Why 1/3 + 1/4 is 7/12, not 2/7
Fractions can be added only after their pieces represent the same size. A common denominator supplies that shared unit.
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One third means one of three equal pieces; one quarter means one of four. Adding the denominators mixes incompatible piece sizes. Split the same whole into twelfths instead: 1/3 = 4/12 and 1/4 = 3/12. There are now seven twelfths altogether, so the sum is 7/12. The denominator describes the size of each piece and stays unchanged during the final addition.
Use the calculator fields
Enter numerator 1 and denominator 3 for the first fraction, choose addition, then numerator 1 and denominator 4 for the second. The calculator returns a reduced fraction and a decimal approximation. Verify that the answer is larger than either input but smaller than 1. For subtraction, keep the same common denominator and subtract the numerators in the stated order.
A denominator is not a label to discard
The least common multiple often gives the smallest useful common denominator, although any nonzero common multiple works before simplification. Never enter zero as a denominator. When combining real measurements, also check that both fractions refer to the same whole: one third of a small container and one quarter of a large container cannot be added as 7/12 of a single unspecified container.
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