Math calculators
Ratio, proportion and number-theory tools that show every step, so you can check your homework or your recipe scaling.
Ratio CalculatorSimplify any ratio, find a missing term, scale a recipe or mix, or divide an amount in a given ratio, with the working shown.Proportion CalculatorSolve a/b = c/d for any missing value with cross multiplication, and check whether two ratios are really in proportion.GCF CalculatorEnter two or more whole numbers to get their greatest common factor, least common multiple, prime factorizations and the Euclidean algorithm worked out.
Math guides
How to Simplify Ratios: Whole Numbers, Decimals, Fractions and Three TermsStep-by-step methods for simplifying any ratio to lowest terms, including ratios with decimals, fractions, mixed units and more than two parts.
How to Divide an Amount in a Given Ratio (with Money, Time and Mixes)Share money, time or materials in any ratio using the parts method. Includes worked examples, three-way splits, rounding money fairly and common mistakes.
Ratio vs. Fraction vs. Percentage: How to Convert Between ThemRatios, fractions and percentages describe relationships in different ways. Learn when each is used and how to convert part-to-part and part-to-whole correctly.
Cooking with Ratios: Bread, Rice, Coffee and Vinaigrette Without a RecipeLearn the classic kitchen ratios for bread, pie crust, rice, coffee and dressings, and how to scale them up or down for any batch size.
Aspect Ratio Explained: 16:9, 4:3, 3:2 and How to Resize Without DistortionWhat aspect ratios mean for screens, photos and video, how to calculate a missing width or height, and how to crop or resize without stretching.
Mixing Ratios Made Easy: 2-Stroke Fuel, Paint, Epoxy and Cleaning SolutionsHow to read and measure mixing ratios such as 50:1 fuel, 2:1 epoxy and 1:10 dilutions, with conversion tables and tips for measuring small amounts accurately.
How to Solve Proportions: Cross Multiplication Step by StepLearn why cross multiplication works, how to solve for x in any position, and how to handle decimals, fractions and word problems without mistakes.
Direct vs. Inverse Proportion: How to Tell Them Apart and Solve EachUnderstand direct and inverse proportion with clear examples, the formulas y = kx and y = k/x, graphs, and a quick test to know which one a problem needs.
Unit Rates and Unit Prices: How to Find the Best BuyCompare prices of different package sizes with unit rates. Learn the formula, handle mixed units and bulk deals, and avoid the traps that make big packs look cheaper.
How to Scale a Recipe Up or Down Using ProportionsDouble, halve or resize any recipe with a single scaling factor. Includes conversions for awkward amounts, tips for eggs and spices, and pan size adjustments.
Map Scales and Scale Drawings: Converting Map Distance to Real DistanceRead ratio scales like 1:24,000, verbal scales and bar scales, convert between map and ground distance, and make your own scale drawings with proportions.
Similar Triangles and Proportions: Find Missing Sides and Measure HeightsUse proportions to find missing sides of similar triangles, measure the height of trees and buildings with shadows, and understand how area and volume scale.
GCF vs. LCM: What's the Difference and When to Use EachThe greatest common factor and least common multiple are easy to confuse. Learn what each one means, how they're related, and which one a word problem needs.
The Euclidean Algorithm: The Fastest Way to Find the GCFHow Euclid's division method finds the greatest common factor of large numbers in a few steps, why it works, and how to extend it to three or more numbers.
Prime Factorization: Factor Trees, Division Ladders and Divisibility RulesBreak any number into prime factors using factor trees or the ladder method, with divisibility shortcuts and examples of using primes to find the GCF and LCM.
Simplifying Fractions with the GCF (Including Mixed Numbers and Algebra)Reduce any fraction to lowest terms in one step using the greatest common factor, with examples for improper fractions, mixed numbers and algebraic fractions.
GCF Word Problems: 8 Worked Examples with Clear ExplanationsPractice greatest common factor word problems about groups, gift bags, tiles, ribbons and teams, with a simple checklist for spotting when to use the GCF.
Factoring Out the GCF in Algebra: Step-by-Step with ExamplesHow to find the greatest common factor of algebraic terms, factor it out of polynomials, handle negatives and binomial factors, and check your work.