Question and Answers Forum

All Questions      Topic List

Algebra Questions

Previous in All Question      Next in All Question      

Previous in Algebra      Next in Algebra      

Question Number 45014 by peter frank last updated on 07/Oct/18

$$6\mathbf{÷}2(1+2)?\mathrm{which}\mathbf{ans}\mathbf{is}\mathbf{correct}\mathbf{between}1\mathbf{or}9$$$$\mathbf{why}\mathbf{do}\mathbf{i}\mathbf{look}\mathbf{at}\mathbf{the}\mathbf{mobile}\mathbf{phone}\mathbf{calculator}\mathbf{is}9\mathbf{and}\mathbf{when}\mathbf{i}\mathbf{check}\mathbf{to}\mathbf{scientific}\mathbf{calculator}\mathbf{the}\mathbf{ans}\mathbf{is}1.\mathbf{i}\mathbf{want}\mathbf{to}\mathbf{clarify}\mathbf{correctly}\mathbf{where}\mathbf{you}\mathbf{are}.$$

Commented by peter frank last updated on 07/Oct/18

$$\mathrm{ajfour},\mathrm{tanmay},\mathrm{MJS},{\mathrm{Mr}}_{}\underset{3}{\mathrm{w}}.$$

Commented by peter frank last updated on 07/Oct/18

$$\mathrm{why}\mathrm{are}\mathrm{the}\mathrm{answers}\mathrm{different}.$$

Commented by MJS last updated on 07/Oct/18

$${\mathrm{there}}^{\prime }\mathrm{s}\mathrm{no}\mathrm{priority}\mathrm{for}\mathrm{implied}\mathrm{multiplication}$$$$\mathrm{although}\mathrm{some}\mathrm{think}\mathrm{there}\mathrm{is}$$$$6\mathbf{÷}2(1+2)=6\mathbf{÷}2\times (1+2)=9$$$$\mathrm{to}\mathrm{get}1\mathrm{you}\mathrm{must}\mathrm{write}6\mathbf{÷}\left(2(1+2)\right)\mathrm{or}$$$$6\mathbf{÷}\left(2\times (1+2)\right)\mathrm{or}\frac{6}{2\times (1+2)}$$

Commented by MJS last updated on 08/Oct/18

$$\mathrm{Sir}\mathrm{Peter}\mathrm{Frank},\mathrm{which}\mathrm{scientific}\mathrm{calculator}$$$$\mathrm{do}\mathrm{you}\mathrm{use}?$$

Commented by peter frank last updated on 08/Oct/18

$$\mathrm{casio}\mathrm{fx}\mathrm{Ms}991$$

Commented by MJS last updated on 08/Oct/18

$$\mathrm{I}\mathrm{just}\mathrm{read}\mathrm{the}\mathrm{manual}\mathrm{online}\mathrm{and}\mathrm{obviously}$$$$\mathrm{the}\mathrm{calculator}\mathrm{is}\mathrm{programed}\mathrm{to}\mathrm{first}\mathrm{calculate}$$$$\mathrm{terms}\mathrm{like}2\pi \mathrm{or}5\sqrt{3}\mathrm{which}seems\mathrm{to}\mathrm{be}\mathrm{a}$$$$\mathrm{simplification}\mathrm{but}\mathrm{it}\mathrm{leads}\mathrm{to}\mathrm{mistakes}.$$$$\mathrm{what}\mathrm{does}\mathrm{this}\mathrm{mean}:$$$$1/2\pi +1/3\pi$$$$\mathrm{standard}\mathrm{math}\mathrm{is}\mathrm{definite}\mathrm{and}\mathrm{precise}$$$$1/2\pi +1/3\pi =\frac{1}{2}\pi +\frac{1}{3}\pi =\frac{5}{6}\pi$$$$1/\left(2\pi \right)+1/\left(3\pi \right)=\frac{1}{2\pi }+\frac{1}{3\pi }=\frac{5}{6\pi }$$$$1/2\sqrt{3}+5=\frac{1}{2}\sqrt{3}+5\mathrm{not}\frac{1}{2\sqrt{3}}+5\mathrm{and}\mathrm{not}\frac{1}{2\sqrt{3}+5}$$$$1/2(\pi +k)=\frac{1}{2}(\pi +k)$$$$\mathrm{sorry}\mathrm{to}\mathrm{say}\mathrm{that}\mathrm{casio}\mathrm{calculators}\mathrm{are}\mathrm{often}$$$$\mathrm{wrong}.\mathrm{buy}\mathrm{a}\mathrm{texas}\mathrm{instruments}\mathrm{or}\mathrm{a}\mathrm{hp}\mathrm{unit}$$$$\mathrm{or}\mathrm{use}\mathrm{a}\mathrm{good}\mathrm{app}\mathrm{like}\mathrm{HiPER}\mathrm{calc}\mathrm{pro}$$

