---
title: "Multiplication & Division"
description: "57 topics in Mathematics, in the order they build on each other."
canonical: https://lightmysky.com/learn/mathematics/areas/multiplication-and-division
source: https://lightmysky.com/learn/mathematics/areas/multiplication-and-division.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`.

# Multiplication & Division

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

Page: https://lightmysky.com/learn/mathematics/areas/multiplication-and-division

- [Division as equal sharing](https://lightmysky.com/learn/mathematics/division-as-equal-sharing-mt_LpSuPgL31x): Understand division as sharing equally into groups or as grouping (how many groups of a given size can be made)
- [Multiplication as repeated addition](https://lightmysky.com/learn/mathematics/multiplication-as-repeated-addition-mt_PZ909yPrEC): Understand multiplication as repeated addition and grouping equal sets
- [Arrays for multiplication](https://lightmysky.com/learn/mathematics/arrays-for-multiplication-mt_GRWwTDZ3wD): Use arrays to represent multiplication and division situations
- [Commutative Multiplication](https://lightmysky.com/learn/mathematics/commutative-multiplication-mt_C9ZfT-4cgn): Understand and apply the commutative property of multiplication and recognise that division is not commutative
- [Odd and even numbers](https://lightmysky.com/learn/mathematics/odd-and-even-numbers-mt_0u4KLbvBa1): Recognise odd and even numbers
- [Times tables](https://lightmysky.com/learn/mathematics/times-tables-mt_HhuSDxwDNM): Recall and use multiplication and division facts for the 2, 5, and 10 multiplication tables
- [Solving multiplication and division problems](https://lightmysky.com/learn/mathematics/solving-multiplication-and-division-problems-mt_wh3UqnWsa7): Solve problems involving multiplication and division using arrays, repeated addition, mental methods, and known facts
- [Arrays for multiplication (age 7+)](https://lightmysky.com/learn/mathematics/arrays-for-multiplication-age-7-mt_B1zj1RwQ3a): Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and 5 columns; write an equation to express the total as a sum of equal addends
- [Rows & Columns in Rectangles](https://lightmysky.com/learn/mathematics/rows-and-columns-in-rectangles-mt_UTnDKQkVX5): Partition a rectangle into rows and columns of same-size squares and count to find the total number of them
- [Times tables (age 7+)](https://lightmysky.com/learn/mathematics/times-tables-age-7-mt_wQ89AEXhz3): Recall and use multiplication and division facts for the 3, 4, and 8 multiplication tables
- [All times tables to 12×12](https://lightmysky.com/learn/mathematics/all-times-tables-to-12-12-mt_K5jM7vlVhA): Recall multiplication and division facts for multiplication tables up to 12 × 12
- [What Multiplication Means](https://lightmysky.com/learn/mathematics/what-multiplication-means-mt_gtTl3R5buH): Interpret products of whole numbers (e.g. 5 × 7 as the total number of objects in 5 groups of 7)
- [Properties of Operations](https://lightmysky.com/learn/mathematics/properties-of-operations-mt_Lb2ZnMdkYR): Apply properties of operations (commutative, associative, distributive) as strategies to multiply and divide
- [Factor Pairs & Commutativity](https://lightmysky.com/learn/mathematics/factor-pairs-and-commutativity-mt_nZkL5-XjRX): Recognise and use factor pairs and commutativity in mental calculations
- [Factors, multiples, and primes](https://lightmysky.com/learn/mathematics/factors-multiples-and-primes-mt_FHIAv6dfhU): Find all factor pairs for numbers to 100, list common factors and multiples, and tell whether a number is prime
- [Multiplicative Comparison as an Equation](https://lightmysky.com/learn/mathematics/multiplicative-comparison-as-an-equation-mt_U4cIBXVug4): Interpret a multiplication equation as a comparison (e.g. 35 = 5 × 7 means 35 is 5 times as many as 7); represent verbal statements of multiplicative comparisons as equations
- [Square and cube numbers](https://lightmysky.com/learn/mathematics/square-and-cube-numbers-mt_gxCIASSezX): Recognise and use square numbers and cube numbers, and the notation for squared (²) and cubed (³)
- [Factors, multiples, squares and cubes (age 9+)](https://lightmysky.com/learn/mathematics/factors-multiples-squares-and-cubes-age-9-mt_0Wg5F97osg): Solve problems involving multiplication and division using knowledge of factors, multiples, squares, and cubes
- [Reading ×, ÷, and = Symbols](https://lightmysky.com/learn/mathematics/reading-and-symbols-mt_zOWwLxa77y): Read, write, and interpret the symbols ×, ÷, and = in multiplication and division number sentences
- [What Division Means](https://lightmysky.com/learn/mathematics/what-division-means-mt_iNdrM2-oJf): Interpret whole-number quotients (e.g. 56 ÷ 8 as the number of objects in each share or the number of equal groups)
