{"id":36280,"date":"2026-03-25T15:00:18","date_gmt":"2026-03-25T08:00:18","guid":{"rendered":"https:\/\/times.edu.vn\/?p=36280"},"modified":"2026-05-08T15:51:51","modified_gmt":"2026-05-08T08:51:51","slug":"igcse-fractions-ratios-and-percentages","status":"publish","type":"post","link":"https:\/\/times.edu.vn\/en\/igcse\/igcse-fractions-ratios-and-percentages\/","title":{"rendered":"IGCSE Maths Fractions, Ratios &#038; Percentages: Foundation Topics A*"},"content":{"rendered":"<p><strong><a href=\"https:\/\/times.edu.vn\/en\/igcse\/what-is-igcse-a-comprehensive-guide-for-students\/\">IGCSE<\/a><\/strong><strong>\u00a0fractions, ratios, and percentages<\/strong>\u00a0focuses on mastering how to compare parts of a whole, share quantities in a ratio, and convert accurately between fractions, decimals, ratios, and percentages.<\/p>\n<p>You must handle numerator\u2013denominator operations, simplify to lowest terms, and use proportional reasoning (unitary method, cross-multiplication) to solve structured word problems.<\/p>\n<p>The highest-impact exam skills are reverse percentages using the multiplier method, and financial math such as percentage change, compound interest, and depreciation. Strong performance comes from choosing the correct representation quickly and showing clean working to secure method marks.<\/p>\n<h2><strong>Understanding IGCSE fractions, ratios, and percentages<\/strong><\/h2>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-36340\" src=\"https:\/\/times.edu.vn\/wp-content\/uploads\/2026\/03\/1-47.webp\" alt=\"IGCSE Fractions, Ratios, and Percentages: A Clear 2026 Guide to Master the Core Basics\" width=\"1000\" height=\"558\" srcset=\"https:\/\/times.edu.vn\/wp-content\/uploads\/2026\/03\/1-47.webp 1000w, https:\/\/times.edu.vn\/wp-content\/uploads\/2026\/03\/1-47-300x167.webp 300w, https:\/\/times.edu.vn\/wp-content\/uploads\/2026\/03\/1-47-768x429.webp 768w\" sizes=\"auto, (max-width: 1000px) 100vw, 1000px\" \/><\/p>\n<p>IGCSE fractions ratios percentages sit at the heart of <a href=\"https:\/\/times.edu.vn\/en\/igcse\/igcse-maths-0580\/\">Cambridge IGCSE Mathematics (0580)<\/a>\u00a0because they test how reliably you can move between forms\u00a0and how accurately you can reason about parts of a whole.<\/p>\n<p>Fractions formalise \u201chow much of something\u201d using the <strong>numerator<\/strong>\u00a0(the counted parts) over the <strong>denominator<\/strong>\u00a0(the total equal parts). Ratios compare quantities directly, and percentages express a fraction \u201cout of 100,\u201d which is why conversion fluency matters more than memorising isolated tricks.<\/p>\n<p>Based on our years of practical tutoring at Times Edu, students do not lose marks because the arithmetic is \u201chard.\u201d They lose marks because they choose the wrong representation, skip a simplification step, or misread what the question is asking for in the final line. If you fix representation and process, your accuracy rises quickly.<\/p>\n<h3><strong>What examiners are really checking<\/strong><\/h3>\n<p>In the IGCSE mark scheme, many questions are structured so that method marks reward a correct strategy even if the final number is off. Your goal is to show clean reasoning using <strong>equivalence<\/strong>, <strong>simplified form<\/strong>, and correct operations.<\/p>\n<p>A solution that uses <strong>cross-multiplication<\/strong>\u00a0or a clear <strong>unitary method<\/strong>\u00a0often earns method marks even when a minor arithmetic slip appears near the end.<\/p>\n<p>Common marking patterns you should expect:<\/p>\n<ul>\n<li><strong>1 <\/strong>M<strong>ark<\/strong>\u00a0for a correct conversion (fraction to percentage, ratio to fraction, recurring decimals to fraction).<\/li>\n<li><strong>1\u20132 <\/strong>M<strong>ethod marks<\/strong>\u00a0for a correct setup (forming an equation for reverse percentages, forming total parts in a ratio).<\/li>\n<li><strong>Final accuracy mark<\/strong>\u00a0for the correct final value and the required format.