (b) 2,5 (c) 5,2 (d) , (e) , (f) a, b
    7 3 3 8
    2. Find x such that
    (a) x : 14 = 18 : 63 (b) 10.2 kg : x :: 3.4 m : 110 m
    1 1
    (c) 4 g : 3 g = x m : 21 m (d) x cm : 2.5 cm = 2.5 cm : 2 cm
    2 2
    3. Find x when
    (a) x, 5, 8 and 10 are in proportion
    (b) x, 8 and 24 are in continued proportion.

    4. Find x in following proportions


    (a) 16 : 18 = x : 96 (b) x : 92 = 87 : 116

    5. Ms Sharma has three sons. The youngest son, Rohit, is 2 years 6 months old and
    the eldest son, Rahul, is 10 years old. The age of the second son, Rakesh, is the mean
    proportional between the ages of the other sons. How old is Rakesh?

    6. In a triangle, the side AB = 4 cm and the side BC = 9 cm. If the side AC is the mean
    proportional to AB and BC, find AC.
    1 + k 2k + 3 4
    7. Find the value of + if k = .
    1 − k 2k − 3 3
    (8x + 13y) 9
    8. If = , find x : y
    (8x − 13y) 7
    Answer Key:

    Classwork:
    Que no. Answer
    1 4
    2 (b) In proportion
    3 6:5
    4 180 km
    5
    6 11:4
    7 Not in proportion
    8 2

    Homework:
    Que no. Answer
    1 (a) 32 (b) 12.5 (c) 0.8
    (d) 343/27 (e) 27/128 (f) b2 /a
    2 (a) 4 (b) 330 (c) 27 (d) 6.25/2
    3 (a) 4 (b) 8/3
    4 (a) 85.3 (b) 69
    5 5 years
    6 AC = 6 cm
    7 -24
    8 13:1

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