[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-207789-en":3,"doc-seo-207789-105":29,"detail-sidebar-cat-0-en-105":88},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":4,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":20,"language":21,"language_code":22,"site_id":23,"html_lang":22,"table_of_contents":24,"faqs":25,"seo_title":26,"seo_description":14,"update_tm":27,"read_time":28},207789,18829141979164,"Cart","https://eur-avatar.wpscdn.com/davatar_6f874abed73319feea01a86fa6f0fab8",4,"Exam","Formulæ - Writing and Substituting into Formulae","Learn how to define and distinguish algebraic expressions from formulas using the equals sign, then practice writing formulas to model relationships between variables. The guide explains substituting values into a formula to compute unknown quantities, including cases with negative values. It also teaches how to identify the subject of a formula and how to rearrange formulas by balancing and inverse operations, with worked examples for changing the subject on one or both sides and checking solutions.","FORMULAE  \nA formula is an algebraic rule that contains a mixture of letters, numbers and mathematical symbols . It uses the letters to represent values that can be changed (variables). A formula is different to an expression as it always contains the ‘=’ sign.  \nWriting a formula This is when we write a rule to describe the relationship between variables using letters instead of words.  \nE. g. Sioned is looking to change her mobile phone contract. The monthly cost is 4p a minute for calls plus £12 for unlimited texts and data plus vat at 5% . If m is the number of minutes used a month, write down the formula for the monthly cost C in terms of m.  \nCost = (£0 . 04 × the number of minutes + £12) × 1·05 C = (0·04 × m + 12) × 1·05  \nC = 1·05(0·04m + 12)  \nSubstituting into a formula This is when we replace the letters in a formula with numbers.  \nE. g.The monthly cost of a mobile phone contract is given by the formula C = 1·05(0·04m + 12) . If m is the number of minutes used a month, find C, the monthly cost, when 250 minutes are used.  \nC = 1·05(0·04m + 12) C = 1·05 × (0·04 × 250 + 12) C = 1·05 × (10 + 12)  \nC = £23.10  \nE. g. The formula to convert Fahrenheit (a) If F = 86, find C.  \nC =  \nC =  \nC =  \n 5  \n9  \n 5  \n9  \n 5  \n9  \n(F – 32)  \n(86 – 32)(54)  \nC = 30  \n(F) to Celsius ( C) is given by C =  (F – 32) .  \n(b) If F = –13, find C.  \nC =  (F – 32)  \nC = (–13 – 32)  \nC = (–45)  \nC = –25  \nThe subject of the formula In m = 3n –p, m is the subject of the formula. It’s the letter that is on its own on one side of the ’=’.  \nIn a = 2b + 3c, a is the subject of the formula. In 5r2 – t = s, s is the subject of the formula.  \nWe can change the subject of the formula by rearranging the formula using the balancing method and our knowledge of inverse operations.  \nTake care when substituting negative values, fractions or decimals into a formula.  \nChanging the subject of the formula when it only appears on one side  \nE. g. 1. Make b the subject of the formula a = 4b – 5  \na + 5 = 4b  \n= b or b =  \nRemember‘=’means equal to so both sides must balance at all times, so make sure you do exactly the same to both sides of the formula.  \nE. g. 3. Make r the subject of the formula V = πr²h  \n÷πh ÷πh  V πh = r²  \n√ √  \n V   \n√ πh = r  \nE. g 4. Make x the subject of the formula y = 5x + z  \n2 2  \n... ...  \ny² = 5x + z  \n–z –z  \ny² –z = 5x ÷5 ÷5  \n2    \ny z  \n= x 5  \nCheck that you:  \n• can use letters to represent unknows  \n• understand the basic rules of algebra for +,–, × and ÷  \n• can +,–, × and ÷ negative numbers, fractions and decimals • recognise expressions and equations  \n• can form an expression given some information  \n• know the inverse of an operation  \n• can solve linear equations e.g. 3x – 7 = 17  \n3x = 24  \nx = 8  \na + 5  \n4  \n+5 +5  \n÷4 ÷4  \na + 5  \n4  \nE. g 2. Make y the subject of the formula 2y + 3x = c  \n–3x –3x  \n2y = c – 3x  ÷2 ÷2   \ny = c – 3x 2  \nChanging the subject of the formula when it appears on both sides  \nWe need to make sure that the subject of the formula only appears on one side. It can’t appear on both.  \nE. g 1. Make a the subject of the formula 4(a + 5b) = 6c – 3a  \n4a + 20b = 6c – 3a  Expand the bracket.  \n +3a +3a   Collect the a terms on the one side ot the equation. 7a + 20b = 6c  \n –20b –20b  Collect everything else on the other side of the 7a = 6c – 20b equation.  \n ÷7 ÷7   \na =  \n6c – 20b  \n7  \nE. g 2. Make x the subject of the formula 6x + 7c = 4y – ax  \n6x + 7c = 4y – ax  \n+ax +ax  \n6x + ax + 7c = 4y  \n –7c –7c  6x + ax = 4y – 7cx(6 + a) = 4y – 7c  \n÷(6 + a) ÷(6 + a)  \nx = 4y – 7c  \n6 + a  \nCollect the x terms on the one side of the equation.  \nCollect everything else on the other side of the equation.  \n Factorise to isolate the x.   \n1 2","cbCairNmJnri5d1Q","https://ap.wps.com/l/cbCairNmJnri5d1Q","pdf",420686,1,"English","en",105,"# Writing a formula\n## Substituting into a formula\n# The subject of a formula\n## Changing the subject using inverse operations\n## Changing the subject when it appears on both sides\n# Checks and solving linear equations","[{\"question\":\"What makes a formula different from an expression?\",\"answer\":\"A formula always includes the '=' sign, while an expression does not necessarily. A formula states a relationship between variables.\"},{\"question\":\"How do you substitute into a formula to find a value?\",\"answer\":\"Replace the letters (variables) in the formula with the given numbers, then simplify step by step to compute the required result.\"},{\"question\":\"How can you change the subject of a formula?\",\"answer\":\"Rearrange the formula so the chosen letter is isolated on one side. Use balancing and inverse operations, applying the same actions to both sides throughout.\"}]","Formulæ - Writing and Substituting into Formulae | PDF",1788601146,3,{"code":4,"msg":30,"data":31},"ok",{"site_id":23,"language":22,"slug":32,"title":13,"keywords":33,"description":14,"schema_data":34,"social_meta":83,"head_meta":85,"extra_data":87,"updated_unix":27},"formulae-writing-and-substituting-into-formulae","",{"@graph":35,"@context":82},[36,51,65],{"@type":37,"itemListElement":38},"BreadcrumbList",[39,43,47,49],{"item":40,"name":41,"@type":42,"position":20},"https://docshare.wps.com","Home","ListItem",{"item":44,"name":45,"@type":42,"position":46},"https://docshare.wps.com/document/","Document",2,{"item":48,"name":12,"@type":42,"position":28},"https://docshare.wps.com/document/exam/",{"item":50,"name":13,"@type":42,"position":11},"https://docshare.wps.com/document/formulae-writing-and-substituting-into-formulae/207789/",{"url":50,"name":13,"@type":52,"author":53,"headline":13,"publisher":55,"fileFormat":58,"inLanguage":22,"description":14,"dateModified":59,"datePublished":59,"encodingFormat":58,"isAccessibleForFree":60,"interactionStatistic":61},"DigitalDocument",{"name":9,"@type":54},"Person",{"url":40,"name":56,"@type":57},"DocShare","Organization","application/pdf","2026-09-05",true,{"@type":62,"interactionType":63,"userInteractionCount":4},"InteractionCounter",{"@type":64},"ViewAction",{"@type":66,"mainEntity":67},"FAQPage",[68,74,78],{"name":69,"@type":70,"acceptedAnswer":71},"What makes a formula different from an expression?","Question",{"text":72,"@type":73},"A formula always includes the '=' sign, while an expression does not necessarily. A formula states a relationship between variables.","Answer",{"name":75,"@type":70,"acceptedAnswer":76},"How do you substitute into a formula to find a value?",{"text":77,"@type":73},"Replace the letters (variables) in the formula with the given numbers, then simplify step by step to compute the required result.",{"name":79,"@type":70,"acceptedAnswer":80},"How can you change the subject of a formula?",{"text":81,"@type":73},"Rearrange the formula so the chosen letter is isolated on one side. Use balancing and inverse operations, applying the same actions to both sides throughout.","https://schema.org",{"og:url":50,"og:type":84,"og:title":13,"og:site_name":56,"og:description":14},"article",{"robots":86,"canonical":50},"index,follow",{"doc_id":7,"site_id":23},{"code":4,"msg":5,"data":89},[90,94,98,101,106,111,116,121,126,129,133],{"id":20,"doc_module":4,"doc_module_name":45,"category_name":91,"show_sort_weight":92,"slug":93},"Story & Novel",90,"story-novel",{"id":46,"doc_module":4,"doc_module_name":45,"category_name":95,"show_sort_weight":96,"slug":97},"Literature",80,"literature",{"id":11,"doc_module":4,"doc_module_name":45,"category_name":12,"show_sort_weight":99,"slug":100},70,"exam",{"id":102,"doc_module":4,"doc_module_name":45,"category_name":103,"show_sort_weight":104,"slug":105},5,"Comic",60,"comic",{"id":107,"doc_module":4,"doc_module_name":45,"category_name":108,"show_sort_weight":109,"slug":110},6,"Technology",50,"technology",{"id":112,"doc_module":4,"doc_module_name":45,"category_name":113,"show_sort_weight":114,"slug":115},7,"Healthcare",40,"healthcare",{"id":117,"doc_module":4,"doc_module_name":45,"category_name":118,"show_sort_weight":119,"slug":120},8,"Research & Report",30,"research-report",{"id":122,"doc_module":4,"doc_module_name":45,"category_name":123,"show_sort_weight":124,"slug":125},9,"Religion & Spirituality",20,"religion-spirituality",{"id":124,"doc_module":4,"doc_module_name":45,"category_name":127,"show_sort_weight":124,"slug":128},"World Cup","world-cup",{"id":130,"doc_module":4,"doc_module_name":45,"category_name":131,"show_sort_weight":130,"slug":132},10,"Lifestyle","lifestyle",{"id":134,"doc_module":4,"doc_module_name":45,"category_name":135,"show_sort_weight":102,"slug":136},19,"General","general"]