---
title: "Fractions"
description: "67 topics in Mathematics, in the order they build on each other."
canonical: https://lightmysky.com/learn/mathematics/areas/fractions
source: https://lightmysky.com/learn/mathematics/areas/fractions.md
retrieved: 2026-10-19
---

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# Fractions

67 topics in Mathematics, in the order they build on each other.

Page: https://lightmysky.com/learn/mathematics/areas/fractions

- [What Is a Half?](https://lightmysky.com/learn/mathematics/what-is-a-half-mt_-hTTat0mBR): Recognise, find, and name a half as one of two equal parts of an object, shape, or quantity
- [Finding quarters (age 5+)](https://lightmysky.com/learn/mathematics/finding-quarters-age-5-mt_g3W0mdADVu): Recognise, find, and name a quarter as one of four equal parts of an object, shape, or quantity
- [Fraction notation](https://lightmysky.com/learn/mathematics/fraction-notation-mt_vKcxX6iNOA): Read and write fraction notation. Name the numerator and denominator and explain equal parts. Use the names unit fraction, non-unit fraction, proper fraction, improper fraction, mixed number, equivalent fraction and simplest form.
- [Fractions of amounts](https://lightmysky.com/learn/mathematics/fractions-of-amounts-mt_cFltwUQi-d): Recognise, find, name, and write fractions 1/3, 1/4, 2/4, and 3/4 of a length, shape, set of objects, or quantity
- [Halves & Quarters of Shapes](https://lightmysky.com/learn/mathematics/halves-and-quarters-of-shapes-mt_xACS3rWWDp): Partition circles and rectangles into two and four equal shares and describe them using the words halves, fourths, and quarters
- [Decomposing a shape into more equal shares](https://lightmysky.com/learn/mathematics/decomposing-a-shape-into-more-equal-shares-mt_hyvHv2BCwb): Understand that decomposing a shape into more equal shares creates smaller shares
- [Fractions of a group of objects](https://lightmysky.com/learn/mathematics/fractions-of-a-group-of-objects-mt_k2WE0-22-4): Recognise, find, and write fractions of a discrete set of objects: unit fractions and non-unit fractions with small denominators
- [Splitting shapes into equal parts (age 7+)](https://lightmysky.com/learn/mathematics/splitting-shapes-into-equal-parts-age-7-mt_Xp-rj46S2w): Partition circles and rectangles into two, three, or four equal shares; describe shares as halves, thirds, and fourths; recognise that equal shares of identical wholes need not have the same shape
- [Tenths](https://lightmysky.com/learn/mathematics/tenths-mt_YzM5goBctT): Count up and down in tenths; recognise that tenths arise from dividing an object into 10 equal parts and from dividing one-digit numbers or quantities by 10
- [Fractions on a number line](https://lightmysky.com/learn/mathematics/fractions-on-a-number-line-mt_Kr3IyA6m-O): Recognise and use fractions as numbers: place unit fractions and non-unit fractions with small denominators on a number line
- [Adding and subtracting fractions with the same bottom number within one whole](https://lightmysky.com/learn/mathematics/adding-and-subtracting-fractions-with-the-same-bottom-number-within-one-whole-mt_a1FdAsRKOF): Add and subtract fractions with the same denominator within one whole (e.g. 5/7 + 1/7 = 6/7)
- [Comparing fractions](https://lightmysky.com/learn/mathematics/comparing-fractions-mt_IfEgu0X449): Compare and order unit fractions, and fractions with the same denominator
- [Solving problems with fractions (age 7+)](https://lightmysky.com/learn/mathematics/solving-problems-with-fractions-age-7-mt_SsLWS_APM7): Solve problems involving counting in tenths, fractions of quantities, equivalence, fraction addition/subtraction, and fraction comparison
- [Adding fractions (same denominator)](https://lightmysky.com/learn/mathematics/adding-fractions-same-denominator-mt_CBHwluE6Lp): Add and subtract fractions with the same denominator, including results greater than one whole (e.g. 5/8 + 6/8 = 11/8)
- [Decimal & Percent Notation](https://lightmysky.com/learn/mathematics/decimal-and-percent-notation-mt_W17Kbwm0-u): Read, write, and use decimal and percentage notation correctly — decimal, decimal point, tenths, hundredths, thousandths, percentage, per cent, % symbol, convert, terminating decimal — and understand the relationships between fractions, decimals, and percentages as three ways of expressing the same value
