AQA · Mathematics · 8300
GCSE Maths: Equations: involving fractions
Algebra · AQA GCSE Maths (8300). Cards are generated from the Corbettmaths practice questions for Equations: involving fractions (Corbettmaths Video 111), 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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Solve: 2a/3 = 8
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a = 12. Multiply both sides by 3 to get 2a = 24, then divide by 2.
Solve: 3w/4 = 1/2
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w = 2/3. Multiply both sides by 4 to get 3w = 2, then divide by 3.
Solve: (2w + 1)/5 = 3/8
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w = -1/16. Multiply both sides by 5 to get 2w + 1 = 15/8, then subtract 1 and divide by 2.
Solve: (10x − 1)/7 = 8
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x = 57/10 or 5.7. Multiply both sides by 7 to get 10x − 1 = 56, add 1 to get 10x = 57, then divide by 10.
Solve: (7c + 4)/8 = 11
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c = 12. Multiply both sides by 8 to get 7c + 4 = 88, subtract 4 to get 7c = 84, then divide by 7.
Solve: (53 − 2x)/5 = 7
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x = 9. Multiply both sides by 5 to get 53 − 2x = 35, subtract 53 to get −2x = −18, then divide by −2.
Solve: (11 − w)/5 = 3 + w
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w = −2/3. Multiply both sides by 5 to get 11 − w = 15 + 5w, rearrange to get 11 − 15 = 6w, so −4 = 6w.
Solve: (x − 8)/3 = 7x/9
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x = −12/5 or −2.4. Multiply both sides by 9 to get 3(x − 8) = 7x, expand to 3x − 24 = 7x, then solve −24 = 4x.
Solve: (w + 7)/4 + (3w + 1)/2 = −3
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w = −2. Find common denominator 4: (w + 7)/4 + (6w + 2)/4 = −3, so 7w + 9 = −12, giving 7w = −21.
Solve: (m + 6)/2 − (2m − 2)/3 = 3
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m = 2. Find common denominator 6: 3(m + 6)/6 − 2(2m − 2)/6 = 3, so 3m + 18 − 4m + 4 = 18, giving −m + 22 = 18.
When solving equations with multiple fractions like a/b + c/d = e, what must you find first?
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The common denominator (often the LCM of the denominators) to combine the fractions.
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