dectofrac 2.5

{ "query": { "display": "decimal to fraction $$2.5$$", "symbolab_question": "PRE_ALGEBRA#dectofrac 2.5" }, "solution": { "level": "PERFORMED", "subject": "Pre Algebra", "topic": "Decimals", "subTopic": "Decimals to Fraction", "default": "2\\frac{1}{2}", "meta": { "showVerify": true } }, "steps": { "type": "interim", "title": "Convert $$2.5$$ to a fraction:$${\\quad}2\\frac{1}{2}$$", "input": "2.5", "steps": [ { "type": "step", "primary": "Rewrite as", "result": "=2+0.5" }, { "type": "interim", "title": "Convert $$0.5$$ to a fraction:$${\\quad}\\frac{1}{2}$$", "input": "0.5", "steps": [ { "type": "step", "primary": "Multiply and divide by 10 for every number after the decimal point<br/>There is $$1$$ digit to the right of the decimal point, therefore multiply and divide by $$10$$", "result": "=\\frac{0.5\\cdot\\:10}{10}" }, { "type": "step", "result": "=\\frac{5}{10}" }, { "type": "interim", "title": "Reduce the fraction $$\\frac{5}{10}:{\\quad}\\frac{1}{2}$$", "input": "\\frac{5}{10}", "steps": [ { "type": "step", "primary": "Find a common factor of $$5$$ and $$10$$ in order to cancel it out " }, { "type": "interim", "title": "Greatest Common Divisor of $$5,\\:10:{\\quad}5$$", "input": "5,\\:10", "steps": [ { "type": "definition", "title": "Greatest Common Divisor (GCD)", "text": "The GCD of $$a,\\:b$$ is the largest positive number that divides both $$a$$ and $$b$$ without a remainder" }, { "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 $$10:{\\quad}2\\cdot\\:5$$", "input": "10", "steps": [ { "type": "step", "primary": "$$10\\:$$divides by $$2\\quad\\:10=5\\cdot\\:2$$", "result": "=2\\cdot\\:5" }, { "type": "step", "primary": "$$2,\\:5$$ are all prime numbers, therefore no further factorization is possible", "result": "=2\\cdot\\:5" } ], "meta": { "solvingClass": "Composite Integer", "interimType": "Prime Fac 1Eq", "gptData": "pG0PljGlka7rWtIVHz2xyoU2cWyPLDgE1QLLHeauuc3PHQdChPJ2JhfqHT+ZU0OMrfn8NOj0LUzuzje6xTyxRvTIRluRNPwUULD5JCqpmdzwPjJo8Fi+uo29zEltAtWEB4gitN/2ICkrV6ivfiR3BLFRzd4QlsM8ugKm4vxBIEBeUcq3/p8vCxgx1MIzcdLE" } }, { "type": "step", "primary": "The prime factors common to $$5,\\:10$$ are ", "result": "=5" } ], "meta": { "solvingClass": "GCD", "interimType": "GCD Top 1Eq" } }, { "type": "step", "primary": "Factor out $$5$$ from the numerator and the denominator<br/>$$5=5\\cdot\\:1,\\:{\\quad}10=5\\cdot\\:2$$", "result": "=\\frac{5\\cdot\\:1}{5\\cdot\\:2}" }, { "type": "step", "primary": "Cancel the common factor: $$5$$", "result": "=\\frac{1}{2}" } ], "meta": { "interimType": "Reduce Fraction 1Eq" } }, { "type": "step", "result": "=\\frac{1}{2}" } ], "meta": { "interimType": "Convert To Fraction 1Eq" } }, { "type": "step", "result": "=2+\\frac{1}{2}" }, { "type": "step", "result": "=2\\frac{1}{2}" } ], "meta": { "solvingClass": "decToFrac" } }, "meta": { "showVerify": true } }