Using Graphing Calculator To Add Fractions

Fraction Addition:

\[ \frac{a}{b} + \frac{c}{d} = \frac{ad + bc}{bd} \]

Result:

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1. Adding Fractions on TI Graphing Calculator

This calculator demonstrates how to add fractions using the standard mathematical method that graphing calculators like the TI-84 use. The process follows the fraction addition formula:

\[ \frac{a}{b} + \frac{c}{d} = \frac{ad + bc}{bd} \]

2. Step-by-Step Process

Steps to add fractions:

Multiply numerator of first fraction (a) by denominator of second fraction (d)
Multiply numerator of second fraction (c) by denominator of first fraction (b)
Add these two products together to get the new numerator
Multiply the denominators (b × d) to get the new denominator
Simplify the resulting fraction by dividing numerator and denominator by their greatest common divisor (GCD)

3. Understanding the Calculation

Mathematical Basis: The calculation finds a common denominator by multiplying the denominators, then adjusts the numerators accordingly before adding them.

Example: 1/2 + 1/4 = (1×4 + 1×2)/(2×4) = 6/8 = 3/4

4. Using This Calculator

Instructions: Enter the numerator and denominator for both fractions. All denominators must be positive integers. The calculator will show both the unsimplified and simplified results.

5. Frequently Asked Questions (FAQ)

Q1: Why do we need a common denominator to add fractions?
A: Fractions represent parts of a whole. To add them meaningfully, they must be parts of the same sized whole, which requires a common denominator.

Q2: How does the TI calculator simplify fractions?
A: The calculator uses the Euclidean algorithm to find the greatest common divisor (GCD) of the numerator and denominator, then divides both by this number.

Q3: What if I get a negative denominator?
A: The calculator automatically adjusts the signs so the denominator is always positive (moving the negative sign to the numerator if needed).

Q4: Can I add mixed numbers with this?
A: First convert mixed numbers to improper fractions, then use this calculator.

Q5: How is this different from multiplying fractions?
A: When multiplying, you simply multiply numerators and denominators directly (a/b × c/d = ac/bd), with no need for a common denominator.