--- title: "Moving between diagrams and equations with fractions" description: "Move fluently between real-world situations, diagrams, number lines, and symbolic equations involving multiplication, fractions, and decimals, explaining what each representation shows" canonical: https://lightmysky.com/learn/mathematics/moving-between-diagrams-and-equations-with-fractions-mt_3VmBdlAeOZ source: https://lightmysky.com/learn/mathematics/moving-between-diagrams-and-equations-with-fractions-mt_3VmBdlAeOZ.md retrieved: 2026-09-02 --- > **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`. # Moving between diagrams and equations with fractions Move fluently between real-world situations, diagrams, number lines, and symbolic equations involving multiplication, fractions, and decimals, explaining what each representation shows Subject: Mathematics · Area: Mathematical Thinking · Ages 8 to 9 Page: https://lightmysky.com/learn/mathematics/moving-between-diagrams-and-equations-with-fractions-mt_3VmBdlAeOZ ## Ready when they can - Represent a sharing problem as both a fraction diagram and a division equation - Explain how a bar model for 4 × 23 connects to the area model and the written method - Translate a decimal on a number line into a fraction and explain the equivalence ## Lesson: Moving between diagrams and equations with fractions A number line is a straight line with numbers marked on it in order. Whole numbers like 0, 1, and 2 are easy to spot. Fractions live between the whole numbers too. A fraction like 3/4 sits between 0 and 1, closer to 1. *(drawing: This line is split into four equal jumps. The hop from 0 to 3 lands on 3/4.)* To name a point, first count how many equal steps make one whole. That count is the bottom number. Then count the steps you take from 0. That count is the top number. Two steps on a line cut into five equal steps is 2/5. Every step has to be the same size, or the names stop working. **Example.** Mia has 3 pizzas to share equally among 4 friends. She draws a bar split into 4 equal parts and shades 3 of them. That is the same as 3 divided by 4, and it lands at 3/4 on the number line. **Example.** A bar model shows multiplication too. Draw 4 equal bars, each worth 23. Split every bar into 20 and 3, and you have an area model: 4 lots of 20 make 80, and 4 lots of 3 make 12. The written method adds those same two pieces: 80 + 12 = 92. **Tip.** You have drawn fraction bars before: split a whole into equal parts, then count how many parts you have. The same bar connects the picture to the number line and to the written fraction. A number line can also show decimals, and the two ways of naming land on the same points. Split 0 to 1 into ten equal steps, and the second step is 2/10 as a fraction and 0.2 as a decimal. One point, two names. Count the steps to name the fraction first, then say that same fraction the decimal way. **Recap.** Fractions and decimals are just different names for the same point on a number line. ## Practice 24 questions on this page, each with its working shown. ## Needs first - [Area and the distributive property](https://lightmysky.com/learn/mathematics/area-and-the-distributive-property-mt_AQo4u7O4sM) - [Moving between situations, diagrams and equations](https://lightmysky.com/learn/mathematics/moving-between-situations-diagrams-and-equations-mt_dXq9VWm31W) - [Decimal equivalents of tenths and hundredths](https://lightmysky.com/learn/mathematics/decimal-equivalents-of-tenths-and-hundredths-mt_TqDq6jyOmL) ## Opens up - [Moving between bar models, number lines and equations](https://lightmysky.com/learn/mathematics/moving-between-bar-models-number-lines-and-equations-mt_CUmjcE7W6c)