Topic Details (Notes format)

How to Divide Fractions

Subject: Mathematics

Book: Maths Mastery

Dividing fractions transforms the problem into multiplication by the reciprocal of the divisor. The formula for (a/b) ÷ (c/d) is (a/b) × (d/c). For instance, (3/5) ÷ (2/7) = (3/5) × (7/2) = 21/10 or 2 1/10. Reciprocal simply means flipping the numerator and the denominator of the divisor. This procedure arises in contexts like distributing resources into fractional segments or converting rates (e.g., speed or density calculations). Consistent practice ensures your ability to handle everyday scenarios, from cooking half a recipe to analyzing productivity rates in a group project.

Practice Questions

If x:y = 2:3 and z:y = 4:3, what is x:z?

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If sin(θ) = 3/5 and θ is an acute angle, what is tan(θ)?

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If a + b = 10 and ab = 21, what is the value of a^2 + b^2?

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A car covers a distance of 150 km in 2.5 hours. What is its average speed?

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If the product of two numbers is 120 and their sum is 26, what are the numbers?

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What is the value of x if 3x + 7 = 16?

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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 base radius of 3 cm and height of 4 cm, what is its slant height?

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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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A cube has a side length of 4 cm. What is its volume?

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