Answered by Joel578 last updated on 07/Oct/18

$$\mathrm{Bracket},\mathrm{then}\mathrm{division},\mathrm{then}\mathrm{multiplication}$$$$6\mathbf{÷}2\times 3$$$$=3\times 3$$$$=9$$

Commented by MJS last updated on 08/Oct/18

$$\mathrm{sorry}\mathrm{but}{\mathrm{that}}^{\prime }\mathrm{s}\mathrm{not}\mathrm{standard}\mathrm{mathematic}$$$$\mathrm{where}\mathrm{have}\mathrm{you}\mathrm{learned}\mathrm{this}?$$

Commented by Rasheed.Sindhi last updated on 08/Oct/18

$$6\mathbf{÷}2(1+2)\mathrm{and}6\mathbf{÷}2\times (1+2)\mathrm{are}\mathrm{different}.$$$$\mathrm{In}6\mathbf{÷}2(1+2),2(1+2)\mathrm{is}\mathrm{like}\mathrm{a}\mathrm{single}$$$$\mathrm{term}\mathrm{which}\mathrm{should}\mathrm{be}\mathrm{calculated}\mathrm{first}.$$$$(\mathrm{In}\mathrm{other}\mathrm{words}\mathrm{x}\mathbf{÷}\mathrm{yz}\ne \mathrm{x}\mathbf{÷}\mathrm{y}\times \mathrm{z}$$$$\ast \mathrm{x}\mathbf{÷}\mathrm{yz}=\frac{\mathrm{x}}{\mathrm{yz}}$$$$\ast \mathrm{x}\mathbf{÷}\mathrm{y}\times \mathrm{z}=\frac{\mathrm{x}}{\mathrm{y}}\times \mathrm{z}=\frac{\mathrm{xz}}{\mathrm{y}})$$$$\mathrm{So},$$$$6\mathbf{÷}2(1+2)=6\mathbf{÷}2\left(3\right)=6\mathbf{÷}6=1$$$$(9\mathrm{is}\mathrm{not}\mathrm{correct}.)$$

Commented by Rasheed.Sindhi last updated on 08/Oct/18

$$\mathrm{In}\mathrm{other}\mathrm{words}\mathrm{implicit}\mathrm{multiplication}$$$$\mathrm{has}\mathrm{priority}\mathrm{over}\mathrm{division}\mathrm{and}\mathrm{division}$$$$\mathrm{have}\mathrm{priority}\mathrm{over}\mathrm{explicit}\mathrm{multiplication}....$$$$\mathrm{Although}\mathrm{at}\mathrm{the}\mathrm{moment}\mathrm{I}{\mathrm{haven}}^{\prime }\mathrm{t}\mathrm{a}\mathrm{reference}.$$

