// Numbas version: exam_results_page_options {"name": "Bill's copy of Rearranging equations by multiplying or dividing: One step", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"functions": {}, "ungrouped_variables": [], "name": "Bill's copy of Rearranging equations by multiplying or dividing: One step", "tags": ["algebra", "balancing equations", "ephlth", "Linear equations", "linear equations", "one step equations", "rearranging equations", "solving equations", "Solving equations"], "advice": "", "rulesets": {}, "parts": [{"stepsPenalty": "1", "prompt": "

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

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

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

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

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

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

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

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$z=$ [[0]]

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

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

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 $\\displaystyle{\\frac{z}{f}}$ $=$ $g$ $\\displaystyle{\\frac{z}{f}}\\times f$ $=$ $g\\times f$ $z$ $=$ $fg$
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We input our answer as f*g or g*f.

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

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$a=$ [[0]]

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

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

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

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$c=$ [[0]]

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

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

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1. multiply both sides by $c$ to get $c$ off the bottom of the fraction, then
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3. divide both sides by $a$ to get $c$ by itself.
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 $a$ $=$ $\\displaystyle{\\frac{b}{c}}$ $a\\times c$ $=$ $\\displaystyle{\\frac{b}{c}}\\times c$ (see step 1 above) $ac$ $=$ $b$ $\\displaystyle{\\frac{ac}{a}}$ $=$ $\\displaystyle{\\frac{b}{a}}$ (see step 2 above) $c$ $=$ $\\displaystyle{\\frac{b}{a}}$
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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 $t$.

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$t=$ [[0]]

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

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

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1. multiply both sides by $t$ to get $t$ off the bottom of the fraction, then
2. \n
3. divide both sides by $s$ to get $t$ by itself.
4. \n
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 $s$ $=$ $\\displaystyle{\\frac{d}{t}}$ $s\\times t$ $=$ $\\displaystyle{\\frac{d}{t}}\\times t$ (see step 1 above) $st$ $=$ $d$ $\\displaystyle{\\frac{st}{s}}$ $=$ $\\displaystyle{\\frac{d}{s}}$ (see step 2 above) $t$ $=$ $\\displaystyle{\\frac{d}{s}}$
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Notice, it looks like we have just swapped $s$ and $t$ diagonally over the equals sign.

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If need be I can make the equations with words that are relevant to nursing.... maybe even randomise them? I need to be told what equations though.

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