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Equations with fractions worksheets

An equation with a fraction on each side gets simpler the moment both denominators are gone. These free printable worksheets put x plus a number over one denominator on the left, and a fraction or x over another number on the right, and every solution is a whole number.

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Equations with fractions
Equations with fractions worksheet — Whole-number solutions, free printable with answer key

The answer key prints on a separate page.

What's on this sheet

Cross-multiplying is the first move, and it is the same as multiplying both sides by both denominators at once. (x + 1)/6 = 7/3 becomes 3(x + 1) = 42, and (x + 9)/4 = x/3 becomes 3(x + 9) = 4x. The worked answers write that line first, then expand the bracket, collect and divide, so a student who stalls can see exactly which step it was.

Why this sheet works

Two shapes share each page, and they finish differently. With a number on the right, the cross-multiplied line is a two-step equation: 3x + 3 = 42, so x = 13. With x on the right, x turns up on both sides — 3x + 27 = 4x — and has to be collected before anything is divided, which is the step a student used to the first shape tends to skip. The bracket is the other trap: 3(x + 9) is 3x + 27, and writing 3x + 9 gives an answer that fails the check.

How this one works

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3(x + 1) = 42
3x + 3 = 42
3x + 3=42
3x + 3=42
3x=39
3x=39
x=13
3x + 3=42
3x=39
x=13
  1. Both sides are fractions, so clear them: multiply both sides by 6 and by 3 — the two bottoms.
  2. That is 3 × (x + 1) on the left and 6 × 7 = 42 on the right, so 3x + 3 = 42.
  3. Two things were done to x: multiplied by 3, then 3 added. Undo them in reverse order — whatever happened last comes off first.
  4. The 3 went on last, so it comes off first — from both sides, to keep them equal. 42 − 3 = 39.
  5. That leaves 3x, so divide both sides by 3: 39 ÷ 3 = 13.
  6. Check by putting it back: 3(13) + 3 = 42. It holds, so x = 13.

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