Triplicate Ratio: Formula, Rules and Solved Questions
Triplicate Ratio is formed by taking the cubes of the two terms of a given ratio. For a ratio a:b, its triplicate ratio is a³:b³. This page explains the formula, simplification method, reverse calculation and solved examples involving cubed ratios.
What Is Triplicate Ratio?
To find a triplicate ratio, cube the first term and the second term separately. If the given ratio is m:n, then its triplicate ratio is m³:n³. The terms may be simplified after cubing, although reducing the original ratio first is usually quicker. For example, 4:6 becomes 2:3, and its triplicate ratio is 2³:3³ = 8:27.
Triplicate Ratio Formula & Tricks
Important Formulas
Cube each term of the given ratio separately and write the resulting cubes in the same order.
A ratio a:b can be written as a fraction a/b; cubing the ratio gives a³/b³.
Take the cube root of both terms when the given triplicate-ratio terms are perfect cubes.
Quick Tricks
First reduce the given ratio to its simplest form, then cube the smaller terms. This avoids unnecessary large calculations.
Remember common cubes such as 2³ = 8, 3³ = 27, 4³ = 64 and 5³ = 125.
The first term remains the numerator or first term after cubing, and the second term remains the second term.
Triplicate Ratio Concepts
Calculating the Triplicate Ratio
If the ratio is a:b, calculate a × a × a and b × b × b. The result is a³:b³. For example, for 3:4, 3³:4³ = 27:64.
Triplicate Ratio After Simplification
If a:b = c:d, then a³:b³ = c³:d³. Therefore, simplify common factors first. For 8:12, division by 4 gives 2:3, so the triplicate ratio is 8:27.
Finding the Original Ratio from a Triplicate Ratio
If the triplicate ratio is A:B = a³:b³, then the original ratio is ∛A:∛B. The ratio should be simplified if the cube roots have a common factor.
Comparing a Ratio with Its Triplicate Ratio
For a:b, multiplying both terms by 3 gives 3a:3b, which is equivalent to a:b. Triplication instead gives a³:b³. For example, the triplicate ratio of 2:5 is 8:125, not 6:15.
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Duplicate, Triplicate and Sub-Duplicate Ratios
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Triplicate Ratio: Quick Revision
Use these rules to calculate and reverse triplicate ratios.
- For a:b, the triplicate ratio is a³:b³.
- Cube the two terms separately and preserve their order.
- Simplify the given ratio before cubing to reduce calculation.
- The triplicate ratio of 2:3 is 8:27.
- To reverse a triplicate ratio A:B, take ∛A:∛B when the terms are perfect cubes.
- Triplicate ratio means cubing the terms, not multiplying them by 3.
Triplicate Ratio FAQs
What is the triplicate ratio formula?
For a ratio a:b, the triplicate ratio is a³:b³. For example, the triplicate ratio of 2:5 is 8:125.
What is the triplicate ratio of 6:9?
First simplify 6:9 to 2:3. Its triplicate ratio is 2³:3³ = 8:27.
What is the triplicate ratio of 4:7?
Cube both terms: 4³:7³ = 64:343.
How is triplicate ratio different from multiplying a ratio by 3?
Triplicate ratio cubes each term. Thus, the triplicate ratio of 2:3 is 8:27, whereas multiplying both terms by 3 gives the equivalent ratio 6:9.
How do you find the original ratio from 27:64 as a triplicate ratio?
Take cube roots of both terms: ∛27:∛64 = 3:4. Therefore, the original ratio is 3:4.
What is the triplicate ratio of 10:15?
Simplify 10:15 to 2:3, then cube the terms. The triplicate ratio is 8:27.