<\/li>\n<\/ul>\n<h3><strong>Common misconceptions that repeatedly cost marks<\/strong><\/h3>\n<p>These errors appear every exam season and are predictable:<\/p>\n<ul>\n<li>Treating a ratio like a fraction without checking the \u201ctotal parts.\u201d For 3:23:2, students write 3223\u200b when the question actually wants 3553\u200b of the total.<\/li>\n<li>Mixing up percentage change direction in <strong>financial math<\/strong>, especially depreciation. \u201cDepreciates by 12%\u201d means multiply by 0.880.88, not 1.121.12.<\/li>\n<li>Adding fractions by adding denominators. This signals weak denominator thinking: The <strong>denominator<\/strong>\u00a0is the unit size, not a number to combine.<\/li>\n<li>Dropping the recurring bar in <strong>recurring decimals<\/strong>\u00a0and rounding too early, then failing to state exact form.<\/li>\n<li>Overcomplicating proportional reasoning when a unitary method would be faster and safer.<\/li>\n<\/ul>\n<h3><strong>Skill map for high scores in IGCSE fractions ratios percentages<\/strong><\/h3>\n<p>You should train these five linked skills, not separate chapters:<\/p>\n<ul>\n<li><strong>Equivalence and simplified form:<\/strong>\u00a0Simplify fractions\/ratios early to reduce error.<\/li>\n<li><strong>Conversion control:<\/strong>\u00a0Move between fraction, decimal, ratio, and percentage without hesitation.<\/li>\n<li><strong>Proportional reasoning:<\/strong>\u00a0Understand scaling using multipliers and unit rates.<\/li>\n<li><strong>Arithmetic discipline:<\/strong>\u00a0Manage mixed numbers, improper fractions, and operations cleanly.<\/li>\n<li><strong>Financial math:<\/strong>\u00a0Apply multiplier method confidently for repeated percentage change.<\/li>\n<\/ul>\n<p><strong style=\"color: #f00;\">&gt;&gt;&gt; Read more:<\/strong> <a class=\"xem-them-link\" href=\"https:\/\/times.edu.vn\/en\/igcse\/igcse-maths-past-paper-strategy\/\">IGCSE Maths Past Paper Strategy for 2026: How to Practice Smarter and Raise Your Grade<\/a><\/p>\n<h2><strong>Converting between decimals, fractions, and percentages<\/strong><\/h2>\n<p>From our direct experience with international school curricula, conversion questions are where top students \u201cbank\u201d marks quickly. The exam rarely rewards complexity; it rewards precision and format control.<\/p>\n<h3><strong>A conversion framework you can apply to any question<\/strong><\/h3>\n<p>Use this order to minimize mistakes:<\/p>\n<ul>\n<li>Convert ratios to fractions by identifying <strong>total parts<\/strong>.<\/li>\n<li>Convert fractions to decimals by division if needed.<\/li>\n<li>Convert decimals to percentages by multiplying by 100.<\/li>\n<li>Keep exact values as fractions unless the question demands decimals.<\/li>\n<\/ul>\n<p>A critical detail most students overlook in the 2026 exam cycle is that many paper setters include \u201ctrap\u201d answer formats. They may accept a fraction but ask for a percentage, or they may expect an exact fraction rather than a rounded decimal. The final command word matters.<\/p>\n<h3><strong>Quick reference table: <\/strong><strong>W<\/strong><strong>hat to do, and when<\/strong><\/h3>\n<table>\n<tbody>\n<tr>\n<th colspan=\"1\" rowspan=\"1\"><strong>Form given<\/strong><\/th>\n<th colspan=\"1\" rowspan=\"1\"><strong>Form needed<\/strong><\/th>\n<th colspan=\"1\" rowspan=\"1\"><strong>Fastest method<\/strong><\/th>\n<th colspan=\"1\" rowspan=\"1\"><strong>Typical pitfall<\/strong><\/th>\n<\/tr>\n<tr>\n<td colspan=\"1\" rowspan=\"1\">Fraction abba\u200b<\/td>\n<td colspan=\"1\" rowspan=\"1\">Percentage<\/td>\n<td colspan=\"1\" rowspan=\"1\">ab\u00d7100%ba\u200b\u00d7100%<\/td>\n<td colspan=\"1\" rowspan=\"1\">Rounding too early<\/td>\n<\/tr>\n<tr>\n<td colspan=\"1\" rowspan=\"1\">Percentage p%p%<\/td>\n<td colspan=\"1\" rowspan=\"1\">Decimal<\/td>\n<td colspan=\"1\" rowspan=\"1\">p\/100p\/100<\/td>\n<td colspan=\"1\" rowspan=\"1\">Forgetting to divide by 