2*(4/3-5/6)

{ "query": { "display": "$$2\\cdot\\:\\left(\\frac{4}{3}-\\frac{5}{6}\\right)$$", "symbolab_question": "PEMDAS#2\\cdot (\\frac{4}{3}-\\frac{5}{6})" }, "solution": { "level": "PERFORMED", "subject": "Pre Algebra", "topic": "Order of Operations", "subTopic": "Other", "default": "1", "meta": { "showVerify": true } }, "steps": { "type": "interim", "title": "$$2\\left(\\frac{4}{3}-\\frac{5}{6}\\right)=1$$", "input": "2\\left(\\frac{4}{3}-\\frac{5}{6}\\right)", "steps": [ { "type": "step", "primary": "Follow the PEMDAS order of operations", "meta": { "title": { "extension": "P-Parentheses<br/>E-Exponents<br/>M-Multiply<br/>D-Divide<br/>A-Add<br/>S-Subtract" } } }, { "type": "interim", "title": "Calculate within parentheses $$\\left(\\frac{4}{3}-\\frac{5}{6}\\right)\\::{\\quad}\\frac{1}{2}$$", "input": "\\frac{4}{3}-\\frac{5}{6}", "steps": [ { "type": "interim", "title": "$$\\frac{4}{3}-\\frac{5}{6}=\\frac{1}{2}$$", "input": "\\frac{4}{3}-\\frac{5}{6}", "steps": [ { "type": "interim", "title": "Least Common Multiplier of $$3,\\:6:{\\quad}6$$", "input": "3,\\:6", "steps": [ { "type": "definition", "title": "Least Common Multiplier (LCM)", "text": "The LCM of $$a,\\:b$$ is the smallest positive number that is divisible by both $$a$$ and $$b$$" }, { "type": "interim", "title": "Prime factorization of $$3:{\\quad}3$$", "input": "3", "steps": [ { "type": "step", "primary": "$$3$$ is a prime number, therefore no factorization is possible", "result": "=3" } ], "meta": { "solvingClass": "Composite Integer", "interimType": "Prime Fac 1Eq", "gptData": "pG0PljGlka7rWtIVHz2xyoU2cWyPLDgE1QLLHeauuc3PHQdChPJ2JhfqHT+ZU0OMrfn8NOj0LUzuzje6xTyxRlqnfsqoQ6VBiS8EyG3E6Oc/y9DKGIPglJ+qMi9xDu2KE1OovxZAaXg7BtrFPk4UcCzRnGgMN6CYRfod7Mq0dp39nbJbLYrlgLb4BA6ndvX8" } }, { "type": "interim", "title": "Prime factorization of $$6:{\\quad}2\\cdot\\:3$$", "input": "6", "steps": [ { "type": "step", "primary": "$$6\\:$$divides by $$2\\quad\\:6=3\\cdot\\:2$$", "result": "=2\\cdot\\:3" }, { "type": "step", "primary": "$$2,\\:3$$ are all prime numbers, therefore no further factorization is possible", "result": "=2\\cdot\\:3" } ], "meta": { "solvingClass": "Composite Integer", "interimType": "Prime Fac 1Eq", "gptData": "pG0PljGlka7rWtIVHz2xyoU2cWyPLDgE1QLLHeauuc3PHQdChPJ2JhfqHT+ZU0OMrfn8NOj0LUzuzje6xTyxRuUHkFwKrCGUG/pR2kioRow/y9DKGIPglJ+qMi9xDu2KE1OovxZAaXg7BtrFPk4UcCzRnGgMN6CYRfod7Mq0dp1AjXz67i9oO9i25G22wINi" } }, { "type": "step", "primary": "Multiply each factor the greatest number of times it occurs in either $$3$$ or $$6$$", "result": "=3\\cdot\\:2" }, { "type": "step", "primary": "Multiply the numbers: $$3\\cdot\\:2=6$$", "result": "=6" } ], "meta": { "solvingClass": "LCM", "interimType": "LCM Top 1Eq" } }, { "type": "interim", "title": "Adjust