- [Fractions of a whole](https://lightmysky.com/learn/mathematics/fractions-of-a-whole-mt_ndGqFPWyen): Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a/b as a parts of size 1/b
- [Comparing fractions (age 8+)](https://lightmysky.com/learn/mathematics/comparing-fractions-age-8-mt_HnKbuCliNS): Compare two fractions with the same numerator or the same denominator by reasoning about size; record comparisons with >, =, or < symbols
- [Fractions as parts of shapes](https://lightmysky.com/learn/mathematics/fractions-as-parts-of-shapes-mt_idbKDrf9qZ): Partition shapes into parts with equal areas and express the area of each part as a unit fraction of the whole
- [Fractions of amounts (harder)](https://lightmysky.com/learn/mathematics/fractions-of-amounts-harder-mt_3y7xKP9MjU): Solve problems involving increasingly harder fractions to calculate quantities, including non-unit fractions where the answer is a whole number
- [Fractions on a number line (age 8+)](https://lightmysky.com/learn/mathematics/fractions-on-a-number-line-age-8-mt_NoB20kVa4w): Represent fractions on a number line: partition the interval 0 to 1 into b equal parts to locate 1/b, then mark off a lengths of 1/b from 0 to locate a/b
- [Hundredths (age 8+)](https://lightmysky.com/learn/mathematics/hundredths-age-8-mt_doX1BhmFgk): Count up and down in hundredths; recognise that hundredths arise when dividing an object by 100 or dividing tenths by 10
- [Decimal equivalents of tenths and hundredths](https://lightmysky.com/learn/mathematics/decimal-equivalents-of-tenths-and-hundredths-mt_TqDq6jyOmL): Recognise and write decimal equivalents of any number of tenths or hundredths (e.g. 3/10 = 0.3, 27/100 = 0.27)
- [Comparing two-decimal numbers](https://lightmysky.com/learn/mathematics/comparing-two-decimal-numbers-mt_IegHBHERVa): Compare numbers with the same number of decimal places up to two decimal places
- [Decimals and fractions](https://lightmysky.com/learn/mathematics/decimals-and-fractions-mt_wB-GBDkoNr): Solve simple measure and money problems involving fractions and decimals to two decimal places
- [Dividing by 10 and 100](https://lightmysky.com/learn/mathematics/dividing-by-10-and-100-mt_kDMKJ5Ztt6): Find the effect of dividing a one- or two-digit number by 10 and 100, identifying the value of the digits as ones, tenths, and hundredths
- [Rounding decimals to whole numbers](https://lightmysky.com/learn/mathematics/rounding-decimals-to-whole-numbers-mt_Fl7b8q9pI1): Round decimals with one decimal place to the nearest whole number
- [Whole numbers as fractions](https://lightmysky.com/learn/mathematics/whole-numbers-as-fractions-mt_AYzE1EAvI0): Express whole numbers as fractions (e.g. 3 = 3/1) and recognise fractions equivalent to whole numbers (e.g. 4/4 = 1, 6/1 = 6)
- [Rounding decimals (age 9+)](https://lightmysky.com/learn/mathematics/rounding-decimals-age-9-mt_Ii1hV4V5ql): Round decimals with two decimal places to the nearest whole number and to one decimal place
- [Understanding fractions (age 9+)](https://lightmysky.com/learn/mathematics/understanding-fractions-age-9-mt_09sySPqM9Z): Understand a fraction a/b with a > 1 as a sum of fractions 1/b (e.g. 3/5 = 1/5 + 1/5 + 1/5)
- [Fraction addition concepts](https://lightmysky.com/learn/mathematics/fraction-addition-concepts-mt_VgOePicFYK): Understand addition and subtraction of fractions as joining and separating parts; decompose a fraction into a sum of fractions with the same denominator in more than one way
- [Mixed numbers and improper fractions](https://lightmysky.com/learn/mathematics/mixed-numbers-and-improper-fractions-mt_o_p-3tCxiM): Recognise mixed numbers and improper fractions; convert from one form to the other (e.g. 2/5 + 4/5 = 6/5 = 1 1/5)
- [Adding and subtracting mixed numbers](https://lightmysky.com/learn/mathematics/adding-and-subtracting-mixed-numbers-mt_70qDTI14td): Add and subtract mixed numbers with like denominators, including by converting to improper fractions or using properties of operations
- [Multiplying fractions](https://lightmysky.com/learn/mathematics/multiplying-fractions-mt_TgHxujL81r): Understand a/b as a multiple of 1/b; multiply proper fractions and mixed numbers by whole numbers, supported by visual models (e.g. 3 × 2/5 = 6/5 = 1 1/5)
- [Fractions of a whole (age 9+)](https://lightmysky.com/learn/mathematics/fractions-of-a-whole-age-9-mt_HJA2Oz-Zh1): Solve word problems involving multiplication of a fraction by a whole number using visual models and equations
