// Numbas version: exam_results_page_options {"duration": 0, "question_groups": [{"pickQuestions": 1, "pickingStrategy": "all-ordered", "name": "Group", "questions": [{"name": "Rearranging equations by multiplying or dividing: One step", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Julie Crowley", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/113/"}], "functions": {}, "ungrouped_variables": [], "tags": ["algebra", "balancing equations", "ephlth", "linear equations", "Linear equations", "one step equations", "rearranging equations", "REBEL", "rebel", "rebelmaths", "Solving equations", "solving equations"], "preamble": {"css": "", "js": ""}, "advice": "

Here is a video on Transposition  https://www.youtube.com/watch?v=0oq4arfe-SM 

", "rulesets": {}, "parts": [{"stepsPenalty": "1", "prompt": "

Given $ax=b$, we can rearrange the equation to that find $x=$ [[0]].

\n

\n

Note: Use / to signify division and * to signify multiplication.

", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "steps": [{"prompt": "

Given $ax=b$, we divide both sides by $a$ to get $x$ by itself.

\n

\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
$ax$$=$$b$
 
$\\displaystyle{\\frac{ax}{a}}$$=$$\\displaystyle{\\frac{b}{a}}$
 
$x$$=$$\\displaystyle{\\frac{b}{a}}$
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Given $cy=d$,  $y=$ [[0]].

\n

\n

Note: Use / to signify division and * to signify multiplication.

", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "steps": [{"prompt": "

Given $cy=d$, we divide both sides by $c$ to get $y$ by itself.

\n

\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
$cy$$=$$d$
 
$\\displaystyle{\\frac{cy}{c}}$$=$$\\displaystyle{\\frac{d}{c}}$
 
$y$$=$$\\displaystyle{\\frac{d}{c}}$
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Rearrange $\\displaystyle{\\frac{z}{f}=g}$ to determine the value of $z$.

\n

$z=$ [[0]]

\n

\n

Note: Use / to signify division and * to signify multiplication.

", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "steps": [{"prompt": "

Given $\\displaystyle{\\frac{z}{f}}=g$, we multiply both sides by $f$ to get $z$ by itself.

\n

\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
$\\displaystyle{\\frac{z}{f}}$$=$$g$
 
$\\displaystyle{\\frac{z}{f}}\\times f$$=$$g\\times f$
 
$z$$=$$fg$
\n

\n

We input our answer as f*g or g*f.

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Solve $\\displaystyle{h=-\\frac{a}{j}}$ for $a$.

\n

$a=$ [[0]]

\n

\n

Note: Use / to signify division and * to signify multiplication.

", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "steps": [{"prompt": "

Given $\\displaystyle{h=-\\frac{a}{j}}$, we multiply both sides by $-j$ to get $a$ by itself.

\n

\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
$h$$=$$\\displaystyle{-\\frac{a}{j}}$
 
$h\\times(-\\var{j})$$=$$\\displaystyle{-\\frac{a}{j}\\times(-j)}$
 
$-hj$$=$$a$
 
$a$$=$$-hj$
\n

\n

We input our answer as -h*j or -j*h.

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Rearrange $\\displaystyle{a=\\frac{b}{c}}$ to determine the value of $c$.

\n

$c=$ [[0]]

\n

\n

Note: Use / to signify division and * to signify multiplication.

", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "steps": [{"prompt": "

Given $\\displaystyle{a=\\frac{b}{c}}$, we need to do two things to get $c$ by itself:

\n
    \n
  1. multiply both sides by $c$ to get $c$ off the bottom of the fraction, then
    2. \n
  2. divide both sides by $a$ to get $c$ by itself.
    3. \n
\n

\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
$a$$=$$\\displaystyle{\\frac{b}{c}}$
 
$a\\times c$$=$$\\displaystyle{\\frac{b}{c}}\\times c$ (see step 1 above)
 
$ac$$=$$b$
 
$\\displaystyle{\\frac{ac}{a}}$$=$ $\\displaystyle{\\frac{b}{a}}$(see step 2 above)
$c$$=$$\\displaystyle{\\frac{b}{a}}$
\n

\n

Notice, it looks like we have just swapped $a$ and $c$ diagonally over the equals sign.