100<\/td>\n<\/tr>\n<tr>\n<td colspan=\"1\" rowspan=\"1\">Ratio x:yx:y<\/td>\n<td colspan=\"1\" rowspan=\"1\">Fractions of total<\/td>\n<td colspan=\"1\" rowspan=\"1\">xx+y,yx+yx+yx\u200b,x+yy\u200b<\/td>\n<td colspan=\"1\" rowspan=\"1\">Using xyyx\u200b incorrectly<\/td>\n<\/tr>\n<tr>\n<td colspan=\"1\" rowspan=\"1\">Decimal (terminating)<\/td>\n<td colspan=\"1\" rowspan=\"1\">Fraction<\/td>\n<td colspan=\"1\" rowspan=\"1\">Write over power of 10 then simplify<\/td>\n<td colspan=\"1\" rowspan=\"1\">Not simplifying to lowest terms<\/td>\n<\/tr>\n<tr>\n<td colspan=\"1\" rowspan=\"1\">Recurring decimal<\/td>\n<td colspan=\"1\" rowspan=\"1\">Fraction<\/td>\n<td colspan=\"1\" rowspan=\"1\">Algebra method (see below)<\/td>\n<td colspan=\"1\" rowspan=\"1\">Using rounding instead of exact<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h3><strong>Recurring decimals to fractions (exact method)<\/strong><\/h3>\n<p>If x=0.3\u203ex=0.3, then:<\/p>\n<ul>\n<li>10X=3.3\u203e10x=3.3<\/li>\n<li>Subtract: 10x\u2212x=3.3\u203e\u22120.3\u203e10x\u2212x=3.3\u22120.3<\/li>\n<li>9X=39x=3 so x=13x=31\u200b<\/li>\n<\/ul>\n<p>For a two-digit repeat, x=0.27\u203ex=0.27:<\/p>\n<ul>\n<li>100X=27.27\u203e100x=27.27<\/li>\n<li>Subtract: 100x\u2212x=27100x\u2212x=27<\/li>\n<li>99X=2799x=27 so x=2799=311x=9927\u200b=113\u200b in simplified form.<\/li>\n<\/ul>\n<p>If there is a non-repeating part first, x=0.16\u203ex=0.16:<\/p>\n<ul>\n<li>Multiply to shift past the non-repeating digit: 10x=1.6\u203e10x=1.6<\/li>\n<li>Now remove the recurring: 100(10x)=1000x=166.6\u203e100(10x)=1000x=166.6<\/li>\n<li>Subtract: 1000x\u2212100x=166.6\u203e\u221216.6\u203e=1501000x\u2212100x=166.6\u221216.6=150<\/li>\n<li>900X=150900x=150 so x=150900=16x=900150\u200b=61\u200b<\/li>\n<\/ul>\n<p>This method is examiner-friendly because it shows clear arithmetic and equivalence reasoning.<\/p>\n<h3><strong>Fractions, mixed numbers, and improper fractions<\/strong><\/h3>\n<p>High-achievers treat mixed numbers as a format, not a separate topic. Convert to an improper fraction early:<\/p>\n<ul>\n<li>213=73231\u200b=37\u200b<\/li>\n<\/ul>\n<p>Then operate:<\/p>\n<ul>\n<li>Multiplication: 73\u00d735=7537\u200b\u00d753\u200b=57\u200b<\/li>\n<li>Division: 73\u00f735=73\u00d753=35937\u200b\u00f753\u200b=37\u200b\u00d735\u200b=935\u200b<\/li>\n<\/ul>\n<p>Avoid switching back to mixed numbers until the final line unless the question requests it.<\/p>\n<p><strong style=\"color: #f00;\">&gt;&gt;&gt; Read more:<\/strong> <a class=\"xem-them-link\" href=\"https:\/\/times.edu.vn\/en\/igcse\/igcse-maths-explain-questions\/\">IGCSE Maths \u201cExplain\u201d Questions 2026: What Examiners Want + How to Get Full Marks<\/a><\/p>\n<h2><strong>Solving reverse percentage problems<\/strong><\/h2>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-36342\" src=\"https:\/\/times.edu.vn\/wp-content\/uploads\/2026\/03\/2-49.webp\" alt=\"IGCSE Fractions, Ratios, and Percentages: A Clear 2026 Guide to Master the Core Basics\" width=\"1000\" height=\"558\" srcset=\"https:\/\/times.edu.vn\/wp-content\/uploads\/2026\/03\/2-49.webp 1000w, https:\/\/times.edu.vn\/wp-content\/uploads\/2026\/03\/2-49-300x167.webp 300w, https:\/\/times.edu.vn\/wp-content\/uploads\/2026\/03\/2-49-768x429.webp 768w\" sizes=\"auto, (max-width: 1000px) 100vw, 1000px\" \/><\/p>\n<p>Reverse percentages are a frequent discriminator topic because they test proportional reasoning, not just calculation. The correct mindset is: The final value is a percentage of the original, so the original is found by dividing by the right multiplier.<\/p>\n<h3><strong>Core principle: <\/strong><strong>M<\/strong><strong>ultiplier method<\/strong><\/h3>\n<p>If an amount increases by r%r%, the new value is:<\/p>\n<ul>\n<li>New=Original\u00d7(1+r\/100)New=Original\u00d7(1+r\/100)<\/li>\n<\/ul>\n<p>So:<\/p>\n<ul>\n<li>Original=New\u00f7(1+r\/100)Original=New\u00f7(1+r\/100)<\/li>\n<\/ul>\n<p>If an amount decreases by r%r%, the multiplier is:<\/p>\n<ul>\n<li>1\u2212R\/1001\u2212r\/100<\/li>\n<\/ul>\n<h3><strong>Worked exam-style examples<\/strong><\/h3>\n<p><strong>Example 1 (reverse increase): <\/strong>A jacket costs $72 after a 20% increase. Find the original price.