{"id":134,"date":"2022-01-26T12:00:01","date_gmt":"2022-01-26T17:00:01","guid":{"rendered":"https:\/\/pressbooks.bccampus.ca\/hfriedman\/?post_type=chapter&p=134"},"modified":"2024-01-09T17:32:45","modified_gmt":"2024-01-09T22:32:45","slug":"proposed-alf-math-book-6-corrections","status":"web-only","type":"chapter","link":"https:\/\/pressbooks.bccampus.ca\/hfriedman\/chapter\/proposed-alf-math-book-6-corrections\/","title":{"raw":"Proposed ALF Math Book 6 Corrections","rendered":"Proposed ALF Math Book 6 Corrections"},"content":{"raw":"*Note: For this to chapter to display properly, QuickLaTeX plugin must be deactivated.\r\n\r\nThis chapter details the issues and proposed changes from the Adult Literacy Fundamental Mathematics \u2013 Book 6<\/a>.\r\n\r\nThe following solutions work with Apple's screen reading software. Other screen readers have not been tested.\r\n

Operands within fractions<\/h1>\r\nThere are several examples as well as Exercises that use the format [latex]\\dfrac{4}{5}\\left(\\dfrac{\\times2}{\\times2}\\right)[\/latex]. The two multiplication signs within the parenthesis are not read out correctly. The proposed change is to move the multiplication (or division sign in some cases) outside the parentheses.\r\n
\r\n

Example A: Original<\/p>\r\n\r\n<\/header>\r\n

\r\n\r\nExpress [latex]4:5[\/latex] in higher terms.\r\n\r\n[latex]4:5=\\dfrac{4}{5}\\longrightarrow\\dfrac{4}{5}\\times\\left(\\dfrac{\\times2}{\\times2}\\right)\\longrightarrow\\dfrac{8}{10}[\/latex]\r\n\r\n[latex]4:5[\/latex] is equivalent to [latex]8:10[\/latex]\r\n\r\n<\/div>\r\n<\/div>\r\n
\r\n

Example A: Proposed solution<\/p>\r\n\r\n<\/header>\r\n

\r\n\r\nExpress [latex]4:5[\/latex] in higher terms.\r\n\r\n[latex]4:5=\\dfrac{4}{5}\\longrightarrow\\dfrac{4}{5}\\times\\left(\\dfrac{2}{2}\\right)\\longrightarrow\\dfrac{8}{10}[\/latex]\r\n\r\n[latex]4:5[\/latex] is equivalent to [latex]8:10[\/latex]\r\n\r\n<\/div>\r\n<\/div>\r\n
\r\n

Example A: Edited proposed solution<\/p>\r\n\r\n<\/header>\r\n

\r\n\r\nExpress [latex]4:5[\/latex] in higher terms.\r\n\r\n[latex]4:5=\\dfrac{4}{5}\\longrightarrow\\dfrac{4}{5}\\times\\left(\\dfrac{2}{2}\\right)\\longrightarrow \\dfrac{4\\times2}{5\\times2}\\longrightarrow\\dfrac{8}{10}[\/latex]\r\n\r\n[latex]4:5[\/latex] is equivalent to [latex]8:10[\/latex]\r\n\r\n<\/div>\r\n<\/div>\r\nThis issue is seen in Unit 1 (Topic A, B, C).\r\n

Crossed-off numbers when simplifying equations<\/h1>\r\nFrequently, the book shows numbers or variables being struck through as a visual shorthand to show the number being reduced through simplification of fractions, such as [latex]\\begin{equation}\\begin{split}\r\n\\dfrac{\\cancel{6}\\textit{N}}{\\cancel{6}}\\end{split}\\end{equation}[\/latex]. The screenreader doesn't acknowledge this strike through (\\cancel command) and simply reads the number as normal.\r\n

Adding an extra equation<\/h2>\r\nIn most cases, the surrounding text provides enough context that we can simply add an extra equation that shows the equation before and after simplification, like the example below.\r\n
\r\n