- [Word problems adding and subtracting fractions](https://lightmysky.com/learn/mathematics/word-problems-adding-and-subtracting-fractions-mt_ZLqYE7la4Z): Solve word problems involving addition and subtraction of fractions with like denominators, using visual models and equations
- [Writing simple fractions](https://lightmysky.com/learn/mathematics/writing-simple-fractions-mt_MyGblah2yY): Write simple fractions (e.g. 1/2 of 6 = 3) and recognise the equivalence of 2/4 and 1/2
- [Equivalent fractions](https://lightmysky.com/learn/mathematics/equivalent-fractions-mt_FbDKeLfBCo): Recognise and show, using diagrams, equivalent fractions with small denominators
- [Equivalent fractions on a number line](https://lightmysky.com/learn/mathematics/equivalent-fractions-on-a-number-line-mt_Ep7TDFuYUa): Understand two fractions as equivalent if they are the same size or the same point on a number line; recognise and show families of common equivalent fractions using diagrams
- [Equivalent fractions (age 8+)](https://lightmysky.com/learn/mathematics/equivalent-fractions-age-8-mt_FP-mjXaq3B): Generate simple equivalent fractions and explain why they are equivalent using visual fraction models
- [Fraction-Decimal Equivalents](https://lightmysky.com/learn/mathematics/fraction-decimal-equivalents-mt_DRlbMok2lT): Recognise and write decimal equivalents of 1/4, 1/2, and 3/4
- [Equivalent fractions (age 9+)](https://lightmysky.com/learn/mathematics/equivalent-fractions-age-9-mt_ebPelt-qAl): Explain why a fraction a/b is equivalent to (n×a)/(n×b) using visual models; use this principle to recognise and generate equivalent fractions, including tenths and hundredths
- [Adding fractions (different denominators)](https://lightmysky.com/learn/mathematics/adding-fractions-different-denominators-mt_-V7EnqU7gG): Add and subtract fractions when one denominator is a multiple of the other by rewriting with a common denominator.
- [Comparing fractions (age 9+)](https://lightmysky.com/learn/mathematics/comparing-fractions-age-9-mt_SXbZ3bC9z7): Compare and order fractions with different numerators and denominators by creating common denominators/numerators or comparing to a benchmark such as 1/2; justify conclusions with visual models
- [Converting tenths to hundredths](https://lightmysky.com/learn/mathematics/converting-tenths-to-hundredths-mt_NaqEP8xDhZ): Express a fraction with denominator 10 as an equivalent fraction with denominator 100 and use this to add fractions with denominators 10 and 100 (e.g. 3/10 + 4/100 = 34/100)
- [Decimals for Tenths & Hundredths](https://lightmysky.com/learn/mathematics/decimals-for-tenths-and-hundredths-mt_Vi4Vo5xs_g): Use decimal notation for fractions with denominators 10 or 100; read and write decimal numbers as fractions (e.g. 0.62 = 62/100, 0.71 = 71/100)
- [Understanding Percentages](https://lightmysky.com/learn/mathematics/understanding-percentages-mt_ZM9mhHsyYZ): Understand the per cent symbol (%); know that per cent means ‘number of parts per hundred’; write percentages as a fraction with denominator 100 and as a decimal
- [Percentage and decimal equivalents](https://lightmysky.com/learn/mathematics/percentage-and-decimal-equivalents-mt_4ubP_RMg9o): Solve problems requiring knowledge of percentage and decimal equivalents of 1/2, 1/4, 1/5, 2/5, 4/5 and fractions with denominators that are multiples of 10 or 25
- [Simplifying Fractions](https://lightmysky.com/learn/mathematics/simplifying-fractions-mt_b7T-CjOYUR): Use common factors to simplify fractions to their simplest form; use common multiples to express fractions with a common denominator
- [Adding fractions (unlike denominators)](https://lightmysky.com/learn/mathematics/adding-fractions-unlike-denominators-mt_14T5yPXUq_): Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions to produce a common denominator
- [Comparing fractions (age 10+)](https://lightmysky.com/learn/mathematics/comparing-fractions-age-10-mt_PL9VkDwXfh): Compare and order fractions including fractions greater than 1, by converting to common denominators or using benchmarks
- [Fraction word problems](https://lightmysky.com/learn/mathematics/fraction-word-problems-mt_e7filQgayF): Solve word problems involving addition and subtraction of fractions with unlike denominators, using visual models and benchmark fractions to estimate and assess reasonableness