- [Division as Unknown Factor](https://lightmysky.com/learn/mathematics/division-as-unknown-factor-mt_GDG9_SZmsO): Understand division as an unknown-factor problem (e.g. find 32 ÷ 8 by finding the number that makes 32 when multiplied by 8)
- [Fluent multiplication and division facts](https://lightmysky.com/learn/mathematics/fluent-multiplication-and-division-facts-mt_WX30dzi4dt): Fluently multiply and divide within 100 using strategies such as the relationship between multiplication and division
- [Multiplication and Division Word Problems](https://lightmysky.com/learn/mathematics/multiplication-and-division-word-problems-mt_Zdv-b-iW5K): Use multiplication and division within 100 to solve word problems involving equal groups, arrays, and measurement quantities
- [Patterns in addition and multiplication tables](https://lightmysky.com/learn/mathematics/patterns-in-addition-and-multiplication-tables-mt_w6MxaaoMXZ): Identify arithmetic patterns (including patterns in the addition table or multiplication table) and explain them using properties of operations
- [Unknown in Multiplication & Division](https://lightmysky.com/learn/mathematics/unknown-in-multiplication-and-division-mt_xZvDCYA5Ae): Determine the unknown whole number in a multiplication or division equation relating three whole numbers (e.g. 8 × ? = 48, ? × 6 = 42)
- [Generating a pattern from a rule](https://lightmysky.com/learn/mathematics/generating-a-pattern-from-a-rule-mt_A-FyLLLLzy): Generate a number or shape pattern that follows a given rule; identify apparent features of the pattern not explicit in the rule and explain informally why they occur
- [Multiplicative Comparison Word Problems](https://lightmysky.com/learn/mathematics/multiplicative-comparison-word-problems-mt_6-j1NO2ZUH): Solve word problems involving multiplicative comparison using drawings and equations with a symbol for the unknown number
- [Scaling by fractions and simple rates](https://lightmysky.com/learn/mathematics/scaling-by-fractions-and-simple-rates-mt_ZOJ6EbdPOb): Solve problems involving scaling by simple fractions and problems involving simple rates
- [Short division](https://lightmysky.com/learn/mathematics/short-division-mt_MCu_SNg_OW): Divide numbers up to four digits by a one-digit number using short division (and place-value/array strategies); interpret remainders appropriately for the context
- [Prime numbers](https://lightmysky.com/learn/mathematics/prime-numbers-mt_y1XCVsIelg): Know and use the vocabulary of prime numbers, prime factors, and composite numbers; establish whether a number up to 100 is prime; recall prime numbers up to 19
- [Factors, multiples, and primes (age 11+)](https://lightmysky.com/learn/mathematics/factors-multiples-and-primes-age-11-mt_xhoOWnhtHq): Use the concepts and vocabulary of prime numbers, factors, multiples, common factors, common multiples, highest common factor (HCF), lowest common multiple (LCM), and prime factorisation including product notation and the unique factorisation property
- [Written Multiplication & Division](https://lightmysky.com/learn/mathematics/written-multiplication-and-division-mt_DyGBW3ZHh3): Write and calculate mathematical statements for multiplication and division using known tables, including two-digit × one-digit, using mental and progressing to formal written methods
- [Multi-Step Multiply & Divide](https://lightmysky.com/learn/mathematics/multi-step-multiply-and-divide-mt_EmR5n58jZt): Solve problems involving multiplication and division, including scaling problems and correspondence problems where n objects are connected to m objects
- [Multiplying by Tens](https://lightmysky.com/learn/mathematics/multiplying-by-tens-mt_isojCL9yy-): Multiply one-digit whole numbers by multiples of 10 in the range 10–90 using strategies based on place value and properties of operations
- [Written Multiplication](https://lightmysky.com/learn/mathematics/written-multiplication-mt_18fK9sQdIz): Multiply two-digit and three-digit numbers by a one-digit number using formal written layout
- [Multiply & Add Problems](https://lightmysky.com/learn/mathematics/multiply-and-add-problems-mt_AR-K72OIIO): Solve problems involving multiplying and adding, including using the distributive law, integer scaling problems, and harder correspondence problems
- [Long multiplication](https://lightmysky.com/learn/mathematics/long-multiplication-mt_q9EaJc2FP8): Multiply a whole number of up to four digits by a one-digit number, and multiply two two-digit numbers, using formal written methods including long multiplication; illustrate with area models
- [Multi-step word problems with remainders](https://lightmysky.com/learn/mathematics/multi-step-word-problems-with-remainders-mt_p-nbe0w_lf): Solve multi-step word problems using the four operations with whole numbers, including interpreting remainders in context; represent with equations using a letter for the unknown; check with estimation