Example B: Original<\/p>\r\n\r\n<\/header>\r\n

\r\n\r\n[latex]\\dfrac{6}{7}=\\dfrac{24}{\\textit{N}}[\/latex]\r\n\r\nCross multiply:\r\n[latex]\r\n\\begin{equation}\\begin{split}\r\n6\\times\\textit{N} &= 7\\times24 \\\\\r\n6\\textit{N} &= 168\r\n\\end{split}\\end{equation}[\/latex]\r\nDivide both sides by 6. The 6's with the N<\/em> will cancel (reduce), and the N<\/em> will be alone.\r\n[latex]\\begin{equation}\\begin{split}\r\n\\dfrac{\\cancel{6}\\textit{N}}{\\cancel{6}} &= \\dfrac{168}{6} \\\\\r\n\\\\\r\n\\textit{N} &= 168\\div6 \\\\\r\n\\\\\r\n\\textit{N} &= 28 \\\\\r\n\\\\\r\n\\dfrac{6}{7} &= \\dfrac{24}{28}\r\n\\end{split}\\end{equation}[\/latex]\r\nCheck by cross-multiplying:\r\n[latex]\\begin{equation}\\begin{split}\r\n\\text{Is }6\\times28 &= 7\\times24? \\\\\r\n6\\times28 &= 168 \\\\\r\n7\\times24 &= 168 \\\\\r\n\\text{the cross-product }168 &= \\text{the cross-product }168 \\\\\r\n\\text{Yes - }6:7 &= 24:28\r\n\\end{split}\\end{equation}[\/latex]\r\n\r\n<\/div>\r\n<\/div>\r\n
\r\n

Example B: Proposed solution<\/p>\r\n\r\n<\/header>\r\n

\r\n\r\n[latex]\\dfrac{6}{7}=\\dfrac{24}{\\textit{N}}[\/latex]\r\n\r\nCross multiply:\r\n[latex]\r\n\\begin{equation}\\begin{split}\r\n6\\times\\textit{N} &= 7\\times24 \\\\\r\n6\\textit{N} &= 168\r\n\\end{split}\\end{equation}[\/latex]\r\nDivide both sides by 6. The 6's with the N<\/em> will cancel (reduce), and the N<\/em> will be alone.\r\n[latex]\\begin{equation}\\begin{split}\r\n\\dfrac{{6}\\textit{N}}{{6}} &= \\dfrac{168}{6} \\\\\r\n\\\\\r\n\r\nN &=\\dfrac{168}{6} \\\\\r\n\r\n\\\\\r\n\\textit{N} &= 168\\div6 \\\\\r\n\\\\\r\n\\textit{N} &= 28 \\\\\r\n\\\\\r\n\\dfrac{6}{7} &= \\dfrac{24}{28}\r\n\\end{split}\\end{equation}[\/latex]\r\nCheck by cross-multiplying:\r\n[latex]\\begin{equation}\\begin{split}\r\n\\text{Is }6\\times28 &= 7\\times24? \\\\\r\n6\\times28 &= 168 \\\\\r\n7\\times24 &= 168 \\\\\r\n\\text{the cross-product }168 &= \\text{the cross-product }168 \\\\\r\n\\text{Yes - }6:7 &= 24:28\r\n\\end{split}\\end{equation}[\/latex]\r\n\r\n<\/div>\r\n<\/div>\r\nThis solution can be used in Units 1 Topic C, Unit 2 Topic A, Unit 3 Topic A, Unit 4 Topic A.\r\n

Adding an additional text explanation<\/h2>\r\nIn other cases, more explanation may be necessary. In this case, we'll opt to put the equation into a table so we can provide more of an explanation when we remove the strike-throughs.\r\n
\r\n

Example A: Original<\/p>\r\n\r\n<\/header>\r\n

[latex]\\begin{equation}\\begin{split}\r\n\\frac{3}{4} &= \\text{_____}\\% \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ &\\frac{3}{4} &\\times 100\\% \\ &= \\frac{3}{\\cancel{4} 1} &\\times \\frac{\\cancel{100} 25}{1} \\ &= 75\\% \\\\\r\n1\\frac{1}{5} &= \\text{_____}\\% \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ 1&\\frac{1}{5} &\\times 100\\% \\ &= \\frac{6}{\\cancel{5} 1} &\\times \\frac{\\cancel{120} 20}{1} \\ &= 120\\%\r\n\\end{split}\\end{equation}[\/latex]<\/div>\r\n<\/div>\r\n
\r\n

