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Mathematics · pattern A, Numeric fields

Add, subtract, multiply and divide two fractions.

Enter two fractions to see all four operations at once, each with its exact result and decimal equivalent.

Inputs

The formula used

a/b + c/d = (ad + cb) ÷ bd; a/b × c/d = ac ÷ bd

Addition needs a common denominator; multiplication does not. That asymmetry is the single most useful thing to understand about fractions.

Sum

1.150000

Sum as a fraction
23/20
Difference
0.350000
Product
0.300000
Quotient
1.875000
Common denominator
20
Lowest common denominator
20

Why addition needs a common denominator and multiplication does not.

Adding requires the pieces to be the same size, which is exactly what a common denominator provides. Multiplying asks for a fraction of a fraction, so the sizes multiply directly — three quarters of two fifths is six twentieths with no conversion at all.

Questions about fraction

Why does dividing by a fraction multiply by its reciprocal?
Because dividing by a half asks how many halves fit, which is twice as many. The reciprocal expresses that inversion.
Do I need the lowest common denominator?
Not for a correct answer — any common denominator works. The lowest one keeps the numbers small.
When should I leave an answer as a fraction?
Whenever the decimal does not terminate. A third is exact; 0.333 is not, and marks usually go to the exact form.

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A calculator handles the arithmetic. It cannot teach you the method.

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Arithmetic runs in double-precision floating point, so results beyond about fifteen significant figures are not exact. Where a question wants an exact fraction or surd, keep the exact form rather than a decimal.