these from smallest to largest:\n\n$$60\\% < 62\\% < 65\\% < 66.7\\% < 70\\%$$"},{"type":"text","order":4,"title":"Write the final answer","content":"Now, we write down the original numbers corresponding to our sorted percentages:\n\n$$\\frac{3}{5}, \\quad 0.62, \\quad 65\\%, \\quad \\frac{2}{3}, \\quad 0.7$$"}]},{"id":"c833cc77-d988-4962-973f-f840dc9dc09a:fractions","label":"Converting to Fractions","steps":[{"type":"text","order":0,"title":"Identify the goal","content":"To compare and order these numbers, we can convert all of them into fractions with a common denominator. This allows us to easily compare them by looking at their numerators.\n\nThe numbers to order are:\n\n$$65\\%, \\quad \\frac{3}{5}, \\quad 0.62, \\quad 0.7, \\quad \\frac{2}{3}$$"},{"type":"text","order":1,"title":"Convert to basic fractions","content":"First, let's write each percentage and decimal as a fraction:\n\n* **Percentage:** \n $$65\\% = \\frac{65}{100}$$\n\n* **Decimals:** \n $$0.62 = \\frac{62}{100}$$\n $$0.7 = \\frac{7}{10}$$\n\nNow, the list of numbers in fractional form is:\n\n$$\\frac{65}{100}, \\quad \\frac{3}{5}, \\quad \\frac{62}{100}, \\quad \\frac{7}{10}, \\quad \\frac{2}{3}$$"},{"type":"text","order":2,"title":"Find a common denominator","content":"Next, we find a common denominator for the denominators $100$, $5$, $10$, and $3$. \n\nThe lowest common multiple (LCM) of $100$, $5$, and $10$ is $100$. \n\nMultiplying this by $3$, we find that a convenient common denominator for all five fractions is **$300$**."},{"type":"hyper_latex","block":{"nodes":[{"latex":"$$$65\\% = \\frac{65 \\times 3}{100 \\times 3} = \\htmlData{anchor=val1}{\\frac{195}{300}}$$"},{"latex":"$$$\\frac{3}{5} = \\frac{3 \\times 60}{5 \\times 60} = \\htmlData{anchor=val2}{\\frac{180}{300}}$$"},{"latex":"$$$0.62 = \\frac{62 \\times 3}{100 \\times 3} = \\htmlData{anchor=val3}{\\frac{186}{300}}$$"},{"latex":"$$$0.7 = \\frac{7 \\times 30}{10 \\times 30} = \\htmlData{anchor=val4}{\\frac{210}{300}}$$"},{"latex":"$$$\\frac{2}{3} = \\frac{2 \\times 100}{3 \\times 100} = \\htmlData{anchor=val5}{\\frac{200}{300}}$$"}],"highlights":[{"color":"sky","style":"box","anchor":"val2"},{"color":"green","style":"box","anchor":"val3"},{"color":"amber","style":"box","anchor":"val1"},{"color":"purple","style":"box","anchor":"val5"},{"color":"pink","style":"box","anchor":"val4"}],"connections":null},"order":3,"title":"Convert each fraction","description":"Now, we convert each of our fractions to have a denominator of $300$ by multiplying the numerator and denominator by the same number."},{"type":"text","order":4,"title":"Compare and order","content":"Now we can compare the numerators to order the fractions from smallest to largest:\n\n$$180 < 186 < 195 < 200 < 210$$\n\nThis corresponds to:\n\n$$\\frac{180}{300} < \\frac{186}{300} < \\frac{195}{300} < \\frac{200}{300} < \\frac{210}{300}$$\n\nWriting these back in their original format gives the final correct order:\n\n$$\\frac{3}{5}, \\quad 0.62, \\quad 65\\%, \\quad \\frac{2}{3}, \\quad 0.7$$"}]}],"generatedAt":"2026-06-12T18:36:25.319Z","modelVersion":"gemini-3.5-flash","explanationVersion":"v2"},"firstAttemptFullMarks":{"percent":96},"walkthroughVideo":{"url":"https://assets.mathsgenie.co.uk/walkthroughs/videos/667e529e-d913-49f4-be39-cacff863f319.mp4","durationSeconds":66,"posterUrl":"https://assets.mathsgenie.co.uk/walkthroughs/videos/667e529e-d913-49f4-be39-cacff863f319.jpg"}}],"subjectCode":"gcse_maths__aqa","summaries":[{"id":"95918f15-191c-452e-8874-e489baf86c47","difficultyBand":"easy","calculatorUse":"non_calc","totalMarks":1},{"id":"0bd73670-44c0-4bfd-86e8-2e06098f9a07","difficultyBand":"medium","calculatorUse":"non_calc","totalMarks":2},{"id":"16fb65c5-965d-4e6c-9987-56daf65a67d1","difficultyBand":"easy","calculatorUse":"non_calc","totalMarks":1},{"id":"22e12be8-b849-46be-8d19-6dd0df7b88a1","difficultyBand":"easy","calculatorUse":"non_calc","totalMarks":1},{"id":"31a78172-a921-4404-9013-8c1b94be153b","difficultyBand":"easy","calculatorUse":"non_calc","totalMarks":1},{"id":"33654e5b-b812-4637-bac0-a909513fc73

Fractions, Decimals and Percentages

Question 7

Fractions, Decimals and Percentages Questions

Fractions, Decimals and Percentages

Question 7

Fractions, Decimals and Percentages Questions