(7/3+1/2 \div 3)+6

{ "query": { "display": "$$\\left(\\frac{7}{3}+\\frac{1}{2}\\div\\:3\\right)+6$$", "symbolab_question": "PEMDAS#(\\frac{7}{3}+\\frac{1}{2}\\div 3)+6" }, "solution": { "level": "PERFORMED", "subject": "Pre Algebra", "topic": "Order of Operations", "subTopic": "Other", "default": "8\\frac{1}{2}", "meta": { "showVerify": true } }, "steps": { "type": "interim", "title": "$$\\left(\\frac{7}{3}+\\frac{1}{2}\\div\\:3\\right)+6=8\\frac{1}{2}$$", "input": "\\left(\\frac{7}{3}+\\frac{1}{2}\\div\\:3\\right)+6", "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 $$\\left(\\frac{7}{3}+\\frac{1}{2}\\div\\:3\\right)\\::{\\quad}\\frac{5}{2}$$", "input": "\\frac{7}{3}+\\frac{1}{2}\\div\\:3", "steps": [ { "type": "interim", "title": "Multiply and divide (left to right) $$\\frac{1}{2}\\div\\:3\\::{\\quad}\\frac{1}{6}$$", "input": "\\frac{1}{2}\\div\\:3", "steps": [ { "type": "step", "primary": "Convert element to fraction: $$3=\\frac{3}{1}$$", "result": "=\\frac{1}{2}\\div\\:\\frac{3}{1}" }, { "type": "step", "primary": "Apply the fraction rule: $$\\frac{a}{b}\\div\\frac{c}{d}=\\frac{a}{b}\\times\\frac{d}{c}$$", "result": "=\\frac{1}{2}\\cdot\\:\\frac{1}{3}" }, { "type": "step", "primary": "Multiply fractions: $$\\frac{a}{b}\\cdot\\frac{c}{d}=\\frac{a\\:\\cdot\\:c}{b\\:\\cdot\\:d}$$", "result": "=\\frac{1\\cdot\\:1}{2\\cdot\\:3}" }, { "type": "step", "primary": "Multiply the numbers: $$1\\cdot\\:1=1$$", "result": "=\\frac{1}{2\\cdot\\:3}" }, { "type": "step", "primary": "Multiply the numbers: $$2\\cdot\\:3=6$$", "result": "=\\frac{1}{6}" } ], "meta": { "interimType": "Pemdas MultDiv Step Title 1Eq", "gptData": "pG0PljGlka7rWtIVHz2xymbOTBTIQkBEGSNjyYYsjjDErT97kX84sZPuiUzCW6s79Kg+idP5vLVrjUll6eMdYtKpTf+/QbeCzZiYbI+QmNXolA9Pg+RElWf+NNICVTRK5f47gxYZ2pPMMA78zz9LT5HHUW+62CFsaYJjUiZROsjPqpGpOIfuupUKCw8Hn7hAc/eqAjZ4KrrC05PYrASKPKahD6vvdbp8uJrNE9gjI4XcFTxg6QCrTB1yVDCOiPMeo3oe/oyhMy2+1TQhDBd2f60ISZzDcJTIRwqEQb3IwO2zKbkZBc+SjKz4XmmUhtFnAkyMUr2WoZ0RU8v7EBVepVaJDVyPTg+XK7loR9BrvbmwiNrEngO+NNvZ9sqNu+2V" } }, { "type": "step", "result": "=\\frac{7}{3}+\\frac{1}{6}" }, { "type": "interim", "title": "Add and subtract (left to right) $$\\frac{7}{3}+\\frac{1}{6}\\::{\\quad}\\frac{5}{2}$$", "input": "\\frac{7}{3}+\\frac{1}{6}", "steps": [ { "type": "interim", "title": "$$\\frac{7}{3}+\\frac{1}{6}=\\frac{5}{2}$$", "input": "\\frac{7}{3}+\\frac{1}{6}", "result": "=\\frac{5}{2}", "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 $$\\frac{7}{3}:\\:$$multiply the denominator and numerator by $$2$$", "result": "\\frac{7}{3}=\\frac{7\\cdot\\:2}{3\\cdot\\:2}=\\frac{14}{6}" } ], "meta": { "interimType": "LCD Adjust Fractions 1Eq" } }, { "type": "step", "result": "=\\frac{14}{6}+\\frac{1}{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{14+1}{6}" }, { "type": "step", "primary": "Add the numbers: $$14+1=15$$", "result": "=\\frac{15}{6}" }, { "type": "step", "primary": "Cancel the common factor: $$3$$", "result": "=\\frac{5}{2}" } ], "meta": { "solvingClass": "Solver", "interimType": "Solver", "gptData": "pG0PljGlka7rWtIVHz2xymbOTBTIQkBEGSNjyYYsjjDErT97kX84sZPuiUzCW6s7Rc++H2Lclp1qFPE6Q6KSMbXBrTm8Pzewt3GUAGaMaKXdd47a0hQ8flDbGsI5To1dYDPq1Ru8svsR9Rij2+7AABUU/lo+nxKGmc+Xvlo3QeIr1rouySJ2YSRpUl+icLdaoMti06dJX6cHtePlYI4dfrHVLNBl8xumXA/lczVPMsU=" } } ], "meta": { "interimType": "Pemdas AddSub Step Title 1Eq" } }, { "type": "step", "result": "=\\frac{5}{2}" } ], "meta": { "interimType": "Pemdas Parentheses Step Title 1Eq", "gptData": "pG0PljGlka7rWtIVHz2xymbOTBTIQkBEGSNjyYYsjjDErT97kX84sZPuiUzCW6s7PYIowdXt2t1vjFLpvo+g6C29phFEFSeEt+NOlpAd3Px0lUe3NPGVHBUAS+030T5HcBi7b38Ql3VpY8X+Y0rYCWVZIhzvL4w8nPTfMjKbNG8V/Nte9cn1BgJbS5BIPRheobPyLFAzhpYHQp9fWxHejVBqj6xU8uFdiArjbgibsaIgHP4YqWkh5OOHaSrQ/l8R+eIZu8ytA7w82fBOZW8u5vC30sSftAIFS6Qkpy19Ikq9qz+geQ7BUGC6UMUea5zT+3pnp57Bw1ApQ3uiYpVaCCcDgBPIEdBcLB6B0uqH2/5z96oCNngqusLTk9isBIo8uEAoKzUcoUqc6BkNG0slrw==" } }, { "type": "step", "result": "=\\frac{5}{2}+6" }, { "type": "interim", "title": "Add and subtract (left to right) $$\\frac{5}{2}+6\\::{\\quad}\\frac{17}{2}$$", "input": "\\frac{5}{2}+6", "steps": [ { "type": "interim", "title": "$$\\frac{5}{2}+6=\\frac{17}{2}$$", "input": "\\frac{5}{2}+6", "result": "=\\frac{17}{2}", "steps": [ { "type": "step", "primary": "Convert element to fraction: $$6=\\frac{6\\cdot\\:2}{2}$$", "result": "=\\frac{6\\cdot\\:2}{2}+\\frac{5}{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{6\\cdot\\:2+5}{2}" }, { "type": "interim", "title": "$$6\\cdot\\:2+5=17$$", "input": "6\\cdot\\:2+5", "steps": [ { "type": "step", "primary": "Multiply the numbers: $$6\\cdot\\:2=12$$", "result": "=12+5" }, { "type": "step", "primary": "Add the numbers: $$12+5=17$$", "result": "=17" } ], "meta": { "solvingClass": "Solver", "interimType": "Solver", "gptData": "pG0PljGlka7rWtIVHz2xymbOTBTIQkBEGSNjyYYsjjDErT97kX84sZPuiUzCW6s7hXOQluxvKwY90ouPTkaIYt6GQqufR6tr2vPxOUv7H+/wtXnAQBZdyITGiT4+kdRJyn3U44f2hLwHmnaEOl/a4syKk2ninfwO4yTH6QoNElo=" } }, { "type": "step", "result": "=\\frac{17}{2}" } ], "meta": { "solvingClass": "Solver", "interimType": "Solver", "gptData": "pG0PljGlka7rWtIVHz2xymbOTBTIQkBEGSNjyYYsjjDErT97kX84sZPuiUzCW6s7lfWgWBOoy2LEuEGoS5409ACWKUbvV6WK3fDUgFtg3Q/ysS6ztOAKKFAEXmiY4WQmQgHvU1p3tTfoU+d8m/W6E81bIZxfodm3UsZcfZAZr4ucsOMuz+ZEQ5fUx9LmVaymAKhXt4fwZWdb8EC1UKLM2g==" } } ], "meta": { "interimType": "Pemdas AddSub Step Title 1Eq" } }, { "type": "step", "result": "=\\frac{17}{2}" }, { "type": "interim", "title": "Convert improper fractions to mixed numbers:$${\\quad}\\frac{17}{2}=8\\frac{1}{2}$$", "steps": [ { "type": "interim", "title": "$$\\frac{17}{2}=8\\quad\\:$$Remainder$$\\quad\\:1$$", "input": "\\frac{17}{2}", "steps": [ { "type": "step", "primary": "Write