Adding and Subtracting Fractions Calculator

Fraction Addition/Subtraction Formula:

\[ \frac{a}{b} \pm \frac{c}{d} = \frac{a \times d \pm b \times c}{b \times d} \]

First Fraction Numerator (a):

First Fraction Denominator (b):

Operation:

Second Fraction Numerator (c):

Second Fraction Denominator (d):

Result:

Decimal Equivalent:

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1. What is Fraction Addition/Subtraction?

Fraction addition and subtraction are fundamental arithmetic operations that combine two fractions into a single fraction. The key principle is finding a common denominator before performing the operation on the numerators.

2. How Does the Calculator Work?

The calculator uses the standard fraction arithmetic formula:

\[ \frac{a}{b} \pm \frac{c}{d} = \frac{a \times d \pm b \times c}{b \times d} \]

Where:

\( a \) — Numerator of first fraction
\( b \) — Denominator of first fraction
\( c \) — Numerator of second fraction
\( d \) — Denominator of second fraction
\( \pm \) — Addition or subtraction operation

Explanation: The calculator first finds a common denominator (b×d), then performs the operation on the numerators, and finally simplifies the resulting fraction.

3. Importance of Common Denominator

Details: Fractions can only be directly added or subtracted when they share the same denominator. The common denominator is the product of the individual denominators.

4. Using the Calculator

Tips: Enter numerators and denominators for both fractions, select the operation (addition or subtraction). Denominators must be positive integers.

5. Frequently Asked Questions (FAQ)

Q1: What if I get a negative result?
A: Negative results are valid and indicate the combined value is less than zero.

Q2: How are fractions simplified?
A: The calculator finds the greatest common divisor (GCD) of numerator and denominator and divides both by it.

Q3: What if denominators are the same?
A: The calculation is simpler: (a±c)/b, but the calculator will still give the correct result.

Q4: Can I use this for mixed numbers?
A: First convert mixed numbers to improper fractions before using the calculator.

Q5: What about reducing to lowest terms?
A: The calculator automatically simplifies the result to its lowest terms.