Example A: Proposed solution<\/p>\r\n\r\n<\/header>\r\n

[latex]\\frac{3}{4} = \\text{_____}\\%[\/latex]<\/div>\r\n
\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
[latex]\\frac{3}{4}[\/latex]<\/td>\r\n<\/td>\r\n<\/tr>\r\n
[latex]\\frac{3}{4} \\times 100\\%[\/latex]<\/td>\r\nMultiply by 100%<\/td>\r\n<\/tr>\r\n
[latex]\\frac{3}{4} \\times \\frac{100}{1}\\%[\/latex]<\/td>\r\nConvert 100% to a fraction.<\/td>\r\n<\/tr>\r\n
[latex]\\frac{3}{1} \\times \\frac{25}{1}\\%[\/latex]<\/td>\r\nDivide 100 by 4. The 4 cancels and 100 is reduced to 25.<\/td>\r\n<\/tr>\r\n
[latex]3 \\times 25\\%[\/latex]<\/td>\r\nMultiply 3 by 25%.<\/td>\r\n<\/tr>\r\n
[latex]75\\%[\/latex]<\/td>\r\n<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n
<\/div>\r\n
[latex]1\\frac{1}{5} = \\text{_____}\\%[\/latex]<\/div>\r\n
\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
[latex]1\\frac{1}{5}[\/latex]<\/td>\r\n<\/td>\r\n<\/tr>\r\n
[latex]\\frac{6}{5}[\/latex]<\/td>\r\nConvert number to a fraction.<\/td>\r\n<\/tr>\r\n
[latex]\\frac{6}{5} \\times 100\\%[\/latex]<\/td>\r\nMultiply by 100%.<\/td>\r\n<\/tr>\r\n
[latex]\\frac{6}{5} \\times \\frac{100}{1}\\%[\/latex]<\/td>\r\nConvert 100% to a fraction.<\/td>\r\n<\/tr>\r\n
[latex]\\frac{6}{1} \\times \\frac{20}{1}\\%[\/latex]<\/td>\r\nDivide 100 by 5. The 5 cancels and 100 is reduced to 20.<\/td>\r\n<\/tr>\r\n
[latex]6 \\times 20\\%[\/latex]<\/td>\r\nMultiply 6 by 20%.<\/td>\r\n<\/tr>\r\n
[latex]120\\%[\/latex]<\/td>\r\n<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<\/div>\r\nThis solution can be used in Unit 2 Topic A.\r\n

Arrows<\/h1>\r\nThis author uses arrows to indicate when the student should move the decimal point to the left or right while converting between decimals and percentages, which looks like [latex] \\begin{equation}\\begin{split} &\\curvearrowright \\\\ 0&.125 \\end{split}\\end{equation}[\/latex]. This symbol isn't accessible as a screen reader does not pronounce it.\r\n

Removing the arrows and showing moved decimal point<\/h2>\r\nIn some cases, the surrounding text gives us adequate instructions or explanations so that we are able to simply remove the number with the arrow.\r\n\r\nIn this particular example, the following textbox is directly before the example:\r\n
To change a decimal to a percent, move the decimal point two places to the right and then write the percent sign after the number.<\/div>\r\n
\r\n

Example B: Original<\/p>\r\n\r\n<\/header>\r\n

Change each decimal to a percent.<\/div>\r\n
[latex]\r\n\\begin{equation}\\begin{split}\r\n&\\curvearrowright \\\\\r\n0.125=0&.125=12.5\\%\r\n\\end{split}\\end{equation}[\/latex]<\/div>\r\n
[latex]\r\n\\begin{equation}\\begin{split}\r\n&\\curvearrowright \\\\\r\n1.375=1&.375=137.5\\%\r\n\\end{split}\\end{equation}[\/latex]<\/div>\r\n<\/div>\r\n
\r\n

Example B: Proposed solution<\/p>\r\n\r\n<\/header>\r\n

Change each decimal to a percent.<\/div>\r\n
<\/div>\r\n
[latex]\r\n\\begin{equation}\\begin{split}\r\n0.125=12.5\\%\r\n\\end{split}\\end{equation}[\/latex]<\/div>\r\n
[latex]\r\n\\begin{equation}\\begin{split}\r\n1.375=137.5\\%\r\n\\end{split}\\end{equation}[\/latex]<\/div>\r\n<\/div>\r\nThis solution can be used in Unit 2 Topic A.\r\n