<\/p>\n<ul>\n<li>Multiplier =1.20=1.20<\/li>\n<li>Original =72\u00f71.20=60=72\u00f71.20=60<\/li>\n<\/ul>\n<p><strong>Example 2 (reverse discount): <\/strong>A phone is sold for $425 after a 15% discount. Find the original price.<\/p>\n<ul>\n<li>Multiplier =0.85=0.85<\/li>\n<li>Original =425\u00f70.85=500=425\u00f70.85=500<\/li>\n<\/ul>\n<h3><strong>Table: <\/strong><strong>T<\/strong><strong>ypical reverse percentage prompts<\/strong><\/h3>\n<table>\n<tbody>\n<tr>\n<th colspan=\"1\" rowspan=\"1\"><strong>Wording in question<\/strong><\/th>\n<th colspan=\"1\" rowspan=\"1\"><strong>Operation needed<\/strong><\/th>\n<th colspan=\"1\" rowspan=\"1\"><strong>Multiplier<\/strong><\/th>\n<\/tr>\n<tr>\n<td colspan=\"1\" rowspan=\"1\">\u201cafter a 12% increase\u201d<\/td>\n<td colspan=\"1\" rowspan=\"1\">Divide to reverse<\/td>\n<td colspan=\"1\" rowspan=\"1\">1.121.12<\/td>\n<\/tr>\n<tr>\n<td colspan=\"1\" rowspan=\"1\">\u201cafter a 12% decrease\u201d<\/td>\n<td colspan=\"1\" rowspan=\"1\">Divide to reverse<\/td>\n<td colspan=\"1\" rowspan=\"1\">0.880.88<\/td>\n<\/tr>\n<tr>\n<td colspan=\"1\" rowspan=\"1\">\u201creduced to 70% of original\u201d<\/td>\n<td colspan=\"1\" rowspan=\"1\">Divide to reverse<\/td>\n<td colspan=\"1\" rowspan=\"1\">0.700.70<\/td>\n<\/tr>\n<tr>\n<td colspan=\"1\" rowspan=\"1\">\u201cis now 140% of original\u201d<\/td>\n<td colspan=\"1\" rowspan=\"1\">Divide to reverse<\/td>\n<td colspan=\"1\" rowspan=\"1\">1.401.40<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h3><strong>Common misconception: <\/strong><strong>R<\/strong><strong>eversing by subtracting<\/strong><\/h3>\n<p>Students often do \u201creverse\u201d by subtracting the percentage from the final number. That only works when the percentage is of the original, which is unknown. Reverse percentages are proportional, so division by the multiplier is the correct structure.<\/p>\n<h3><strong>Grade-boundary thinking: <\/strong><strong>W<\/strong><strong>hy this topic matters<\/strong><\/h3>\n<p>When grade boundaries tighten, the middle of the paper becomes more important than the hardest last question. Reverse percentage items frequently sit in that middle zone, and they are designed to be \u201cclean marks\u201d for prepared students. If you master the multiplier method and show working clearly, you pick up method marks consistently.<\/p>\n<h3><strong>Subject-choice implications for study abroad profiles<\/strong><\/h3>\n<p>From our direct experience advising international applicants, strong IGCSE Mathematics performance supports competitive progression into <a href=\"https:\/\/times.edu.vn\/en\/ib\/the-ultimate-ib-diploma-program-ibdp-guide\/\">IB<\/a>\u00a0AA, <a href=\"https:\/\/times.edu.vn\/en\/a-level\/what-is-a-level\/\">A-Level<\/a>\u00a0Mathematics, Economics, Business, and many STEM pathways.<\/p>\n<p>If your target is Economics, Business, or Engineering, reverse percentages and financial math competence often correlate with stronger performance later in compound interest, growth models, and ratio-based reasoning in data interpretation tasks.<\/p>\n<p><strong style=\"color: #f00;\">&gt;&gt;&gt; Read more:<\/strong> <a class=\"xem-them-link\" href=\"https:\/\/times.edu.vn\/en\/igcse\/igcse-maths-mistakes\/\">IGCSE Maths Mistakes 2026: The Most Common Errors and How to Stop Repeating Them<\/a><\/p>\n<h2><strong>Simplifying complex ratios and sharing quantities<\/strong><\/h2>\n<p>Ratios are not only about simplification; they are about structure. You must interpret what each \u201cpart\u201d represents, then apply proportional reasoning using either the <strong>unitary method<\/strong>\u00a0or a multiplier approach.