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

If x = 2 and y = 3, what is the value of (x^2 + y^2)?

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If a:b = 2:3 and b:c = 4:5, what is a:c?

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If a cone has a radius of 5 cm and a height of 12 cm, what is its slant height?

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If x^2 - 5x + 6 = 0, what are the roots?

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The perimeter of a rectangle is 40 cm, and its length is 12 cm. What is its width?

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The angles of a quadrilateral are in the ratio 3:4:5:6. What is the largest angle?

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A man invests Rs. 5000 at 5% per annum simple interest. What is the total amount after 3 years?

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If the perimeter of a square is 36 cm, what is the length of its diagonal?

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The sides of a triangle are 7, 24, and 25. Is this a right triangle?

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A sum triples in 20 years at simple interest. What is the rate of interest per annum?

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