the problem in long division format", "result": "\\begin{matrix}2\\overline{|\\kern0.1em17}\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\end{matrix}" }, { "type": "interim", "title": "Divide $$17\\:$$by $$2\\:$$to get $$8$$", "input": "\\:", "result": "\\begin{array}{l}\\:\\:\\:\\:\\:\\:8\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\\\2\\overline{|\\kern0.1em17}\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\\\\\:\\:\\:\\:\\underline{16}\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\\\\\:\\:\\:\\:\\:\\:1\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\end{array}", "steps": [ { "type": "step", "primary": "Divide $$17\\:$$by $$2\\:$$to get $$8$$", "result": "\\begin{array}{l}\\:\\:\\:\\:\\:\\:8\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\\\2\\overline{|\\kern0.1em17}\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\end{array}" }, { "type": "step", "primary": "Multiply the quotient digit $$\\left(8\\right)\\:$$by the divisor $$2$$", "result": "\\begin{array}{l}\\:\\:\\:\\:\\:\\:8\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\\\2\\overline{|\\kern0.1em17}\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\\\\\:\\:\\:\\:\\underline{16}\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\end{array}" }, { "type": "step", "primary": "Subtract $$16\\:$$from $$17$$", "result": "\\begin{array}{l}\\:\\:\\:\\:\\:\\:8\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\\\2\\overline{|\\kern0.1em17}\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\\\\\:\\:\\:\\:\\underline{16}\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\\\\\:\\:\\:\\:\\:\\:1\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\end{array}" } ], "meta": { "interimType": "Long Division Divide 3Eq", "gptData": "pG0PljGlka7rWtIVHz2xymbOTBTIQkBEGSNjyYYsjjAuRbUqF0v2PpVuPGQH4dLbLeu+MH3/4O31zRKyMpNuXtAM4L+5fXXw9GSOcy6r170IfS3eMwojOQOGbYhlsYiaJhhOUJ4+b0sozmBJodb1hZEQlrQ67quu86RDujFLtS4MFqKw/8t9EClN8IIY1ne3pYjhLyI4O9fRUicEgQufHB3Z7lLRz+FS/MwAm7CZoks=" } }, { "type": "step", "primary": "The solution for Long Division of $$\\frac{17}{2}\\:$$is $$8\\:$$with remainder of $$1$$", "result": "8\\quad\\:\\mathrm{Remainder}\\quad\\:1" } ], "meta": { "solvingClass": "StepsLongDivisionDecimals", "interimType": "StepsLongDivisionDecimals" } }, { "type": "step", "primary": "Convert to mixed number: Quotient$$\\frac{\\mathrm{Remainder}}{\\mathrm{Divisor}}$$", "secondary": [ "$$\\frac{17}{2}=8\\frac{1}{2}$$" ] }, { "type": "step", "result": "=8\\frac{1}{2}" } ], "meta": { "solvingClass": "MixedNumbers", "interimType": "Convert to Mixed Numbers Top 0Eq" } }, { "type": "step", "result": "=8\\frac{1}{2}" } ], "meta": { "solvingClass": "Pemdas", "practiceLink": "/practice/order-of-operations-whole-practice", "practiceTopic": "Order of Operations" } }, "meta": { "showVerify": true } }