<\/p>\n<h3><strong>Simplifying ratios correctly<\/strong><\/h3>\n<p>To simplify 18:2418:24:<\/p>\n<ul>\n<li>Divide both terms by the highest common factor, 6<\/li>\n<li>18:24=3:418:24=3:4<\/li>\n<\/ul>\n<p>For ratios with units, convert first:<\/p>\n<ul>\n<li>2.4 Kg:600 g2.4 kg:600 g<\/li>\n<li>Convert 2.4 kg=2400 g2.4 kg=2400 g<\/li>\n<li>2400:600=4:12400:600=4:1<\/li>\n<\/ul>\n<h3><strong>Sharing a quantity in a ratio<\/strong><\/h3>\n<p><strong>Example:<\/strong>\u00a0Share $360 in the ratio 2:3:42:3:4.<\/p>\n<ul>\n<li>Total parts =2+3+4=9=2+3+4=9<\/li>\n<li>One part =360\u00f79=40=360\u00f79=40<\/li>\n<li>Shares: 2\u22c540=802\u22c540=80, 3\u22c540=1203\u22c540=120, 4\u22c540=1604\u22c540=160<\/li>\n<\/ul>\n<p>This is the <strong>unitary method<\/strong>: Find 1 part, then scale.<\/p>\n<h3><strong>Ratios, fractions, and equivalence<\/strong><\/h3>\n<p>If the ratio of boys to girls is 3:53:5, the fraction of boys is:<\/p>\n<ul>\n<li>33+5=383+53\u200b=83\u200b<\/li>\n<\/ul>\n<p>The percentage of girls is:<\/p>\n<ul>\n<li>58\u00d7100%=62.5%85\u200b\u00d7100%=62.5%<\/li>\n<\/ul>\n<p>Students who write 3553\u200b here are confusing \u201cpart-to-part\u201d with \u201cpart-to-whole.\u201d That is a structural error, not an arithmetic one.<\/p>\n<h3><strong>Using cross-multiplication safely<\/strong><\/h3>\n<p>Cross-multiplication is efficient when comparing ratios or solving proportion equations:<\/p>\n<ul>\n<li>If ab=cdba\u200b=dc\u200b, then ad=bcad=bc<\/li>\n<\/ul>\n<p><strong>Example:<\/strong>\u00a0If x:12=5:8x:12=5:8, find xx.<\/p>\n<ul>\n<li>X12=5812x\u200b=85\u200b<\/li>\n<li>8X=608x=60<\/li>\n<li>X=7.5x=7.5<\/li>\n<\/ul>\n<p>Keep the equation in fraction form first. It reduces confusion and shows clean proportional reasoning to the examiner.<\/p>\n<h3><strong>Table: <\/strong><strong>C<\/strong><strong>hoosing the best method<\/strong><\/h3>\n<table>\n<tbody>\n<tr>\n<th colspan=\"1\" rowspan=\"1\"><strong>Task type<\/strong><\/th>\n<th colspan=\"1\" rowspan=\"1\"><strong>Best method<\/strong><\/th>\n<th colspan=\"1\" rowspan=\"1\"><strong>Why it works<\/strong><\/th>\n<\/tr>\n<tr>\n<td colspan=\"1\" rowspan=\"1\">Share a total in a ratio<\/td>\n<td colspan=\"1\" rowspan=\"1\">Unitary method<\/td>\n<td colspan=\"1\" rowspan=\"1\">Makes \u201cone part\u201d explicit<\/td>\n<\/tr>\n<tr>\n<td colspan=\"1\" rowspan=\"1\">Compare two ratios<\/td>\n<td colspan=\"1\" rowspan=\"1\">Cross-multiplication<\/td>\n<td colspan=\"1\" rowspan=\"1\">Avoids rounding errors<\/td>\n<\/tr>\n<tr>\n<td colspan=\"1\" rowspan=\"1\">Scale a recipe or map<\/td>\n<td colspan=\"1\" rowspan=\"1\">Multiplier method<\/td>\n<td colspan=\"1\" rowspan=\"1\">Direct proportional scaling<\/td>\n<\/tr>\n<tr>\n<td colspan=\"1\" rowspan=\"1\">Convert ratio to percent<\/td>\n<td colspan=\"1\" rowspan=\"1\">Convert to fraction of total<\/td>\n<td colspan=\"1\" rowspan=\"1\">Matches part-to-whole meaning<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><strong style=\"color: #f00;\">&gt;&gt;&gt; Read more:<\/strong> <a class=\"xem-them-link\" href=\"https:\/\/times.edu.vn\/en\/igcse\/top-common-igcse-maths-mistakes-to-avoid\/\">Top Common IGCSE Maths Mistakes to Avoid<\/a><\/p>\n<h2><strong>Compound interest and depreciation formulas<\/strong><\/h2>\n<p>IGCSE percentages often move into repeated change, and this is where students must treat percentages as multipliers, not add-ons. This is pure financial math and it is highly mark-efficient once understood.<\/p>\n<h3><strong>Compound interest (growth)<\/strong><\/h3>\n<p>If a value increases by r%r% each period for nn periods:<\/p>\n<ul>\n<li>Final=Initial\u00d7(1+r\/100)nFinal=Initial\u00d7(1+r\/100)n<\/li>\n<\/ul>\n<p><strong>Example:<\/strong>\u00a0$800 at 5% compound interest for 3 years:<\/p>\n<ul>\n<li>Final =800\u00d71.053=800\u00d71.053<\/li>\n<li>1.053=1.05\u00d71.05\u00d71.05=1.1576251.053=1.05\u00d71.05\u00d71.05=1.157625<\/li>\n<li>Final =800\u00d71.157625=926.1=800\u00d71.157625=926.1<\/li>\n<li>Depending on context, round to $926.10<\/li>\n<\/ul>\n<h3><strong>Depreciation (decay)<\/strong><\/h3>\n<p>If