Averages

Weighted Average vs. Simple Average

Compare simple and weighted averages, choose meaningful weights, handle frequency and percentage weights, and combine unequal groups correctly.

6 min read · Practical examplesFractions

Improper Fractions and Mixed Numbers Explained

Convert between improper fractions and mixed numbers using quotient and remainder, including negative values, whole-number results, and simplification.

6 min read · Practical examplesRatios

Ratio vs. Proportion: What Is the Difference?

Distinguish ratios, rates, equivalent ratios, and proportions, with unit, order, and cross-product examples.

6 min read · Practical examplesFactors and multiples

The Euclidean Algorithm Explained Step by Step

Find a greatest common divisor with repeated remainders, extend the method to multiple integers, and understand tool limits for zero, signs, and large values.

6 min read · Practical examplesFractions

How to Find the Least Common Denominator Using LCM

Use the LCM of positive denominators to build equivalent fractions for addition, subtraction, and comparison, then simplify the result.

6 min read · Practical examplesDecimals

How to Convert Decimals to Fractions

Convert terminating decimals to exact simplified fractions and understand why rounded repeating decimals require different treatment.

6 min read · Practical examplesRatios

Direct Proportion: Formula and Real-World Examples

Recognize and use direct proportion y = kx through unit-price, speed, recipe, and scale examples while rejecting nonproportional relationships.

6 min read · Practical examplesNumber theory

Prime vs. Composite Numbers

Classify positive integers by factor structure and understand why zero, one, negatives, odd numbers, and perfect squares need careful treatment.

6 min read · Practical examplesTrigonometry

Degrees vs. Radians in Trigonometry

Compare degree and radian angle measures, convert between them, and use radian values correctly with NumUtility's degree-only trigonometric functions.

6 min read · Practical examplesDates and time

How to Calculate Time Duration Across Midnight

Calculate overnight duration with complete dates, correct AM/PM or 24-hour notation, multiple midnights, and explicit DST assumptions.

6 min read · Practical examples