--- title: "Ratio & Proportion" description: "24 topics in Mathematics, in the order they build on each other." canonical: https://lightmysky.com/learn/mathematics/areas/ratio-and-proportion source: https://lightmysky.com/learn/mathematics/areas/ratio-and-proportion.md retrieved: 2026-10-19 --- > **Agent view.** This is the Markdown twin of the page, for tools and assistants. > When to use this site, and the call that answers each job: https://lightmysky.com/agent-instructions.md > API description (OpenAPI 3.1): https://lightmysky.com/openapi.json · Authentication: https://lightmysky.com/auth.md > Pricing: https://lightmysky.com/pricing.md · Catalog: https://lightmysky.com/llms.txt · Full catalog: https://lightmysky.com/llms-full.txt > Every machine-readable file on this domain: https://lightmysky.com/.well-known/ai-catalog.json > Ask for Markdown with `Accept: text/markdown`, a `.md` address, or `?mode=agent`. # Ratio & Proportion 24 topics in Mathematics, in the order they build on each other. Page: https://lightmysky.com/learn/mathematics/areas/ratio-and-proportion - [Ratio and proportion vocabulary](https://lightmysky.com/learn/mathematics/ratio-and-proportion-vocabulary-mt_ESgc4YBw-a): Know and use the vocabulary of ratio and proportion — ratio, proportion, percentage, scale, equivalent, unequal, relative size, part-to-part, part-to-whole, and out of — and understand the difference between ratio (comparing parts to parts) and proportion (comparing a part to the whole) - [Bar Models for Ratios](https://lightmysky.com/learn/mathematics/bar-models-for-ratios-mt_ePXg_XyCKU): Represent ratio and proportion problems using bar models (rectangular strips divided into equal parts labelled with quantities) and tape diagrams (segmented strips showing part-to-part and part-to-whole relationships); use these visual models to set up and solve unequal sharing, scaling, and percentage problems — drawing the diagram first, then reading off the answer - [Calculating percentages](https://lightmysky.com/learn/mathematics/calculating-percentages-mt_PNSyfH56eQ): Solve problems involving the calculation of percentages of amounts (e.g. 15% of 360) and the use of percentages for comparison - [Ratio Problems](https://lightmysky.com/learn/mathematics/ratio-problems-mt_h0gJcSuwdL): Solve problems involving the relative sizes of two quantities where missing values can be found by using integer multiplication and division facts - [Scale and similar shapes](https://lightmysky.com/learn/mathematics/scale-and-similar-shapes-mt_2OtRUM_0zW): Solve problems involving similar shapes where the scale factor is known or can be found - [Unequal sharing and grouping](https://lightmysky.com/learn/mathematics/unequal-sharing-and-grouping-mt_FnUJMXPUZX): Solve problems involving unequal sharing and grouping using knowledge of fractions and multiples - [Ratio Notation](https://lightmysky.com/learn/mathematics/ratio-notation-mt_XWSGuFW7It): Use ratio notation to describe the relationship between two or more quantities, simplify ratios to their simplest form, and convert between ratio and fraction representations - [Proportion Graphs](https://lightmysky.com/learn/mathematics/proportion-graphs-mt_FspV_imUGK): Represent proportional relationships using double number lines (two parallel number lines aligned at 0) and ratio tables; recognise that equivalent ratios generate straight lines through the origin when graphed - [Proportional Reasoning Vocabulary](https://lightmysky.com/learn/mathematics/proportional-reasoning-vocabulary-mt_ATYLKt0je-): Know and use advanced vocabulary of multiplicative reasoning — direct proportion, inverse proportion, ratio, rate, unit rate, compound unit, scale factor — accurately in problem-solving contexts - [Dividing Quantities by Ratio](https://lightmysky.com/learn/mathematics/dividing-quantities-by-ratio-mt_nOCPx5qw0Z): Divide a given quantity into two parts in a given part:part or part:whole ratio, and express the division as a fraction of the whole - [One Quantity as a Fraction](https://lightmysky.com/learn/mathematics/one-quantity-as-a-fraction-mt_xAf2bu9wYK): Express one quantity as a fraction of another where the result may be less than 1 or greater than 1, and interpret the meaning in context - [Unit Conversions](https://lightmysky.com/learn/mathematics/unit-conversions-mt_tpT9brpI6D): Convert freely between related standard units of measurement (time, length, area, volume/capacity, mass) using decimal notation to up to three decimal places where appropriate - [Scale drawings and maps](https://lightmysky.com/learn/mathematics/scale-drawings-and-maps-mt_1badik7iKJ): Use scale factors to interpret and create scale diagrams and maps, calculating real-life distances from map measurements and vice versa - [Ratio Notation and Relationships](https://lightmysky.com/learn/mathematics/ratio-notation-and-relationships-mt_yK51ZnKA8m): Understand that a multiplicative relationship between two quantities can be expressed as a ratio; use ratio notation; simplify ratios - [Proportion](https://lightmysky.com/learn/mathematics/proportion-mt_5mIcmKRCgA): Recognise and solve problems involving direct proportion (as one quantity increases, the other increases at a constant rate) and inverse proportion (as one increases, the other decreases), including graphical and algebraic representations - [Percentages as fractions](https://lightmysky.com/learn/mathematics/percentages-as-fractions-mt_ALUrJpY0cZ): Define percentage as 'number of parts per hundred'; interpret percentages and percentage changes as a fraction or a decimal; express one quantity as a percentage of another; compare quantities using percentages; work with percentages greater than 100% - [Percentages (age 12+)](https://lightmysky.com/learn/mathematics/percentages-age-12-mt_iEXqN48w3x): Solve problems involving percentage increase, percentage decrease, finding the original value after a percentage change, and calculating simple interest - [Compound Interest and Repeated Percentage Change](https://lightmysky.com/learn/mathematics/compound-interest-and-repeated-percentage-change-mt_2vJz9VKle_): Applying a percentage change again and again multiplies rather than adds, so the multiplier raised to a power gives the answer in one step. The same calculation covers savings growing, a debt growing, and a value depreciating. - [Percentage Change with Multipliers](https://lightmysky.com/learn/mathematics/percentage-change-with-multipliers-mt_uqclfF4OBR): Use one multiplier for an increase or a decrease, chain multipliers for repeated changes, and divide by the multiplier to find the original amount. - [Compound Growth and Decay](https://lightmysky.com/learn/mathematics/compound-growth-and-decay-mt_xf5FQ2sugf): Apply a repeated percentage change as a multiplier raised to a power, for savings, depreciation and populations, and find how many steps it takes to pass a target. - [Compound Units](https://lightmysky.com/learn/mathematics/compound-units-mt_kLQOzZYrd5): Use compound units such as speed (distance ÷ time), unit pricing (cost ÷ quantity), and density (mass ÷ volume); solve problems involving compound units - [Ratio Problems: Sharing, Changing and Combining](https://lightmysky.com/learn/mathematics/ratio-problems-sharing-changing-and-combining-mt_vJelayH4uv): Solve ratio problems where a total is shared, one part is known, a ratio changes, or two ratios have to be joined through the quantity they share. - [Direct Proportion as a Formula](https://lightmysky.com/learn/mathematics/direct-proportion-as-a-formula-mt_nhSf9I7Bjz): Write y = kx for two quantities in direct proportion, find k from one pair of values, and use the formula to predict others. - [Inverse Proportion](https://lightmysky.com/learn/mathematics/inverse-proportion-mt_ZbbN2x6tcL): Use y = k/x when one quantity falls as the other rises, find k from a given pair, and recognise the curve it produces.