a value decreases by r%r% each period:<\/p>\n<ul>\n<li>Final=Initial\u00d7(1\u2212r\/100)nFinal=Initial\u00d7(1\u2212r\/100)n<\/li>\n<\/ul>\n<p><strong>Example:<\/strong>\u00a0A laptop worth $1200 depreciates by 20% per year for 2 years:<\/p>\n<ul>\n<li>Final =1200\u00d70.82=1200\u00d70.64=768=1200\u00d70.82=1200\u00d70.64=768<\/li>\n<\/ul>\n<h3><strong>Simple interest vs compound interest<\/strong><\/h3>\n<p>Simple interest adds interest on the original amount only:<\/p>\n<ul>\n<li>Final=P(1+rn)Final=P(1+rn) when rr is in decimal, nn in periods<\/li>\n<\/ul>\n<p>Compound interest grows on the updated amount each period:<\/p>\n<ul>\n<li>Final=P(1+r)nFinal=P(1+r)n<\/li>\n<\/ul>\n<h3><strong>Misconceptions to eliminate<\/strong><\/h3>\n<ul>\n<li>Applying P(1+rn)P(1+rn) to a compound problem. This produces an underestimate and is a conceptual mismatch.<\/li>\n<li>Adding percentages across years instead of multiplying by repeated multipliers. \u201c10% for 3 years\u201d is not \u201c30% total\u201d under compound growth.<\/li>\n<li>Rounding the multiplier too early, especially when nn is large. Keep full calculator precision until the final line.<\/li>\n<\/ul>\n<h3><strong>Exam technique: <\/strong><strong>S<\/strong><strong>how the structure<\/strong><\/h3>\n<p>Even if you use a calculator, you should write the formula line:<\/p>\n<ul>\n<li>V=800\u00d71.053V=800\u00d71.053<\/li>\n<\/ul>\n<p>That line often secures method marks, and it reduces the risk of \u201canswer-only\u201d loss when the examiner expects reasoning.<\/p>\n<p><strong style=\"color: #f00;\">&gt;&gt;&gt; Read more:<\/strong> <a class=\"xem-them-link\" href=\"https:\/\/times.edu.vn\/en\/igcse\/igcse-tutor\/\">IGCSE Tutor 2026: How to Choose the Right One<\/a><\/p>\n<h2><strong>Frequently Asked Questions<\/strong><\/h2>\n<div class=\"hoi-dap-thok-new low-faq\">\n<div class=\"thong-tin-dai\">\n<p class=\"tit-dai\"><strong>How do you calculate reverse percentages in IGCSE?<\/strong><\/p>\n<div class=\"chi-tiet-thong-tin\">Use the multiplier method. If the final value is after an increase of r%r%, divide by 1+r\/1001+r\/100; if after a decrease of r%r%, divide by 1\u2212r\/1001\u2212r\/100. Show one clear equation so the examiner can award method marks.<\/div>\n<\/div>\n<div class=\"thong-tin-dai\">\n<p class=\"tit-dai\"><strong>What is the difference between simple and compound interest?<\/strong><\/p>\n<div class=\"chi-tiet-thong-tin\">Simple interest is calculated only on the original principal each period, so growth is linear. Compound interest recalculates interest on the updated balance each period, so growth is exponential. In IGCSE financial math questions, the presence of \u201ceach year\u201d plus \u201cnew balance\u201d language typically signals compound interest.<\/div>\n<\/div>\n<div class=\"thong-tin-dai\">\n<p class=\"tit-dai\"><strong>How to simplify algebraic fractions?<\/strong><\/p>\n<div class=\"chi-tiet-thong-tin\">Factor numerator and denominator fully, then cancel common factors, keeping restrictions in mind. For example, x2\u22129&#215;2\u2212x\u22126=(x\u22123)(x+3)(x\u22123)(x+2)=x+3x+2&#215;2\u2212x\u22126&#215;2\u22129\u200b=(x\u22123)(x+2)(x\u22123)(x+3)\u200b=x+2x+3\u200b, with x\u22603x=3 and x\u2260\u22122x=\u22122. Always present the final expression in simplified form.<\/div>\n<\/div>\n<div class=\"thong-tin-dai\">\n<p class=\"tit-dai\"><strong>How do you divide a quantity in a given ratio?<\/strong><\/p>\n<div class=\"chi-tiet-thong-tin\">Add the ratio parts to get total parts, divide the total quantity by that number to get one part, then multiply back. This is the unitary method and it is the most reliable way to avoid part-to-whole errors.<\/div>\n<\/div>\n<div class=\"thong-tin-dai\">\n<p class=\"tit-dai\"><strong>How to convert recurring decimals to fractions?<\/strong><\/p>\n<div class=\"chi-tiet-thong-tin\">Let the recurring decimal equal xx, multiply by a power of 10 (or 100, 1000) to align the recurring digits, then subtract to eliminate the recurring part. Solve for xx and simplify. This produces an exact fraction and avoids rounding.