Topic Details (Notes format)

How to Solve Proportions (Cross-Multiplication)

Subject: Mathematics

Book: Maths Mastery

Proportions equate two ratios, like a/b = c/d. Cross-multiplication states ad = bc. For example, if 2/5 = x/15, then 2 × 15 = 5 × x, meaning 30 = 5x, so x = 6. Proportions answer real-world questions: “If 2 liters costs ₹100, what does 5 liters cost?” or “If 3 out of 10 students prefer a subject, how many out of 50 might prefer it?” The technique is vital for scaling recipes, resizing images, or solving geometry similarity. Consistent practice ensures you can set up and solve ratio-based statements in a single, efficient step.

Practice Questions

What is the value of log₃(27)?

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What is the 7th term of the arithmetic progression 3, 6, 9, 12,...?

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The sides of a triangle are 13 cm, 14 cm, and 15 cm. What is its area?

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How many diagonals does a pentagon have?

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What is the HCF of 72 and 120?

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What is the area of a circle with a diameter of 14 cm?

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What is the remainder when 5^100 is divided by 3?

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

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If a:b = 5:7 and b:c = 6:11, what is a:c?

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If x² - 9x + 18 = 0, what are the roots of the equation?

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