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Rearrange $\\displaystyle{s=\\frac{d}{t}}$ to determine the value of $t$.

\n

$t=$ [[0]]

\n

\n

Note: Use / to signify division and * to signify multiplication.

", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "steps": [{"prompt": "

Given $\\displaystyle{s=\\frac{d}{t}}$, we need to do two things to get $t$ by itself:

\n
    \n
  1. multiply both sides by $t$ to get $t$ off the bottom of the fraction, then
    2. \n
  2. divide both sides by $s$ to get $t$ by itself.
    3. \n
\n

\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
$s$$=$$\\displaystyle{\\frac{d}{t}}$
 
$s\\times t$$=$$\\displaystyle{\\frac{d}{t}}\\times t$ (see step 1 above)
 
$st$$=$$d$
 
$\\displaystyle{\\frac{st}{s}}$$=$ $\\displaystyle{\\frac{d}{s}}$(see step 2 above)
$t$$=$$\\displaystyle{\\frac{d}{s}}$
\n

\n

Notice, it looks like we have just swapped $s$ and $t$ diagonally over the equals sign.

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Rearranging equations by multiplying or dividing: One step

\n

rebelmaths

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Transpose the formula $y=x+\\var{a}$ to make $x$ the subject

\n

$x= $[[0]]

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Write $x$ in terms of $y$ if 

\n

$y =\\dfrac{x}{\\var{b}}$.

\n

$x= $[[0]]

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Make $c$ the subject of the formula $y=\\var{c}x+c$.

\n

$c= $[[0]] 

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Make $x$ the subject of the formula $y=\\var{a}x+\\var{b}$.

\n

$x= $[[0]]

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Find $x$ in terms of $y$ if

\n

$\\var{c}y  =  \\var{c}x+\\var{a}$

\n

$x= $[[0]]

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Find $y$ in terms of $x$ if     

\n

$\\var{a}y=\\var{c}x+\\var{a}$

\n

$y= $[[0]]

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Note: to input the answer \"$x=y+2$\" the \"$x=$\" is already given and you just need to input \"$y+2$\".

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Transposition

\n

rebelmaths

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Make x the subject of

\n

$y = \\var{m} x + \\var{c}$

\n

$x = $[[0]]

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Make x the subject of

\n

$\\var{a}y = \\var{m} x + \\var{c}$

\n

$x = $[[0]]

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Make R the subject of

\n

$I=\\frac{V}{R}$

\n

$R = $[[0]]

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Make P the subject of

\n

$A = P(1+r)^n$

\n

$P=$[[0]]

\n

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rebelmaths

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$\\simplify[std]{{a}y + {b}x = {c} + {d}xy}\\;$

\n

$y =$ [[0]]

\n

You can click on \"Show steps\" for more information, but you will lose one mark if you do so.

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To re-arrange $ay + bx = c + dxy$ we should first collect all of the terms involving $y$ to the one side

\n

$ay - dxy = c - bx$

\n

we should then factorize out $y$ to find

\n

$y(a-dx) = c - bx$

\n

and then divide by $a-dx$ to get $y$ on its own

\n

$y = \\frac{c - bx}{a - dx}$

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Another transposition question.

\n

rebalmaths

", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "

Rearrange the following equation to make $y$ the subject. 

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The formula $P=\\frac{F}{A}$ is used in mechanics where $P=$Pressure, $F=$Force and $A=$Area.

\n

Rearrange the forumla to make $F$ the subject. 

\n

Note if inputting $xy$ for an  answer you need to input $x*y$.

\n

$F=$[[0]]

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The formula $v=u+at$ is used in mechanics where $v=$final velocity, $u=$initial velocity and $t=$time.

\n

Rearrange the forumla to make $u$ the subject. 

\n

$u=$[[0]]

\n

Rearrange the forumla to make $a$ the subject. 

\n

$a=$[[1]]

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rebelmaths

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Practice of basic transpositions. Doesn't include roots

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