- [Multiplying fractions (age 10+)](https://lightmysky.com/learn/mathematics/multiplying-fractions-age-10-mt_AabJisinfi): Multiply a fraction or whole number by a fraction, including proper fractions by proper fractions; interpret (a/b) × q as a parts of q partitioned into b equal parts; write answers in simplest form
- [Area with Fractions](https://lightmysky.com/learn/mathematics/area-with-fractions-mt_gx6KQK5-Kx): Find the area of a rectangle with fractional side lengths by tiling with unit-fraction squares; show that the area equals the product of the side lengths
- [Multiplication as scaling](https://lightmysky.com/learn/mathematics/multiplication-as-scaling-mt_VKW8lOcFaw): Interpret multiplication as scaling (resizing): compare the size of a product to a factor based on the size of the other factor without computing; explain the effect of multiplying by fractions greater than, equal to, or less than 1
- [Real-world fraction multiplication](https://lightmysky.com/learn/mathematics/real-world-fraction-multiplication-mt_lvaSGHwvQ5): Solve real-world problems involving multiplication of fractions and mixed numbers, using visual fraction models or equations
- [Fractions of a whole (age 10+)](https://lightmysky.com/learn/mathematics/fractions-of-a-whole-age-10-mt_4Km38F4L-6): Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b); solve word problems involving division of whole numbers leading to fractional or mixed-number answers
- [Decimals and fractions (age 10+)](https://lightmysky.com/learn/mathematics/decimals-and-fractions-age-10-mt_4K1dr204Hi): Associate a fraction with division and calculate decimal fraction equivalents for simple fractions (e.g. 3/8 = 0.375); recall and use equivalences between simple fractions, decimals, and percentages in different contexts
- [Dividing fractions (unit fractions)](https://lightmysky.com/learn/mathematics/dividing-fractions-unit-fractions-mt_ifPDOYvUqm): Interpret and compute division of a unit fraction by a non-zero whole number (e.g. 1/3 ÷ 4 = 1/12); use visual models and the relationship between multiplication and division to explain the result
- [Dividing by Fractions](https://lightmysky.com/learn/mathematics/dividing-by-fractions-mt_1PAWhRhpdg): Interpret and compute division of a positive whole number by a positive unit fraction below 1; use visual models and the relationship between multiplication and division to explain why the quotient is larger than the dividend.
- [Dividing unit fractions and whole numbers](https://lightmysky.com/learn/mathematics/dividing-unit-fractions-and-whole-numbers-mt_rCMdwG-YOE): Solve real-world problems involving division of unit fractions by whole numbers and whole numbers by unit fractions, using visual models and equations
- [Calculations with fractions, decimals and negatives](https://lightmysky.com/learn/mathematics/calculations-with-fractions-decimals-and-negatives-mt_gNUE4B3vuk): Use the four operations with formal written methods applied to integers, decimals, proper and improper fractions, and mixed numbers, all both positive and negative
- [Decimals and fractions (age 11+)](https://lightmysky.com/learn/mathematics/decimals-and-fractions-age-11-mt_SBkTGjiZjZ): Work interchangeably with terminating decimals and their corresponding fractions (such as 3.5 and 7/2 or 0.375 and 3/8); convert fluently between the two forms
- [Thousandths (age 9+)](https://lightmysky.com/learn/mathematics/thousandths-age-9-mt_kdWoAel3Zl): Recognise and use thousandths; relate them to tenths, hundredths, and their decimal equivalents (e.g. 1/1000 = 0.001, 35/1000 = 0.035)
- [Comparing Decimals](https://lightmysky.com/learn/mathematics/comparing-decimals-mt_933BohS9BH): Compare two decimals to hundredths (or up to three decimal places) by reasoning about size using place-value understanding; record with >, =, <
- [Decimals to three places](https://lightmysky.com/learn/mathematics/decimals-to-three-places-mt_sA2OvTiech): Solve problems involving numbers with up to three decimal places
- [Fractions and percentages of amounts](https://lightmysky.com/learn/mathematics/fractions-and-percentages-of-amounts-mt_J339bO7qLe): Interpret fractions and percentages as operators — find a fraction or percentage of an amount by multiplying, understanding that 'of' means multiply (e.g., 3/4 of 200 = 3/4 × 200 = 150)
- [Dividing fractions](https://lightmysky.com/learn/mathematics/dividing-fractions-mt_9Y96vxG_LH): Divide a fraction by a fraction using the 'keep-change-flip' method and visual models; interpret and solve word problems involving division of fractions by fractions