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

{ "query": { "display": "$$\\left(3+\\frac{1}{2}\\right)\\div\\:3\\frac{1}{2}$$", "symbolab_question": "PEMDAS#(3+\\frac{1}{2})\\div 3\\frac{1}{2}" }, "solution": { "level": "PERFORMED", "subject": "Pre Algebra", "topic": "Order of Operations", "subTopic": "Other", "default": "1", "meta": { "showVerify": true } }, "steps": { "type": "interim", "title": "$$\\left(3+\\frac{1}{2}\\right)\\div\\:3\\frac{1}{2}=1$$", "input": "\\left(3+\\frac{1}{2}\\right)\\div\\:3\\frac{1}{2}", "steps": [ { "type": "interim", "title": "Convert mixed numbers to improper fractions:$${\\quad}3\\frac{1}{2}=\\frac{7}{2}$$", "input": "3\\frac{1}{2}", "result": "=\\left(3+\\frac{1}{2}\\right)\\div\\:\\frac{7}{2}", "steps": [ { "type": "step", "primary": "Convert mixed numbers to improper fraction: $$a\\frac{b}{c}=\\frac{a\\cdot\\:c+b}{c}$$", "secondary": [ "$$3\\frac{1}{2}=\\frac{3\\cdot2+1}{2}$$" ], "result": "=\\frac{7}{2}" } ], "meta": { "interimType": "Convert from Mixed Numbers Top 0Eq" } }, { "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 $$\\left(3+\\frac{1}{2}\\right)\\::{\\quad}\\frac{7}{2}$$", "input": "3+\\frac{1}{2}", "steps": [ { "type": "interim", "title": "$$3+\\frac{1}{2}=\\frac{7}{2}$$", "input": "3+\\frac{1}{2}", "steps": [ { "type": "step", "primary": "Convert element to fraction: $$3=\\frac{3\\cdot\\:2}{2}$$", "result": "=\\frac{3\\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{3\\cdot\\:2+1}{2}" }, { "type": "interim", "title": "$$3\\cdot\\:2+1=7$$", "input": "3\\cdot\\:2+1", "steps": [ { "type": "step", "primary": "Multiply the numbers: $$3\\cdot\\:2=6$$", "result": "=6+1" }, { "type": "step", "primary": "Add the numbers: $$6+1=7$$", "result": "=7" } ], "meta": { "solvingClass": "Solver", "interimType": "Solver", "gptData": "pG0PljGlka7rWtIVHz2xymbOTBTIQkBEGSNjyYYsjjDErT97kX84sZPuiUzCW6s7ksWDPsxIbGkmQroaF3uT7d6GQqufR6tr2vPxOUv7H+9MTg4418YnsnbKpNwPhLduVnEva1E6F4KI9o/Cnut2g24/Va/+G3hLP9WfhSb3X+c=" } }, { "type": "step", "result": "=\\frac{7}{2}" } ], "meta": { "solvingClass": "Solver", "interimType": "Solver", "gptData": "pG0PljGlka7rWtIVHz2xymbOTBTIQkBEGSNjyYYsjjDErT97kX84sZPuiUzCW6s7MmSqozMv7oVtkaHLhrItpwCWKUbvV6WK3fDUgFtg3Q/ysS6ztOAKKFAEXmiY4WQm1trQzF0YpMRKwaUZHQYXSnw5yz5ZzM5DU9uwDFmBpkv1IkW8shQ/F3u3t+miAoMpbqwnNL+vkns16SbvknXX+A==" } }, { "type": "step", "result": "=\\frac{7}{2}" } ], "meta": { "interimType": "Pemdas Parentheses Step Title 1Eq", "gptData": "pG0PljGlka7rWtIVHz2xymbOTBTIQkBEGSNjyYYsjjDErT97kX84sZPuiUzCW6s79kQR19ILVCSqMsdpzkHwqsOEtogatd43uJEGnSo+OgsTS6w7ONKk0836AQWRqOeE0vWZUBNt1bTaGANlW8kK2bcHwgcHnSs1Nr7IuLqambSgxyiDE33sG7fNh56WZxnHKL4I1YqgjrajEEaL+lQ82U/QYMzREewyYhmRoDar7odg1n3gey4D9tafPOGf56bpTeQKHeh69S6dnv9vSoUoFG5cLXY2/x8k2DiWeCUO6mM1tEMUqbxlHo5ze5sG0HT0nKiLeY6XiDE4MsROGNOYrb8yD3hLQ33B7/8/LpbPE3o=" } }, { "type": "step", "result": "=\\frac{7}{2}\\div\\:\\frac{7}{2}" }, { "type": "interim", "title": "Multiply and divide (left to right) $$\\frac{7}{2}\\div\\:\\frac{7}{2}\\::{\\quad}1$$", "input": "\\frac{7}{2}\\div\\:\\frac{7}{2}", "steps": [ { "type": "step", "primary": "Apply the fraction rule: $$\\frac{a}{b}\\div\\frac{c}{d}=\\frac{a}{b}\\times\\frac{d}{c}$$", "result": "=\\frac{7}{2}\\cdot\\:\\frac{2}{7}" }, { "type": "step", "primary": "Multiply fractions: $$\\frac{a}{b}\\cdot\\frac{c}{d}=\\frac{a\\:\\cdot\\:c}{b\\:\\cdot\\:d}$$", "result": "=\\frac{7\\cdot\\:2}{2\\cdot\\:7}" }, { "type": "step", "primary": "Cancel the common factor: $$7$$", "result": "=\\frac{2}{2}" }, { "type": "step", "primary": "Cancel the common factor: $$2$$", "result": "=1" } ], "meta": { "interimType": "Pemdas MultDiv Step Title 1Eq", "gptData": "pG0PljGlka7rWtIVHz2xymbOTBTIQkBEGSNjyYYsjjDErT97kX84sZPuiUzCW6s79Kg+idP5vLVrjUll6eMdYrVFC+rJ0eHjrdGypAmhBJP5EmgEOqgzoWjc4O01HnNk7BQOxr2jLPn85Q45pXFUV0o9eKFj1RN6kR7BNMWF7q4CnCpI6f1+7JR3uOjiBcBpv9MSspsWqUPp5ZuL8IpsL4rkX+U/8EaY/srocmCPXD3ngu8QOaLRTSdsDF8R530J72wZm7kDUxdE6YSmfEbr2okaNrC9eWe0SgEH0crqKCG9SuDGHyuGjLqyzox95B6+EvH87+M7UaQy5mpOUCoHWrVFC+rJ0eHjrdGypAmhBJNLckEHWB1FMZsuskJ4BViY" } }, { "type": "step", "result": "=1" } ], "meta": { "solvingClass": "Pemdas", "practiceLink": "/practice/order-of-operations-whole-practice", "practiceTopic": "Order of Operations" } }, "meta": { "showVerify": true } }