// 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, "typeendtoleave": 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]].
\n\nNote: Use / to signify division and * to signify multiplication.
", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"vsetrangepoints": 5, "expectedvariablenames": ["b", "a"], "checkingaccuracy": 0.001, "type": "jme", "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "answer": "b/a", "marks": 1, "checkvariablenames": true, "checkingtype": "absdiff", "vsetrange": [0, 1]}], "steps": [{"prompt": "Given $ax=b$, we divide both sides by $a$ to get $x$ by itself.
\n\n$ax$ | \n$=$ | \n$b$ | \n
\n | \n | \n |
$\\displaystyle{\\frac{ax}{a}}$ | \n$=$ | \n$\\displaystyle{\\frac{b}{a}}$ | \n
\n | \n | \n |
$x$ | \n$=$ | \n$\\displaystyle{\\frac{b}{a}}$ | \n
Given $cy=d$, $y=$ [[0]].
\n\nNote: Use / to signify division and * to signify multiplication.
", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"vsetrangepoints": 5, "expectedvariablenames": ["d", "c"], "checkingaccuracy": 0.001, "type": "jme", "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "answer": "d/c", "marks": 1, "checkvariablenames": true, "checkingtype": "absdiff", "vsetrange": [0, 1]}], "steps": [{"prompt": "Given $cy=d$, we divide both sides by $c$ to get $y$ by itself.
\n\n$cy$ | \n$=$ | \n$d$ | \n
\n | \n | \n |
$\\displaystyle{\\frac{cy}{c}}$ | \n$=$ | \n$\\displaystyle{\\frac{d}{c}}$ | \n
\n | \n | \n |
$y$ | \n$=$ | \n$\\displaystyle{\\frac{d}{c}}$ | \n
Rearrange $\\displaystyle{\\frac{z}{f}=g}$ to determine the value of $z$.
\n$z=$ [[0]]
\n\nNote: Use / to signify division and * to signify multiplication.
", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"vsetrangepoints": 5, "expectedvariablenames": ["f", "g"], "checkingaccuracy": 0.001, "type": "jme", "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "answer": "f*g", "marks": 1, "checkvariablenames": true, "checkingtype": "absdiff", "vsetrange": [0, 1]}], "steps": [{"prompt": "Given $\\displaystyle{\\frac{z}{f}}=g$, we multiply both sides by $f$ to get $z$ by itself.
\n\n$\\displaystyle{\\frac{z}{f}}$ | \n$=$ | \n$g$ | \n
\n | \n | \n |
$\\displaystyle{\\frac{z}{f}}\\times f$ | \n$=$ | \n$g\\times f$ | \n
\n | \n | \n |
$z$ | \n$=$ | \n$fg$ | \n
We input our answer as f*g or g*f.
", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "marks": 0, "scripts": {}, "showCorrectAnswer": true, "type": "gapfill"}, {"stepsPenalty": "1", "prompt": "Solve $\\displaystyle{h=-\\frac{a}{j}}$ for $a$.
\n$a=$ [[0]]
\n\nNote: Use / to signify division and * to signify multiplication.
", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"vsetrangepoints": 5, "expectedvariablenames": ["j", "h"], "checkingaccuracy": 0.001, "type": "jme", "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "answer": "-j*h", "marks": 1, "checkvariablenames": true, "checkingtype": "absdiff", "vsetrange": [0, 1]}], "steps": [{"prompt": "Given $\\displaystyle{h=-\\frac{a}{j}}$, we multiply both sides by $-j$ to get $a$ by itself.
\n\n$h$ | \n$=$ | \n$\\displaystyle{-\\frac{a}{j}}$ | \n
\n | \n | \n |
$h\\times(-\\var{j})$ | \n$=$ | \n$\\displaystyle{-\\frac{a}{j}\\times(-j)}$ | \n
\n | \n | \n |
$-hj$ | \n$=$ | \n$a$ | \n
\n | \n | \n |
$a$ | \n$=$ | \n$-hj$ | \n
We input our answer as -h*j or -j*h.
", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "marks": 0, "scripts": {}, "showCorrectAnswer": true, "type": "gapfill"}, {"stepsPenalty": "1", "prompt": "Rearrange $\\displaystyle{a=\\frac{b}{c}}$ to determine the value of $c$.
\n$c=$ [[0]]
\n\nNote: Use / to signify division and * to signify multiplication.
", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"vsetrangepoints": 5, "expectedvariablenames": ["b", "a"], "checkingaccuracy": 0.001, "type": "jme", "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "answer": "b/a", "marks": 1, "checkvariablenames": true, "checkingtype": "absdiff", "vsetrange": [0, 1]}], "steps": [{"prompt": "Given $\\displaystyle{a=\\frac{b}{c}}$, we need to do two things to get $c$ by itself:
\n$a$ | \n$=$ | \n$\\displaystyle{\\frac{b}{c}}$ | \n\n |
\n | \n | \n | \n |
$a\\times c$ | \n$=$ | \n$\\displaystyle{\\frac{b}{c}}\\times c$ | \n(see step 1 above) | \n
\n | \n | \n | \n |
$ac$ | \n$=$ | \n$b$ | \n\n |
\n | \n | \n | \n |
$\\displaystyle{\\frac{ac}{a}}$ | \n$=$ | \n$\\displaystyle{\\frac{b}{a}}$ | \n(see step 2 above) | \n
\n | \n | \n | \n |
$c$ | \n$=$ | \n$\\displaystyle{\\frac{b}{a}}$ | \n\n |
Notice, it looks like we have just swapped $a$ and $c$ diagonally over the equals sign.
", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "marks": 0, "scripts": {}, "showCorrectAnswer": true, "type": "gapfill"}, {"stepsPenalty": "1", "prompt": "Rearrange $\\displaystyle{s=\\frac{d}{t}}$ to determine the value of $t$.
\n$t=$ [[0]]
\n\nNote: Use / to signify division and * to signify multiplication.
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\n$s$ | \n$=$ | \n$\\displaystyle{\\frac{d}{t}}$ | \n\n |
\n | \n | \n | \n |
$s\\times t$ | \n$=$ | \n$\\displaystyle{\\frac{d}{t}}\\times t$ | \n(see step 1 above) | \n
\n | \n | \n | \n |
$st$ | \n$=$ | \n$d$ | \n\n |
\n | \n | \n | \n |
$\\displaystyle{\\frac{st}{s}}$ | \n$=$ | \n$\\displaystyle{\\frac{d}{s}}$ | \n(see step 2 above) | \n
\n | \n | \n | \n |
$t$ | \n$=$ | \n$\\displaystyle{\\frac{d}{s}}$ | \n\n |
Notice, it looks like we have just swapped $s$ and $t$ diagonally over the equals sign.
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", "description": "", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}], "contributors": [{"name": "Bill Foster", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/6/"}]}]}], "contributors": [{"name": "Bill Foster", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/6/"}]}