1-1/2-1/4

{ "query": { "display": "$$1-\\frac{1}{2}-\\frac{1}{4}$$", "symbolab_question": "PEMDAS#1-\\frac{1}{2}-\\frac{1}{4}" }, "solution": { "level": "PERFORMED", "subject": "Pre Algebra", "topic": "Order of Operations", "subTopic": "Other", "default": "\\frac{1}{4}", "meta": { "showVerify": true } }, "steps": { "type": "interim", "title": "$$1-\\frac{1}{2}-\\frac{1}{4}=\\frac{1}{4}$$", "input": "1-\\frac{1}{2}-\\frac{1}{4}", "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": "step", "primary": "Add and subtract (left to right) " }, { "type": "interim", "title": "$$1-\\frac{1}{2}=\\frac{1}{2}$$", "input": "1-\\frac{1}{2}", "steps": [ { "type": "step", "primary": "Convert element to fraction: $$1=\\frac{1\\cdot\\:2}{2}$$", "result": "=\\frac{1\\cdot\\:2}{2}-\\frac{1}{2}" }, { "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{1\\cdot\\:2-1}{2}" }, { "type": "interim", "title": "$$1\\cdot\\:2-1=1$$", "input": "1\\cdot\\:2-1", "steps": [ { "type": "step", "primary": "Multiply the numbers: $$1\\cdot\\:2=2$$", "result": "=2-1" }, { "type": "step", "primary": "Subtract the numbers: $$2-1=1$$", "result": "=1" } ], "meta": { "solvingClass": "Solver", "interimType": "Solver", "gptData": "pG0PljGlka7rWtIVHz2xymbOTBTIQkBEGSNjyYYsjjDErT97kX84sZPuiUzCW6s7ZV4/pNEFJrYddVkM5e5CpN6GQqufR6tr2vPxOUv7H++P6Ubiv/bIrpol3G9QIK7hP/n/sT8Hudl/0KJRqY9qeRE27+eXjIuK5lxjSi/nI/o=" } }, { "type": "step", "result": "=\\frac{1}{2}" } ], "meta": { "solvingClass": "Solver", "interimType": "Solver", "gptData": "pG0PljGlka7rWtIVHz2xymbOTBTIQkBEGSNjyYYsjjDErT97kX84sZPuiUzCW6s7DEWtR7xIevgCu8jrSCPX+QCWKUbvV6WK3fDUgFtg3Q/ysS6ztOAKKFAEXmiY4WQm1m0btACmSMMJpLyKhwdwNngY3ovothaT9gdWRHxLJgukh5k4FZfAwUEBcKRsoWTbbqwnNL+vkns16SbvknXX+A==" } }, { "type": "step", "result": "=\\frac{1}{2}-\\frac{1}{4}" }, { "type": "interim", "title": "$$\\frac{1}{2}-\\frac{1}{4}=\\frac{1}{4}$$", "input": "\\frac{1}{2}-\\frac{1}{4}", "steps": [ { "type": "interim", "title": "Least Common Multiplier of $$2,\\:4:{\\quad}4$$", "input": "2,\\:4", "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 $$2:{\\quad}2$$", "input": "2", "steps": [ { "type": "step", "primary": "$$2$$ is a prime number, therefore no factorization is possible", "result": "=2" } ], "meta": { "solvingClass": "Composite Integer", "interimType": "Prime Fac 1Eq", "gptData": "pG0PljGlka7rWtIVHz2xyoU2cWyPLDgE1QLLHeauuc3PHQdChPJ2JhfqHT+ZU0OMrfn8NOj0LUzuzje6xTyxRl8ZboA8wPLg0yhI4RzfjFw/y9DKGIPglJ+qMi9xDu2KE1OovxZAaXg7BtrFPk4UcCzRnGgMN6CYRfod7Mq0dp1+G9v2aKasChgV65VW8cTW" } }, { "type": "interim", "title": "Prime factorization of $$4:{\\quad}2\\cdot\\:2$$", "input": "4", "steps": [ { "type": "step", "primary": "$$4\\:$$divides by $$2\\quad\\:4=2\\cdot\\:2$$", "result": "=2\\cdot\\:2" } ], "meta": { "solvingClass": "Composite Integer", "interimType": "Prime Fac 1Eq", "gptData": "pG0PljGlka7rWtIVHz2xyoU2cWyPLDgE1QLLHeauuc3PHQdChPJ2JhfqHT+ZU0OMrfn8NOj0LUzuzje6xTyxRsG/uC0ndYtZpJL4uAxK7FI/y9DKGIPglJ+qMi9xDu2KE1OovxZAaXg7BtrFPk4UcCzRnGgMN6CYRfod7Mq0dp39fF/zAtU5baHQ1hwgXA+n" } }, { "type": "step", "primary": "Multiply each factor the greatest number of times it occurs in either $$2$$ or $$4$$", "result": "=2\\cdot\\:2" }, { "type": "step", "primary": "Multiply the numbers: $$2\\cdot\\:2=4$$", "result": "=4" } ], "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 $$4$$" }, { "type": "step", "primary": "For $$\\frac{1}{2}:\\:$$multiply the denominator and numerator by $$2$$", "result": "\\frac{1}{2}=\\frac{1\\cdot\\:2}{2\\cdot\\:2}=\\frac{2}{4}" } ], "meta": { "interimType": "LCD Adjust Fractions 1Eq" } }, { "type": "step", "result": "=\\frac{2}{4}-\\frac{1}{4}" }, { "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{2-1}{4}" }, { "type": "step", "primary": "Subtract the numbers: $$2-1=1$$", "result": "=\\frac{1}{4}" } ], "meta": { "solvingClass": "Solver", "interimType": "Solver", "gptData": "pG0PljGlka7rWtIVHz2xymbOTBTIQkBEGSNjyYYsjjDErT97kX84sZPuiUzCW6s7bTKLDoXU8hhDfmkYXPEnR0lxhSu42ncd22u2brlC2Czdd47a0hQ8flDbGsI5To1doDDfDl9rb93jWiqTfsVP2lO1T0snFOPqKXL+S6MxVmlH89fIo5qKZTAKJnyTPcfF69lWy3F/WKEuIAOO5d95vigOLL29NH5pzxiXjQdK6Yk=" } }, { "type": "step", "result": "=\\frac{1}{4}" } ], "meta": { "solvingClass": "Pemdas", "practiceLink": "/practice/order-of-operations-whole-practice", "practiceTopic": "Order of Operations" } }, "meta": { "showVerify": true } }