Sizu Riatto
Algebra · Chapter 9

Clear the Fractions

Fractions in an equation are just a step away from whole numbers: multiply every term by the lowest common denominator and solve as usual.

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Opens on Chapter 9’s example: Roz’s boxes: x/4 + x/6 = 10.

1. An equation with fractions
2. Part = percent × whole: fill any two
3. Undo a percent change
4. A proportion a/b = c/d: leave one blank
Enter your numbers, then press Work it out.

How it works

Multiplying every term on both sides by the same number keeps the balance, so choose the lowest number every bottom divides into (for x/4 and x/6 that’s 12): every fraction becomes a whole number and the equation solves as usual. A percent is a fraction of 100, so part = percent × whole, and any one of the three follows from the other two. To undo a percent change, divide by the multiplier: 15% off means paying 85%, so the original is the sale price ÷ 0.85; adding 15% back to the sale price overshoots. In a proportion, cross-multiply: a × d = b × c.

From the book, Chapter 9. (2/3)x = 18 gives 27; x/4 + x/6 = 10 clears with 12 to give 24. $34 after 15% off was $40 (not $39.10); 18 is 24% of 75; 3/8 = c/56 gives 21. $85.60 with 7% tax is $80 plus $5.60 tax (taking 7% off gives the wrong $79.61). (x + 3)/5 = 4 gives $17, x/3 = (x + 4)/5 gives 6, and 12/n = 3 gives 4. Every chapter and its calculator →

Numbers can be typed as 1,450, $38, 0.40, 12%, 1/6 or 2 3/8. The algebra is done with exact fractions, so 1/3 stays 1/3; decimals are rounded half up, the way the book rounds. Everything stays in your browser: no sign-up, nothing stored or sent.