Commented by MJS last updated on 08/Oct/18

$$\mathrm{multiplication}\mathrm{and}\mathrm{division}\mathrm{have}\mathrm{equal}$$$$\mathrm{priority},\mathrm{similar}\mathrm{to}\mathrm{addition}\mathrm{and}\mathrm{subtraction}$$$$5-3+7-8=((5-3)+7)-8=1$$$$5/3\times 7/8=\left(\left(5/3\right)\times 7\right)/8=\frac{35}{24}$$$$$$$$\mathrm{implicit}\mathrm{multiplication}\mathrm{is}\mathrm{just}\mathrm{multiplication}$$$$\mathrm{where}\mathrm{we}\mathrm{left}\mathrm{the}‘‘{\times }^{″}\mathrm{sign}\mathrm{because}{\mathrm{it}}^{\prime }\mathrm{s}\mathrm{less}$$$$\mathrm{writing}\mathrm{work}.{\mathrm{there}}^{\prime }\mathrm{s}\mathrm{no}\mathrm{extra}\mathrm{rule}\mathrm{for}\mathrm{it}.$$$$ab/cd=a\times b/c\times d\mathrm{must}\mathrm{be}\mathrm{calculated}\mathrm{from}$$$$\mathrm{left}\mathrm{to}\mathrm{right}.\mathrm{everything}\mathrm{else}\mathrm{is}\mathrm{sloppy}\mathrm{habit}$$$$\mathrm{people}\mathrm{write}ab/cd\mathrm{instead}\mathrm{of}\frac{ab}{cd},{\mathrm{that}}^{\prime }\mathrm{s}\mathrm{the}$$$$\mathrm{initial}\mathrm{problem}.\mathrm{but}\mathrm{we}\mathrm{have}\mathrm{to}\mathrm{have}one\mathrm{rule}$$$$\mathrm{if}\frac{termA}{termB}=termA/termB\iff \frac{4x+3}{3x-4}=4x+3/3x-4$$$$\mathrm{and}\mathrm{confusion}\mathrm{is}\mathrm{complete}$$$$\mathrm{instead}{\mathrm{it}}^{\prime }\mathrm{s}\frac{termA}{termB}=\left(termA\right)/\left(termB\right)$$$$\Rightarrow 6\mathbf{÷}2(1+2)\ne \frac{6}{2(1+2)}$$

Commented by MJS last updated on 08/Oct/18

$$\mathrm{another}\mathrm{argument}:$$$$\mathrm{implied}\mathrm{multiplication}\mathrm{is}\mathrm{not}\mathrm{defined}\mathrm{for}$$$$a,b\in \mathbb{R}.\mathrm{or}\mathrm{how}\mathrm{can}\mathrm{we}\mathrm{write}ab\mathrm{for}a=7.43$$$$\mathrm{and}b=-2.56?$$$${\mathrm{it}}^{\prime }\mathrm{s}\mathrm{just}\mathrm{writing}\mathrm{shortcut},\mathrm{not}\mathrm{an}\mathrm{operation}$$

Commented by ajfour last updated on 08/Oct/18

$$wherehaveyoubeen,allthiswhile,$$$$RasheedSir?$$

Commented by MJS last updated on 08/Oct/18

$$\mathrm{there}\mathrm{are}\mathrm{some}‘‘\mathrm{bad}{\mathrm{spellings}}^{″},\mathrm{most}\mathrm{of}\mathrm{them}$$$$\mathrm{sloppiness}.\mathrm{but}\mathrm{we}\mathrm{learned}\mathrm{in}\mathrm{school}\mathrm{things}$$$$\mathrm{like}$$$$\frac{35}{4}=8\frac{3}{4}$$$$\mathrm{this}\mathrm{is}\mathrm{just}\mathrm{for}\mathrm{children}\mathrm{to}\mathrm{make}\mathrm{it}\mathrm{visible}\mathrm{for}$$$$\mathrm{them}$$$$\mathrm{standard}\mathrm{math}\mathrm{for}\mathrm{adults};-)$$$$8\frac{3}{4}=8\times \frac{3}{4}=6$$$$\mathrm{because}\mathrm{otherwise}:\mathrm{confusion}.\mathrm{solve}$$$$x\frac{3}{4}=6$$$$\mathrm{hopefully}{\mathrm{it}}^{\prime }\mathrm{s}x=8\mathrm{not}x=\frac{21}{4}$$$$\mathrm{also}{\mathrm{it}}^{\prime }\mathrm{s}\mathrm{not}\mathrm{possible}\mathrm{to}\mathrm{calculate}\mathrm{with}\mathrm{these}$$$$\mathrm{mixed}\mathrm{fractions}$$$$8\frac{3}{4}\pm 3\frac{5}{6}=$$$$8\frac{3}{4}\times 3\frac{5}{6}=$$$$8\frac{3}{4}\mathbf{÷}3\frac{5}{6}=$$$$\mathrm{we}\mathrm{have}\mathrm{to}\mathrm{use}\mathrm{standard}\mathrm{fractions}\mathrm{and}\mathrm{standard}$$$$\mathrm{maths}$$

