AQA · Mathematics · 8300
GCSE Maths: Equations: cross multiplication
Algebra · AQA GCSE Maths (8300). Cards are generated from the Corbettmaths textbook exercise for Equations: cross multiplication (Corbettmaths Video 112), and every card links back to the exact page it came from. Practice tests generate fresh variations of these questions, so the numbers change every attempt. Source material © Corbettmaths — used with attribution.
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What is the first step when solving an equation of the form a/b = c/d using cross multiplication?
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Multiply both sides to get ad = bc (cross multiply the numerators and denominators).
Solve for x: x/7 = 3/2
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x = 10.5 (or 21/2). Cross multiply: 2x = 21, so x = 21/2 = 10.5
Solve for h: 2/11 = 5/h
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h = 27.5 (or 55/2). Cross multiply: 2h = 55, so h = 55/2 = 27.5
Solve for a: 2a/3 = 3/2
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a = 9/4 (or 2.25). Cross multiply: 4a = 9, so a = 9/4
Solve for x: (x + 1)/5 = 3/2
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x = 6.5 (or 13/2). Cross multiply: 2(x + 1) = 15, so 2x + 2 = 15, then 2x = 13, x = 13/2
Solve for x: (3x − 1)/5 = (x + 11)/2
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x = 57. Cross multiply: 2(3x − 1) = 5(x + 11), so 6x − 2 = 5x + 55, then x = 57
Solve for x: 2/(3x − 5) = 1/(x + 8)
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x = 21. Cross multiply: 2(x + 8) = 1(3x − 5), so 2x + 16 = 3x − 5, then x = 21
When solving 2/(x + 2) = (x + 1)/3 by cross multiplication, what equation results?
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6 = (x + 1)(x + 2), which expands to x² + 3x + 2 = 6
What type of equation may result when cross multiplying if the variable appears in both a numerator and a denominator?
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A quadratic equation (x² terms may appear after expanding).
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