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| Ratio |
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| Ratio is the numerical relation of one quantity to another of the same kind. To find the ratio of 2 m 25
cm to 75 cm, we first change 2 m 25 cm into cm, which equals 225 cm. Now, we have to find 225 cm to 75 cm |
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 ratio is  |
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| = 3 : 1 |
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| We can write the above ratio as |
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(i) 3 : 1 or (ii)  or (iii) the ratio 3 to 1 or (iv) 3 |
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| (i) The ratio should be expressed in simplified form. |
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| (ii) Ratio has no units |
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| If the ratio of two similar quantities is a : b, then the first quantity 'a' is called the antecedent; the second quantity 'b' is called the consequent. |
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| Find the ratio of 2 hours 30 minutes to 45 minutes. |
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| 2 hours 30 minutes = 150 minutes |
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 ratio is 150 minutes : 45 minutes or 10:3 |
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| Ans: 10 : 3 |
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Simplify the ratio  |
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 can be rewritten as  or |
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| 9 : 5 |
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| Ans: 9 : 5 |
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| When two or more ratios are multiplied with each other, the resultant simplified ratio is called the compounded ratio. |
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| Let a : b and c : d be two given ratios, then the compounded ratio is |
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 = ac : bd. |
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The ratio a2: b2, obtained by compounding the ratio a : b with itself is called the duplicate ratio,  . |
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| For example, the duplicate ratio of 4 : 9 is 42 : 92 |
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| = 16 : 81 |
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The ratio a3 : b3 obtained by compounding the ratio a : b with itself three times, =  is called the triplicate ratio. |
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| For example, the triplicate ratio of 4 : 9 is 43 : 93 |
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| or 64 : 729 |
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The ratio  obtained by taking the square root of the given ratio a:b is called the sub-duplicate ratio.  is the sub-duplicate ratio of a : b. |
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For example, the sub-duplicate ratio of 4 : 9 is  |
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| or 2 : 3 |
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The ratio  obtained by taking the cube root of the given ratio a : b is called sub-triplicate ratio.  is sub-triplicate ratio of a : b. |
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For example the sub-triplicate ratio of 8a3 : 27b6 is  |
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| or 2a : 3b2. |
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Find the compounded ratio of the duplicate ratio of  ; sub-triplicate ratio of 9261 : 729 and reciprocal ratio of 16 : 15. |
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Duplicate ratio of  |
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| = 12 : 7 |
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Sub-triplicate ratio of 9261 : 729 =  |
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| = 21 : 9 |
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| Reciprocal ratio of 16 : 15 = 15 : 16 |
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 Compounded ratio  |
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| = 15 : 4 |
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| Ans: 15 : 4 |
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| Find the compounded ratio of the following: |
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| Sub-duplicate ratio of x4 y6 : 81a4, |
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| Triplicate ratio of 3a : 2xy2, and |
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| Sub-triplicate ratio of 64x3y9 : 343 b3. |
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| Sub-duplicate ratio of x4y6 : 81a4 |
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| = x2 y3 : 9a2 |
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| Triplicate ratio of 3a : 2xy2 = (3a)3 : (2xy2)3 |
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| = 27a3 : 8x3 y6 |
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| Sub-triplicate ratio of 64x3y9 : 343b3 |
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| = 4xy3 : 7b |
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Compounded ratio  |
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| = 3a : 14 b |
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| Ans: 3a : 14b. |
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