- [Long multiplication (age 10+)](https://lightmysky.com/learn/mathematics/long-multiplication-age-10-mt_XLP1IM3Qbb): Fluently multiply multi-digit whole numbers (up to 4 digits by 2 digits) using the formal written method of long multiplication
- [Brackets in Expressions](https://lightmysky.com/learn/mathematics/brackets-in-expressions-mt_8jFSnXxqQD): Use parentheses, brackets, or braces in numerical expressions and evaluate expressions containing these grouping symbols
- [Division with remainders (age 10+)](https://lightmysky.com/learn/mathematics/division-with-remainders-age-10-mt_WsM4EmdOLe): Divide numbers up to 4 digits by a two-digit divisor using formal written long division, interpreting remainders as whole numbers, fractions, or by rounding as appropriate
- [Dividing by two-digit numbers](https://lightmysky.com/learn/mathematics/dividing-by-two-digit-numbers-mt_FvEq4heNBx): Divide numbers up to 4 digits by a two-digit number using formal written short division where appropriate, interpreting remainders according to context
- [Order of operations](https://lightmysky.com/learn/mathematics/order-of-operations-mt_jHgRQ4hR0g): Understand and apply the conventional order of operations (PEMDAS/BODMAS) to carry out calculations involving the four operations
- [Multi-step problems: choosing operations](https://lightmysky.com/learn/mathematics/multi-step-problems-choosing-operations-mt_RXnyhCRYXA): Solve problems using addition, subtraction, multiplication, and division. Choose the operation and method for each step, then solve multi-step problems in context.
- [Writing Number Sentences](https://lightmysky.com/learn/mathematics/writing-number-sentences-mt_4WaKWECpcv): Write simple numerical expressions that record calculations with numbers, and interpret numerical expressions without evaluating them (e.g. recognise that 3 × (18932 + 921) is three times as large as 18932 + 921)
- [Using inverse operations](https://lightmysky.com/learn/mathematics/using-inverse-operations-mt_VUQNveSYjQ): Recognise inverse relationships between operations and use them to check answers and simplify calculations.
- [Mental multiplication and division](https://lightmysky.com/learn/mathematics/mental-multiplication-and-division-mt_pjfmCMMPjO): Use place value, known and derived facts to multiply and divide mentally, including multiplying by 0 and 1, dividing by 1, and multiplying together three numbers
- [Mental multiplication and division (age 9+)](https://lightmysky.com/learn/mathematics/mental-multiplication-and-division-age-9-mt_8A3pZNOp7Z): Multiply and divide numbers mentally drawing upon known facts, including related facts and place-value adjustments
- [Multiplying and dividing by 10, 100, and 1000](https://lightmysky.com/learn/mathematics/multiplying-and-dividing-by-10-100-and-1000-mt_LlMl2PbaZe): Multiply and divide whole numbers and those involving decimals by 10, 100, and 1000
- [Mental calculation strategies](https://lightmysky.com/learn/mathematics/mental-calculation-strategies-mt_vmW2cb5c7A): Perform mental calculations including with mixed operations and large numbers, using strategies such as partitioning, compensation, and derived facts
- [Order of operations with powers and roots](https://lightmysky.com/learn/mathematics/order-of-operations-with-powers-and-roots-mt_X5cypSGoGU): Use conventional notation for the priority of operations including brackets, powers, roots, and reciprocals; apply BIDMAS/BODMAS consistently to evaluate complex numerical expressions
- [Sign Rules for Multiplication and Division](https://lightmysky.com/learn/mathematics/sign-rules-for-multiplication-and-division-mt_rxInpOQ74w): Multiply and divide with positive and negative integers and rational numbers, understanding the rules for the sign of the product or quotient
- [Multiplying and dividing (age 10+)](https://lightmysky.com/learn/mathematics/multiplying-and-dividing-age-10-mt_wPgpMJ0-PA): Multiply and divide numbers by 10, 100, and 1000 giving answers up to three decimal places, understanding that digits shift position in the place-value chart
- [Division with Decimals](https://lightmysky.com/learn/mathematics/division-with-decimals-mt_lU-2aTRB9f): Use written division methods in cases where the answer has up to two decimal places; divide decimals to hundredths by whole numbers
- [Multiplying decimals by whole numbers](https://lightmysky.com/learn/mathematics/multiplying-decimals-by-whole-numbers-mt_SoDP1fSQEB): Multiply one-digit numbers with up to two decimal places by whole numbers (e.g. 3.47 × 6)
- [Estimation to check answers to calculations](https://lightmysky.com/learn/mathematics/estimation-to-check-answers-to-calculations-mt_ilPrU0cbtT): Use estimation to check answers to calculations and determine, in the context of a problem, an appropriate degree of accuracy
- [Rounding Answers](https://lightmysky.com/learn/mathematics/rounding-answers-mt_QU5R7Aajy9): Solve problems which require answers to be rounded to specified degrees of accuracy