How do Calculators add fractions with different denominators

In summary, computer technology adds fractions with different denominators by using fixed precision floating point format. Early calculators worked in decimal floating point, while modern calculators use binary double precision floating point arithmetic. A calculator performing infinite precision rational arithmetic would evaluate the sum differently, depending on the system. In most cases, the calculator will calculate the sum numerically with limited precision. However, in a computer algebra system, the calculator will calculate the sum by finding the smallest common multiple of the denominators, expanding both fractions, adding them, and simplifying the result.
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matqkks
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How does computer technology add fractions with different denominators?
 
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matqkks said:
How does computer technology add fractions with different denominators?
A desktop calculator will typically work using a fixed precision floating point format. https://en.wikipedia.org/wiki/Floating-point_arithmetic.

My understanding is that the early calculators worked in decimal floating point. For instance, the HP35 and HP45 had 8 decimal digits of accuracy and the SR51 had 10 decimal digits plus three undisplayed guard digits. If you key in "(3/7) + (5/6)", a modern calculator will likely compute 3/7 using binary double precision floating point arithmetic, compute 5/6 using binary double precision floating point arithmetic and add the two binary fractions [after scaling them to share a common binary exponent if needed]. It will convert the result to decimal for display purposes.

A calculator performing infinite precision rational arithmetic would evaluate the sum differently.
 
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It depends on the system. Typically it will just calculate it numerically with limited precision, in that case see the comment above. If you put it into a computer algebra system it will probably calculate it the same way a human does: Find the smallest common multiple of the denominators, expand both fractions to get the same denominator, add them. Alternatively expand both with the denominator of the other, add them, then simplify the result.
 

1. How do calculators add fractions with different denominators?

Calculators use a process called fraction addition algorithm to add fractions with different denominators. This algorithm involves finding the lowest common denominator (LCD) of the fractions, converting both fractions to equivalent fractions with the LCD as the denominator, and then adding the numerators together.

2. Can calculators add mixed numbers with different denominators?

Yes, calculators can add mixed numbers with different denominators by first converting the mixed numbers to improper fractions, then using the fraction addition algorithm to add them together.

3. Do calculators reduce the fractions to simplest form when adding?

No, calculators do not automatically reduce fractions to simplest form when adding. It is important to reduce the fractions yourself after adding if needed.

4. Why do calculators sometimes give a decimal answer when adding fractions?

Calculators may give a decimal answer when adding fractions because the result may not be a whole number or a fraction with a simpler form. In this case, the calculator will give a decimal approximation of the exact answer.

5. Is there a specific order to add fractions with different denominators on a calculator?

No, there is no specific order to add fractions with different denominators on a calculator. However, it is important to make sure that both fractions have the same denominator before adding them together.

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