(2+1/4)(1-4/5)

{ "query": { "display": "$$\\left(2+\\frac{1}{4}\\right)\\left(1-\\frac{4}{5}\\right)$$", "symbolab_question": "PEMDAS#(2+\\frac{1}{4})(1-\\frac{4}{5})" }, "solution": { "level": "PERFORMED", "subject": "Pre Algebra", "topic": "Order of Operations", "subTopic": "Other", "default": "\\frac{9}{20}", "meta": { "showVerify": true } }, "steps": { "type": "interim", "title": "$$\\left(2+\\frac{1}{4}\\right)\\left(1-\\frac{4}{5}\\right)=\\frac{9}{20}$$", "input": "\\left(2+\\frac{1}{4}\\right)\\left(1-\\frac{4}{5}\\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 $$\\left(2+\\frac{1}{4}\\right)\\::{\\quad}\\frac{9}{4}$$", "input": "2+\\frac{1}{4}", "steps": [ { "type": "interim", "title": "$$2+\\frac{1}{4}=\\frac{9}{4}$$", "input": "2+\\frac{1}{4}", "steps": [ { "type": "step", "primary": "Convert element to fraction: $$2=\\frac{2\\cdot\\:4}{4}$$", "result": "=\\frac{2\\cdot\\:4}{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\\cdot\\:4+1}{4}" }, { "type": "interim", "title": "$$2\\cdot\\:4+1=9$$", "input": "2\\cdot\\:4+1", "steps": [ { "type": "step", "primary": "Multiply the numbers: $$2\\cdot\\:4=8$$", "result": "=8+1" }, { "type": "step", "primary": "Add the numbers: $$8+1=9$$", "result": "=9" } ], "meta": { "solvingClass": "Solver", "interimType": "Solver", "gptData": "pG0PljGlka7rWtIVHz2xymbOTBTIQkBEGSNjyYYsjjDErT97kX84sZPuiUzCW6s7rHxsvVEtm563qucb8VzELd6GQqufR6tr2vPxOUv7H+896Wcd/plV45tm+W5sEXki1SvY/eJGzvEmlW7hoPETDl9R9wWaHQ8grlApgKbfxR4=" } }, { "type": "step", "result": "=\\frac{9}{4}" } ], "meta": { "solvingClass": "Solver", "interimType": "Solver", "gptData": "pG0PljGlka7rWtIVHz2xymbOTBTIQkBEGSNjyYYsjjDErT97kX84sZPuiUzCW6s7zHcKUwD7XSna19MvStKAAQCWKUbvV6WK3fDUgFtg3Q/ysS6ztOAKKFAEXmiY4WQmjx6D0MZ1j6OqGR+hYrY8gancoZExPHBXBoEpjaahQGpLfVFoN8Ky2GrpkdHzdDV3uxq/qgrA5qWTcQ1KY33A1Q==" } }, { "type": "step", "result": "=\\frac{9}{4}" } ], "meta": { "interimType": "Pemdas Parentheses Step Title 1Eq", "gptData": "pG0PljGlka7rWtIVHz2xymbOTBTIQkBEGSNjyYYsjjDErT97kX84sZPuiUzCW6s7fF8nmN01brRDviPMqMKkNsHzDu0B8+Bp0dhF7LDJpS5jfTg+AqEqFKfQD4cRP8CllpeMl9X+ei3Sv0uNJeMyMR8JRslkmU4o2zIYcqLbUP0ugZk/gtK/12W124flIYTBAo8Cmc7mr7rtBTZEYu4hzvjzg700n88ODv8BNgwDXps9H1hzM4EIFzgc/zKc8RZs+1vFTLgjEhONKS3QYaJ/Ba71upxafoCdPh6EHIjGDNVUCXY9/axwbjwCJ6KjtM3MdBgQOGjULRqQtqGqXPoG8Q==" } }, { "type": "step", "result": "=\\frac{9}{4}\\left(1-\\frac{4}{5}\\right)" }, { "type": "interim", "title": "Calculate within parentheses $$\\left(1-\\frac{4}{5}\\right)\\::{\\quad}\\frac{1}{5}$$", "input": "1-\\frac{4}{5}", "steps": [ { "type": "interim", "title": "$$1-\\frac{4}{5}=\\frac{1}{5}$$", "input": "1-\\frac{4}{5}", "steps": [ { "type": "step", "primary": "Convert element to fraction: $$1=\\frac{1\\cdot\\:5}{5}$$", "result": "=\\frac{1\\cdot\\:5}{5}-\\frac{4}{5}" }, { "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\\:5-4}{5}" }, { "type": "interim", "title": "$$1\\cdot\\:5-4=1$$", "input": "1\\cdot\\:5-4", "steps": [ { "type": "step", "primary": "Multiply the numbers: $$1\\cdot\\:5=5$$", "result": "=5-4" }, { "type": "step", "primary": "Subtract the numbers: $$5-4=1$$", "result": "=1" } ], "meta": { "solvingClass": "Solver", "interimType": "Solver", "gptData": "pG0PljGlka7rWtIVHz2xymbOTBTIQkBEGSNjyYYsjjDErT97kX84sZPuiUzCW6s7wwe39lm+SIAGFhi0pJUxBd6GQqufR6tr2vPxOUv7H++P6Ubiv/bIrpol3G9QIK7hP/n/sT8Hudl/0KJRqY9qeWHJMlKcRfgjzVAnaQvT/Mo=" } }, { "type": "step", "result": "=\\frac{1}{5}" } ], "meta": { "solvingClass": "Solver", "interimType": "Solver", "gptData": "pG0PljGlka7rWtIVHz2xymbOTBTIQkBEGSNjyYYsjjDErT97kX84sZPuiUzCW6s7iVXFayr8lI2eFRGAEGMvZQCWKUbvV6WK3fDUgFtg3Q/ysS6ztOAKKFAEXmiY4WQmaIXiqzQkGLQ/JVXsUy21fngY3ovothaT9gdWRHxLJgtzVDRQ9nyOtcFTgCOQDfvma8k9T2I2UENz3QepWcEEdw==" } }, { "type": "step", "result": "=\\frac{1}{5}" } ], "meta": { "interimType": "Pemdas Parentheses Step Title 1Eq", "gptData": "pG0PljGlka7rWtIVHz2xymbOTBTIQkBEGSNjyYYsjjDErT97kX84sZPuiUzCW6s79Kg+idP5vLVrjUll6eMdYunqc4g4EpQUZ1E/nJRG3Yulu/Z7IBSFEJttf+N6K1OE+GJUCw9krdwl2yu17HEotbvjyl34qCSgNvx6C8iwh98lgLEfLdRny6NoQS2KyFc3+boTQehoZTDFao5h2IhgfU7o5BZqOsXcGFUMZBGPIaRYVjNwDihplHv2/sl3ET8WiVVmlPB5qIpjfeNkywRFNYiIuF6jHWbVEQd6zS5Jw9dKXrGZyCbQgO62oYM50nMu+l90jTRyXGhU0gzJvl0j7A==" } }, { "type": "step", "result": "=\\frac{9}{4}\\cdot\\:\\frac{1}{5}" }, { "type": "interim", "title": "Multiply and divide (left to right) $$\\frac{9}{4}\\cdot\\:\\frac{1}{5}\\::{\\quad}\\frac{9}{20}$$", "input": "\\frac{9}{4}\\cdot\\:\\frac{1}{5}", "steps": [ { "type": "step", "primary": "Apply the fraction rule: $$\\frac{a}{b}\\cdot\\:\\frac{c}{d}=\\frac{a\\:\\cdot\\:\\:c}{b\\:\\cdot\\:\\:d}$$", "result": "=\\frac{9\\cdot\\:1}{4\\cdot\\:5}" }, { "type": "step", "primary": "Multiply the numbers: $$9\\cdot\\:1=9$$", "result": "=\\frac{9}{4\\cdot\\:5}" }, { "type": "step", "primary": "Multiply the numbers: $$4\\cdot\\:5=20$$", "result": "=\\frac{9}{20}" } ], "meta": { "interimType": "Pemdas MultDiv Step Title 1Eq", "gptData": "pG0PljGlka7rWtIVHz2xymbOTBTIQkBEGSNjyYYsjjDErT97kX84sZPuiUzCW6s79Kg+idP5vLVrjUll6eMdYibcgAM0sRqHF2682GgGzYskVSCIHj2VeqsXz79W+BhDKGh9WyjkgrzO6qb4d3riKbh88F+yPY4Rab474SuJ8cSQChb+Kv/d1bJx2TmxRiF9uphWlAxj4qmgQvqj49x+HU2VVNYRw63nLKn1HtG1E9SBIQdF1r4bkEczkVETb80bfO11GJPvpl3g45U5aVDmGvC30sSftAIFS6Qkpy19IkqZYY9oS23eK9kho9PePsCLXhbADX2gvyKfNKNkOFNCS2W5z0K22p9+YrjejqTA52Sn2ZcGs/Q3w5jWKOBqbUd4DeHLpDyq1pTTKhrazbXoRA==" } }, { "type": "step", "result": "=\\frac{9}{20}" } ], "meta": { "solvingClass": "Pemdas", "practiceLink": "/practice/order-of-operations-whole-practice", "practiceTopic": "Order of Operations" } }, "meta": { "showVerify": true } }