3/5-(1-2/3)

{ "query": { "display": "$$\\frac{3}{5}-\\left(1-\\frac{2}{3}\\right)$$", "symbolab_question": "PEMDAS#\\frac{3}{5}-(1-\\frac{2}{3})" }, "solution": { "level": "PERFORMED", "subject": "Pre Algebra", "topic": "Order of Operations", "subTopic": "Other", "default": "\\frac{4}{15}", "meta": { "showVerify": true } }, "steps": { "type": "interim", "title": "$$\\frac{3}{5}-\\left(1-\\frac{2}{3}\\right)=\\frac{4}{15}$$", "input": "\\frac{3}{5}-\\left(1-\\frac{2}{3}\\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 $$\\left(1-\\frac{2}{3}\\right)\\::{\\quad}\\frac{1}{3}$$", "input": "1-\\frac{2}{3}", "steps": [ { "type": "interim", "title": "$$1-\\frac{2}{3}=\\frac{1}{3}$$", "input": "1-\\frac{2}{3}", "steps": [ { "type": "step", "primary": "Convert element to fraction: $$1=\\frac{1\\cdot\\:3}{3}$$", "result": "=\\frac{1\\cdot\\:3}{3}-\\frac{2}{3}" }, { "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\\:3-2}{3}" }, { "type": "interim", "title": "$$1\\cdot\\:3-2=1$$", "input": "1\\cdot\\:3-2", "steps": [ { "type": "step", "primary": "Multiply the numbers: $$1\\cdot\\:3=3$$", "result": "=3-2" }, { "type": "step", "primary": "Subtract the numbers: $$3-2=1$$", "result": "=1" } ], "meta": { "solvingClass": "Solver", "interimType": "Solver", "gptData": "pG0PljGlka7rWtIVHz2xymbOTBTIQkBEGSNjyYYsjjDErT97kX84sZPuiUzCW6s7bLmfsYnhV12jLF9lERqtHN6GQqufR6tr2vPxOUv7H++P6Ubiv/bIrpol3G9QIK7hP/n/sT8Hudl/0KJRqY9qeahzWhXCYn+CFW32cqz5EpE=" } }, { "type": "step", "result": "=\\frac{1}{3}" } ], "meta": { "solvingClass": "Solver", "interimType": "Solver", "gptData": "pG0PljGlka7rWtIVHz2xymbOTBTIQkBEGSNjyYYsjjDErT97kX84sZPuiUzCW6s7VEFtSaSQXtOZshklwyqvdACWKUbvV6WK3fDUgFtg3Q/ysS6ztOAKKFAEXmiY4WQmWTXpOhYUlDPxgL2OP+4y4ngY3ovothaT9gdWRHxLJgtrPF5b+sI736Uw559JNRE3lccQ6gC27EujtQnS6IoQKA==" } }, { "type": "step", "result": "=\\frac{1}{3}" } ], "meta": { "interimType": "Pemdas Parentheses Step Title 1Eq", "gptData": "pG0PljGlka7rWtIVHz2xymbOTBTIQkBEGSNjyYYsjjDErT97kX84sZPuiUzCW6s79Kg+idP5vLVrjUll6eMdYh1E9bl90IYms+j1J0wGO9E6pPjofsOQlOXLg3ASs77cDGa8CSXrxQm3ymKNWXEpELp/9TkwgwU1VexO++KUwznv9JmUy8OS1Ay8/T8YYrlrOD20Bsie/FWO/IDCy/uXx9Yz0cDRrlUfG7mtZFsbBhVKZwi/MOEiiRh/mdNlF9KxDISqKSldiwE5H/xwv5cEHzJjr4+1bD683CHVG+HnF+e3dDLyucqkwjNK9/tp3HU8cVS6tQsKhjWFP8zjPEG//g==" } }, { "type": "step", "result": "=\\frac{3}{5}-\\frac{1}{3}" }, { "type": "interim", "title": "Add and subtract (left to right) $$\\frac{3}{5}-\\frac{1}{3}\\::{\\quad}\\frac{4}{15}$$", "input": "\\frac{3}{5}-\\frac{1}{3}", "steps": [ { "type": "interim", "title": "$$\\frac{3}{5}-\\frac{1}{3}=\\frac{4}{15}$$", "input": "\\frac{3}{5}-\\frac{1}{3}", "result": "=\\frac{4}{15}", "steps": [ { "type": "interim", "title": "Least Common Multiplier of $$5,\\:3:{\\quad}15$$", "input": "5,\\:3", "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 $$5:{\\quad}5$$", "input": "5", "steps": [ { "type": "step", "primary": "$$5$$ is a prime number, therefore no factorization is possible", "result": "=5" } ], "meta": { "solvingClass": "Composite Integer", "interimType": "Prime Fac 1Eq", "gptData": "pG0PljGlka7rWtIVHz2xyoU2cWyPLDgE1QLLHeauuc3PHQdChPJ2JhfqHT+ZU0OMrfn8NOj0LUzuzje6xTyxRjl/dE9e0owjU0NK6lxSAv4/y9DKGIPglJ+qMi9xDu2KE1OovxZAaXg7BtrFPk4UcCzRnGgMN6CYRfod7Mq0dp3mWpvzkJh0pk9SzVPr3Sj8" } }, { "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": "step", "primary": "Multiply each factor the greatest number of times it occurs in either $$5$$ or $$3$$", "result": "=5\\cdot\\:3" }, { "type": "step", "primary": "Multiply the numbers: $$5\\cdot\\:3=15$$", "result": "=15" } ], "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 $$15$$" }, { "type": "step", "primary": "For $$\\frac{3}{5}:\\:$$multiply the denominator and numerator by $$3$$", "result": "\\frac{3}{5}=\\frac{3\\cdot\\:3}{5\\cdot\\:3}=\\frac{9}{15}" }, { "type": "step", "primary": "For $$\\frac{1}{3}:\\:$$multiply the denominator and numerator by $$5$$", "result": "\\frac{1}{3}=\\frac{1\\cdot\\:5}{3\\cdot\\:5}=\\frac{5}{15}" } ], "meta": { "interimType": "LCD Adjust Fractions 1Eq" } }, { "type": "step", "result": "=\\frac{9}{15}-\\frac{5}{15}" }, { "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{9-5}{15}" }, { "type": "step", "primary": "Subtract the numbers: $$9-5=4$$", "result": "=\\frac{4}{15}" } ], "meta": { "solvingClass": "Solver", "interimType": "Solver", "gptData": "pG0PljGlka7rWtIVHz2xymbOTBTIQkBEGSNjyYYsjjDErT97kX84sZPuiUzCW6s7id94rFlX4IhswKiIJ10Caa4gAwAjkiztFgB6YFNS/pDdd47a0hQ8flDbGsI5To1dKbeg3P2PwBv4YRQ7g4ohnTdlFq7wC9+MuzfsqUygoqNQ/TCF0auEuI0EL4WhFa83X+VgWnSeA4LiDqLGchrSqUaXLnBVFetqa9snQlqlfNI=" } } ], "meta": { "interimType": "Pemdas AddSub Step Title 1Eq" } }, { "type": "step", "result": "=\\frac{4}{15}" } ], "meta": { "solvingClass": "Pemdas", "practiceLink": "/practice/order-of-operations-whole-practice", "practiceTopic": "Order of Operations" } }, "meta": { "showVerify": true } }