comparison of two quantities in terms of how man times is called ratio

ex: lets decide 100 to 2 persons 1:1 ratio

100/2= 50 each

6:8:10 = 24 aboe

1:3 water to squash

**Simple Ratio: lowest **

15:35 = 3:7 (5) 3+7=10 ( 1% of 10 = 1 )

**inverse ratio / reciprocal ratio**

ex a:b=b:a

A income 2x than b

2A=1B

A/B=1/2 1:2

**Equivalent ratio**: ratios are obtained by multiplying or dividing by any counting number are equivalent ratios.

Ratio is comparison between quantities in same measures or units

Duplicate Ratio of a:b = a 2^{:b2} (superscript)

20000 by a:b:c 3:4:5 duplicate ratio

duplicate ratio means square 9:16:25

9+16+25=50 total ratio

20000/50= 400

1=400

400*9=3600

400*16= 6400

400*25=10000 (total 20K)

SUb DUplicate ratio : square root **sQuare root of 400 = 20**

Triplicate Ratio: Menas 3x than current ratio Qube a3

3:4 = 27:64

sub triplicate ratio: root qube

ex: **216:343:729 = 6:7:9**

**Compound Ratio: **

2:3 & 5:2 = (2*5=10) (2*3=6)

10:6=5:3 (divided by 2)

a:b = 4:5

b:c = 5:7

abc = 4:5:7

2nd ex:

a:b= 4:5

b:c=10:9

abc = ?

(4:5)2= 8:10

8:10:9

3rd ex

a:b= 2:3

b:c= 3:4

c:d =6:7

abcd = ?

A | B | C | D |

2: |
3 |
3 | 3 |

3 | 3: |
4 |
4 |

6 | 6 | 6: |
7 |

*step 1: same values occupied left or right*

Step 2 divide by 2 & 3 to get lowest values.

ratio:

6:9:12:14

**2nd ex Multiplication**

a:b = 3:5

b:c = 7:4

d:c (inverse ratio) = 2:3

A | B | C | D |

3: |
5 |
5 | 5 |

7 | 7: |
4 |
4 |

3 | 3 | 3: |
2 |

**Bold marks are originals**

step 1: add same values left or right for occupy

step 2: multiply if divide not possible

7*3=21=3 63, 5*7=35*3=105, (5*4=20*3=60) (5*4=20*2=40)

63:105:60:40

**Proportion **

a:b::c:d or a/b=c/d

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