Commented by Rasheed.Sindhi last updated on 08/Oct/18

$$\mathcal{T}hanksSirajfourformissingme!!!$$$$ActuallyunfortunatelyIlostmyinterest$$$$formathematics!I^{\prime }lltrytoparticipate$$$$intheforumagain.$$$$\mathcal{T}hanksagain!$$

Commented by MJS last updated on 08/Oct/18

$${\mathrm{there}}^{\prime }\mathrm{s}\mathrm{an}\mathrm{international}\mathrm{standard},\mathrm{is}\mathrm{all}{\mathrm{I}}^{\prime }\mathrm{m}$$$$\mathrm{saying}.$$$$\frac{1}{2}\mathrm{is}\mathrm{an}\mathrm{entity},\mathrm{I}\mathrm{can}\mathrm{write}1/2$$$$2\pi \mathrm{is}\mathrm{an}\mathrm{entity},\mathrm{I}\mathrm{can}\mathrm{write}\frac{1}{2\pi }\mathrm{or}1/2\pi$$$$\mathrm{in}1/2\pi ,\mathrm{which}\mathrm{entity}\mathrm{has}\mathrm{priority}?$$$$\mathrm{solve}\mathrm{this}:$$$$x^2+1/2x+1/4=0$$$$\mathrm{is}\mathrm{it}\mathrm{obviously}\mathrm{a}{2}^{\mathrm{nd}}\mathrm{degree}\mathrm{polynome}?\mathrm{or}\mathrm{is}$$$$1/2x\mathrm{a}\mathrm{division}\mathrm{by}2x?$$$$\mathrm{and}\mathrm{this}:\int dx/x^2+1/2x+1/4$$$$\mathrm{or}\sin x+1/2$$$$\mathrm{or}\sqrt{}2x-3$$$${\mathrm{I}}^{\prime }\mathrm{ve}\mathrm{seen}\mathrm{similar}\mathrm{expressions}\mathrm{in}\mathrm{this}\mathrm{forum}$$$$\mathrm{and}\mathrm{I}\mathrm{refused}\mathrm{to}\mathrm{solve}\mathrm{them}\mathrm{sometimes}$$$$\mathrm{because}{\mathrm{it}}^{\prime }\mathrm{s}\mathrm{never}\mathrm{obvious}\mathrm{when}\mathrm{it}\mathrm{comes}$$$$\mathrm{to}\mathrm{mathematics}.{\mathrm{that}}^{\prime }\mathrm{s}\mathrm{the}\mathrm{reason}\mathrm{I}\mathrm{plead}$$$$\mathrm{in}\mathrm{favour}\mathrm{of}\mathrm{the}\mathrm{standard}\mathrm{spelling}\mathrm{of}\mathrm{maths}$$

Commented by MrW3 last updated on 08/Oct/18

$$SirRasheed:$$$$Youaremissedbymetoo.Welcome$$$$back!$$

Commented by Rasheed.Sindhi last updated on 09/Oct/18

$$\mathcal{T}hanks\mathit{s}\mathit{i}\mathit{r}\mathit{M}\mathit{r}\mathit{W}3.$$$$\mathit{S}\mathit{i}\mathit{r}\mathit{M}\mathit{J}\mathit{S}$$$$Samediscussionispresentonthe$$$$followinglink\left(seecommentsbelow\right)$$$$whichsuggestthat{there}^{\prime }snoagreed$$$$internationalstandardinthisconnection.$$$$Bothconventionsarecontinuesimultaneously!!$$

Commented by Rasheed.Sindhi last updated on 09/Oct/18

Commented by Rasheed.Sindhi last updated on 09/Oct/18

Terms of Service

Privacy Policy

Contact: info@tinkutara.com