Topic Details (Notes format)

How to Simplify Complex Fractions

Subject: Mathematics

Book: Maths Mastery

Complex fractions are fractions whose numerator or denominator (or both) contain other fractions. For example, (3/4) / (5/8). Simplify by multiplying the numerator by the reciprocal of the denominator: (3/4) ÷ (5/8) = (3/4) × (8/5) = 24/20 = 6/5. Alternatively, you can combine multiple fraction layers into a single rational expression. Mastering complex fraction simplification is critical for advanced algebra, rational expressions, and practical tasks like comparing multi-layered rate problems. Routine practice ensures that nested fractions never stall your problem-solving progress.

Practice Questions

The simple interest on Rs. 4000 at 5% per annum for 2 years is:

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A sum of money doubles itself in 5 years at simple interest. What is the rate of interest?

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If x^3 - 3x^2 + 4 = 0, what is one root of the equation?

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If the angles of a triangle are in the ratio 2:3:4, what is the measure of the largest angle?

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If a:b = 7:9 and b:c = 5:6, what is a:c?

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A train 120 meters long is moving at a speed of 54 km/h. How long will it take to pass a pole?

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What is the sum of all odd numbers from 1 to 99?

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A sum of money triples itself in 12 years at simple interest. What is the rate of interest per annum?

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If a+b = 10 and ab = 21, what is the value of a^3 + b^3?

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If a:b = 3:4 and b:c = 5:6, what is a:c?

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