<\/div>\n<\/div>\n<div class=\"thong-tin-dai\">\n<p class=\"tit-dai\"><strong>What are the rules for adding and subtracting fractions?<\/strong><\/p>\n<div class=\"chi-tiet-thong-tin\">Make denominators the same using a common denominator (often the LCM). Add or subtract the numerators, keep the denominator, and simplify to lowest terms. Treat denominators as unit sizes, not numbers to add together.<\/div>\n<\/div>\n<div class=\"thong-tin-dai\">\n<p class=\"tit-dai\"><strong>How to calculate percentage increase and decrease?<\/strong><\/p>\n<div class=\"chi-tiet-thong-tin\">Percentage change is differenceoriginal\u00d7100%originaldifference\u200b\u00d7100%. For fast calculation, use multipliers: Increase by r%r% means multiply by 1+r\/1001+r\/100; decrease by r%r% means multiply by 1\u2212r\/1001\u2212r\/100. In multi-step questions, multipliers are safer than repeated subtraction.<\/div>\n<\/div>\n<\/div>\n<h4>Conclusion<\/h4>\n<p>Based on our years of practical tutoring at <a href=\"https:\/\/times.edu.vn\/en\/\">Times Edu<\/a>, the pedagogical approach we recommend for high-achievers is to train representation + method selection\u00a0under time pressure, not to do endless mixed worksheets.<\/p>\n<p>A high-efficiency plan:<\/p>\n<ul>\n<li><strong>Week 1:<\/strong>\u00a0Fractions mastery (numerator\/denominator reasoning, mixed numbers, improper fractions, operations, simplified form).<\/li>\n<li><strong>Week 2:<\/strong>\u00a0Ratio skills (unitary method, cross-multiplication, equivalence, units conversion, sharing problems).<\/li>\n<li><strong>Week 3:<\/strong>\u00a0Percentages (percentage change, reverse percentages, financial math, compound interest and depreciation).<\/li>\n<li><strong>Week 4:<\/strong>\u00a0Mixed exam sets with strict format checking (fraction\/decimal\/percentage required format, rounding rules, method marks).<\/li>\n<\/ul>\n<p>If you want a personalized IGCSE fractions ratios percentages roadmap tied to your current grade, target grade, and study abroad subject pathway, Times Edu can map the exact topics that move your score fastest and train the exam habits that protect method marks.<\/p>\n<p>Share your latest mock paper or topic test results, and we\u2019ll recommend a targeted plan and tutor matching within the Cambridge IGCSE (0580) standard.<\/p>\n\n\n<div class=\"kk-star-ratings kksr-auto kksr-align-right kksr-valign-bottom\"\n    data-payload='{&quot;align&quot;:&quot;right&quot;,&quot;id&quot;:&quot;36280&quot;,&quot;slug&quot;:&quot;default&quot;,&quot;valign&quot;:&quot;bottom&quot;,&quot;ignore&quot;:&quot;&quot;,&quot;reference&quot;:&quot;auto&quot;,&quot;class&quot;:&quot;&quot;,&quot;count&quot;:&quot;1&quot;,&quot;legendonly&quot;:&quot;&quot;,&quot;readonly&quot;:&quot;&quot;,&quot;score&quot;:&quot;5&quot;,&quot;starsonly&quot;:&quot;&quot;,&quot;best&quot;:&quot;5&quot;,&quot;gap&quot;:&quot;5&quot;,&quot;greet&quot;:&quot;\u0110\u00e1nh gi\u00e1 b\u00e0i vi\u1ebft&quot;,&quot;legend&quot;:&quot;5\\\/5 - (1 vote)&quot;,&quot;size&quot;:&quot;24&quot;,&quot;title&quot;:&quot;IGCSE Maths Fractions, Ratios \\u0026amp; Percentages: Foundation Topics A*&quot;,&quot;width&quot;:&quot;142.5&quot;,&quot;_legend&quot;:&quot;{score}\\\/{best} - ({count} {votes})&quot;,&quot;font_factor&quot;:&quot;1.25&quot;}'>\n            \n<div class=\"kksr-stars\">\n    \n<div class=\"kksr-stars-inactive\">\n            <div class=\"kksr-star\" data-star=\"1\" style=\"padding-right: 5px\">\n            \n\n<div class=\"kksr-icon\" style=\"width: 24px; height: 24px;\"><\/div>\n        <\/div>\n            <div class=\"kksr-star\" data-star=\"2\" style=\"padding-right: 5px\">\n            \n\n<div class=\"kksr-icon\" style=\"width: 24px; height: 24px;\"><\/div>\n        <\/div>\n            <div class=\"kksr-star\" data-star=\"3\" style=\"padding-right: 5px\">\n            \n\n<div