Desmos Calculator Fraction Division And Multiplication

Fraction Operations:

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

Numerator 1 (a):

Denominator 1 (b):

Operation:

Numerator 2 (c):

Denominator 2 (d):

Result:

Decimal Value:

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1. What is Fraction Multiplication and Division?

Fraction multiplication and division are fundamental arithmetic operations. Multiplication involves multiplying numerators and denominators directly, while division requires multiplying by the reciprocal of the second fraction.

2. How Does the Calculator Work?

The calculator performs two operations:

\[ \text{Multiplication: } \frac{a}{b} \times \frac{c}{d} = \frac{a \times c}{b \times d} \] \[ \text{Division: } \frac{a}{b} \div \frac{c}{d} = \frac{a \times d}{b \times c} \]

The calculator also simplifies the resulting fraction to its lowest terms using the greatest common divisor (GCD).

3. Mathematical Formulas

Key Concepts:

Fraction multiplication is commutative: \(\frac{a}{b} \times \frac{c}{d} = \frac{c}{d} \times \frac{a}{b}\)
Fraction division is equivalent to multiplying by the reciprocal
Simplification involves dividing numerator and denominator by their GCD

4. Using the Calculator

Instructions: Enter all four values (two numerators and two denominators), select the operation, and click Calculate. Denominators cannot be zero.

5. Frequently Asked Questions (FAQ)

Q1: What if I enter zero for a denominator?
A: The calculator prevents division by zero and will not accept zero denominators.

Q2: How is the simplification performed?
A: The calculator uses the Euclidean algorithm to find the GCD and divides both numerator and denominator by this value.

Q3: Can I enter negative fractions?
A: Yes, the calculator handles negative values. The negative sign can be placed on either numerator or denominator.

Q4: What about mixed numbers?
A: Convert mixed numbers to improper fractions before entering them (e.g., 2½ becomes 5/2).

Q5: How precise are the results?
A: Results are precise to 4 decimal places, with exact fractional representation when possible.