How to Find Modulus on a Calculator Ti-84

Modulus Operation:

\[ a \mod b = remainder \text{ when } a \text{ is divided by } b \]

Modulus Result:

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1. What is Modulus Operation?

The modulus operation finds the remainder after division of one number by another. In mathematics, the result is always non-negative and less than the modulus.

2. How to Calculate Modulus

The modulus can be calculated using the formula:

\[ a \mod b = a - b \times \left\lfloor \frac{a}{b} \right\rfloor \]

Where:

\( a \) — Dividend (the number being divided)
\( b \) — Divisor (the modulus value)
\( \left\lfloor x \right\rfloor \) — Floor function (greatest integer less than or equal to x)

3. Finding Modulus on TI-84 Calculator

Steps to find modulus on TI-84:

Press MATH button
Scroll right to NUM menu
Select 5:remainder(
Enter your numbers as remainder(a,b)
Press ENTER to see result

4. Using the Calculator

Tips: Enter any real number for 'a' and a positive number for 'b'. The calculator will compute a mod b.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between modulus and remainder?
A: For positive numbers they're the same, but differ with negative numbers. Modulus is always non-negative.

Q2: Can modulus be negative?
A: In mathematics, modulus is always non-negative (0 ≤ result < b).

Q3: What if b is zero?
A: Division by zero is undefined, so modulus with zero is also undefined.

Q4: How is modulus used in programming?
A: Often used for cyclic operations, hash functions, and checking even/odd numbers (n mod 2).

Q5: Does this work for decimal numbers?
A: Yes, the calculator handles both integers and decimals.