class=\"kksr-icon\" style=\"width: 24px; height: 24px;\"><\/div>\n        <\/div>\n            <div class=\"kksr-star\" data-star=\"4\" style=\"padding-right: 5px\">\n            \n\n<div class=\"kksr-icon\" style=\"width: 24px; height: 24px;\"><\/div>\n        <\/div>\n            <div class=\"kksr-star\" data-star=\"5\" style=\"padding-right: 5px\">\n            \n\n<div class=\"kksr-icon\" style=\"width: 24px; height: 24px;\"><\/div>\n        <\/div>\n    <\/div>\n    \n<div class=\"kksr-stars-active\" style=\"width: 142.5px;\">\n            <div class=\"kksr-star\" style=\"padding-right: 5px\">\n            \n\n<div class=\"kksr-icon\" style=\"width: 24px; height: 24px;\"><\/div>\n        <\/div>\n            <div class=\"kksr-star\" style=\"padding-right: 5px\">\n            \n\n<div class=\"kksr-icon\" style=\"width: 24px; height: 24px;\"><\/div>\n        <\/div>\n            <div class=\"kksr-star\" style=\"padding-right: 5px\">\n            \n\n<div class=\"kksr-icon\" style=\"width: 24px; height: 24px;\"><\/div>\n        <\/div>\n            <div class=\"kksr-star\" style=\"padding-right: 5px\">\n            \n\n<div class=\"kksr-icon\" style=\"width: 24px; height: 24px;\"><\/div>\n        <\/div>\n            <div class=\"kksr-star\" style=\"padding-right: 5px\">\n            \n\n<div class=\"kksr-icon\" style=\"width: 24px; height: 24px;\"><\/div>\n        <\/div>\n    <\/div>\n<\/div>\n                \n\n<div class=\"kksr-legend\" style=\"font-size: 19.2px;\">\n            5\/5 - (1 vote)    <\/div>\n    <\/div>\n","protected":false},"excerpt":{"rendered":"<p>IGCSE\u00a0fractions, ratios, and percentages\u00a0focuses on mastering how to compare parts of a whole, share quantities in a ratio, and convert accurately between fractions, decimals, ratios, and percentages. You must handle numerator\u2013denominator operations, simplify to lowest terms, and use proportional reasoning (unitary method, cross-multiplication) to solve structured word problems. The highest-impact exam skills are reverse percentages &#8230; <a title=\"IGCSE Maths Fractions, Ratios &#038; Percentages: Foundation Topics A*\" class=\"read-more\" href=\"https:\/\/times.edu.vn\/en\/igcse\/igcse-fractions-ratios-and-percentages\/\" aria-label=\"Read more about IGCSE Maths Fractions, Ratios &#038; Percentages: Foundation Topics A*\">Read more<\/a><\/p>\n","protected":false},"author":7,"featured_media":36281,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"content-type":"","rank_math_title":"","rank_math_description":"Master IGCSE Maths fractions, ratios & percentages \u2014 the foundation for all Paper 4 problems. 8-step framework + worked examples on conversions, increase\/decrease, sharing.","footnotes":""},"categories":[166],"tags":[],"class_list":["post-36280","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-igcse"],"_links":{"self":[{"href":"https:\/\/times.edu.vn\/en\/wp-json\/wp\/v2\/posts\/36280","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/times.edu.vn\/en\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/times.edu.vn\/en\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/times.edu.vn\/en\/wp-json\/wp\/v2\/users\/7"}],"replies":[{"embeddable":true,"href":"https:\/\/times.edu.vn\/en\/wp-json\/wp\/v2\/comments?post=36280"}],"version-history":[{"count":6,"href":"https:\/\/times.edu.vn\/en\/wp-json\/wp\/v2\/posts\/36280\/revisions"}],"predecessor-version":[{"id":39572,"href":"https:\/\/times.edu.vn\/en\/wp-json\/wp\/v2\/posts\/36280\/revisions\/39572"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/times.edu.vn\/en\/wp-json\/wp\/v2\/media\/36281"}],"wp:attachment":[{"href":"https:\/\/times.edu.vn\/en\/wp-json\/wp\/v2\/media?parent=36280"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/times.edu.vn\/en\/wp-json\/wp\/v2\/categories?post=36280"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/times.edu.vn\/en\/wp-json\/wp\/v2\/tags?post=36280"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}