Fractions based on the LCM", "steps": [ { "type": "step", "primary": "Multiply each numerator by the same amount needed to multiply its<br/>corresponding denominator to turn it into the LCM $$6$$" }, { "type": "step", "primary": "For $$\\frac{4}{3}:\\:$$multiply the denominator and numerator by $$2$$", "result": "\\frac{4}{3}=\\frac{4\\cdot\\:2}{3\\cdot\\:2}=\\frac{8}{6}" } ], "meta": { "interimType": "LCD Adjust Fractions 1Eq" } }, { "type": "step", "result": "=\\frac{8}{6}-\\frac{5}{6}" }, { "type": "step", "primary": "Since the denominators are equal, combine the fractions: $$\\frac{a}{c}\\pm\\frac{b}{c}=\\frac{a\\pm\\:b}{c}$$", "result": "=\\frac{8-5}{6}" }, { "type": "step", "primary": "Subtract the numbers: $$8-5=3$$", "result": "=\\frac{3}{6}" }, { "type": "step", "primary": "Cancel the common factor: $$3$$", "result": "=\\frac{1}{2}" } ], "meta": { "solvingClass": "Solver", "interimType": "Solver", "gptData": "pG0PljGlka7rWtIVHz2xymbOTBTIQkBEGSNjyYYsjjDErT97kX84sZPuiUzCW6s7f2sZJkX/A2+g80at8DTE7ZAth8YtpxQi5i4gOD4gedXdd47a0hQ8flDbGsI5To1doDDfDl9rb93jWiqTfsVP2hUU/lo+nxKGmc+Xvlo3QeJKh84moeGJr4lOZIIfcbYVe6gSQaBqYADIe98St1UiSWejVEelOy0RMPolNByipPs=" } }, { "type": "step", "result": "=\\frac{1}{2}" } ], "meta": { "interimType": "Pemdas Parentheses Step Title 1Eq", "gptData": "pG0PljGlka7rWtIVHz2xymbOTBTIQkBEGSNjyYYsjjDErT97kX84sZPuiUzCW6s7huMSaDelSeb8bUf4Nv5R67Jehk5hcQzzx3PJAugOgikelBcMHthYvAWoX1Jx7yk++GJUCw9krdwl2yu17HEotbvjyl34qCSgNvx6C8iwh99eBETcAl6jnWzlRAsZu3muAKiHTFyNBLj89LR2q+0fEXiX35dQ/h01lIvxamZtt5OADx7c569Y528UxBqh5ySwgQUxJPyUNnGfVirkcwpVO9Wb/J40rqUtfCasBv2NG5hezH8Gf4mnFHD3U1BEbH6p081y3yoZR3kcuWRCt6vOOk6Kmigc0pSU+z/t+Cs1Blgkt3WiGR7ZaCaXvz77bMjS" } }, { "type": "step", "result": "=2\\cdot\\:\\frac{1}{2}" }, { "type": "interim", "title": "Multiply and divide (left to right) $$2\\cdot\\:\\frac{1}{2}\\::{\\quad}1$$", "input": "2\\cdot\\:\\frac{1}{2}", "steps": [ { "type": "step", "primary": "Convert element to fraction: $$2=\\frac{2}{1}$$", "result": "=\\frac{2}{1}\\cdot\\:\\frac{1}{2}" }, { "type": "step", "primary": "Cross-cancel common factor: $$2$$", "result": "=1" } ], "meta": { "interimType": "Pemdas MultDiv Step Title 1Eq", "gptData": "pG0PljGlka7rWtIVHz2xymbOTBTIQkBEGSNjyYYsjjDErT97kX84sZPuiUzCW6s73/dc2mBotrOifmjBNFY9yxS5AY53Ma6UkaloVMQObrA9i9oAvf9GdVXNbR3Y4Fbq1o2SXMcP01J2o+iGOwBer3Do2FgNKLDU3THyobcprxRLiySjiSuTfnpIKcTuE6YCSo6LfHuzz1h2O6lTNszydtGr4o+HuruyskgCRCM9ZF16pfF1z6umzUJTJvt+ojYZOffWeDwBZIM7aZgzu83VhIMjPP/F0NWuxu0jLNJ3TEojZx4SgSBRm9P/153+OLg491cn1uNGI5ofVw6zcRR9/A==" } }, { "type": "step", "result": "=1" } ], "meta": { "solvingClass": "Pemdas", "practiceLink": "/practice/order-of-operations-whole-practice", "practiceTopic": "Order of Operations" } }, "meta": { "showVerify": true } }