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

What is the length of the diagonal of a square with a side length of 7 cm?

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If a = 4 and b = 5, what is the value of (a+b)^2?

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A rectangle has a length of 10 cm and a width of 5 cm. What is the diagonal of the rectangle?

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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 2x = 16, what is the value of x?

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If the average of five consecutive odd numbers is 25, what is the largest number?

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

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If x^2 + 4x + 4 = 0, what is the value of x?

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