Removing the arrows and multiplying\/dividing by 100%<\/h2>\r\nIn some cases, it is simply enough to remove the arrows and show that the number or percentage is being multiplied or divided by 100%, respectively, since the surrounding text is enough to explain what is happening.\r\n
\r\n

Exercise 4: Original<\/p>\r\n\r\n<\/header>\r\n

\r\n\r\nChange each percent to its decimal equivalent.\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
<\/th>\r\nPercent<\/th>\r\n\u00f7 100%\r\nMove decimal 2 places to left<\/th>\r\n= Decimal<\/th>\r\n<\/tr>\r\n
A.<\/th>\r\n[latex]23\\%[\/latex]<\/td>\r\n[latex]\\begin{equation}\\begin{split}\r\n&\\curvearrowleft \\\\\r\n& \\ 23.\r\n\\end{split}\\end{equation}[\/latex]<\/td>\r\n[latex]=0.23[\/latex]<\/td>\r\n<\/tr>\r\n
B.<\/th>\r\n[latex]1\\%[\/latex]<\/td>\r\n<\/td>\r\n<\/td>\r\n<\/tr>\r\n
C.<\/th>\r\n[latex]112\\%[\/latex]<\/td>\r\n<\/td>\r\n<\/td>\r\n<\/tr>\r\n
D.<\/th>\r\n[latex]10.3\\%[\/latex]<\/td>\r\n<\/td>\r\n<\/td>\r\n<\/tr>\r\n
E.<\/th>\r\n[latex]36\\%[\/latex]<\/td>\r\n<\/td>\r\n<\/td>\r\n<\/tr>\r\n
F.<\/th>\r\n[latex]147\\%[\/latex]<\/td>\r\n<\/td>\r\n<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nAnswers to Exercise 4<\/strong>\r\n
    \r\n \t
  1. [latex]0.01[\/latex]<\/li>\r\n \t
  2. [latex]1.12[\/latex]<\/li>\r\n \t
  3. [latex]0.103[\/latex]<\/li>\r\n \t
  4. [latex]0.36[\/latex]<\/li>\r\n \t
  5. [latex]1.47[\/latex]<\/li>\r\n<\/ol>\r\n<\/div>\r\n<\/div>\r\n
    \r\n

    Exercise 4: Proposed solution<\/p>\r\n\r\n<\/header>\r\n

    \r\n\r\nChange each percent to its decimal equivalent.\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
    <\/th>\r\nPercent<\/th>\r\n\u00f7 100%\r\nMove decimal 2 places to left<\/th>\r\n= Decimal<\/th>\r\n<\/tr>\r\n
    A.<\/th>\r\n[latex]23\\%[\/latex]<\/td>\r\n[latex]23. \\div 100\\%[\/latex]<\/td>\r\n[latex]=0.23[\/latex]<\/td>\r\n<\/tr>\r\n
    B.<\/th>\r\n[latex]1\\%[\/latex]<\/td>\r\n<\/td>\r\n<\/td>\r\n<\/tr>\r\n
    C.<\/th>\r\n[latex]112\\%[\/latex]<\/td>\r\n<\/td>\r\n<\/td>\r\n<\/tr>\r\n
    D.<\/th>\r\n[latex]10.3\\%[\/latex]<\/td>\r\n<\/td>\r\n<\/td>\r\n<\/tr>\r\n
    E.<\/th>\r\n[latex]36\\%[\/latex]<\/td>\r\n<\/td>\r\n<\/td>\r\n<\/tr>\r\n
    F.<\/th>\r\n[latex]147\\%[\/latex]<\/td>\r\n<\/td>\r\n<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nAnswers to Exercise 4<\/strong>\r\n
      \r\n \t
    1. [latex]0.01[\/latex]<\/li>\r\n \t
    2. [latex]1.12[\/latex]<\/li>\r\n \t
    3. [latex]0.103[\/latex]<\/li>\r\n \t
    4. [latex]0.36[\/latex]<\/li>\r\n \t
    5. [latex]1.47[\/latex]<\/li>\r\n<\/ol>\r\n<\/div>\r\n<\/div>\r\nThis solution can be used in Unit 2 Topic A.\r\n

      Specific changes<\/h1>\r\n

      Unit 1 Topic C<\/h2>\r\nThe author uses [latex]\\dfrac{2}{5}\\rlap{\\nearrow}{\\searrow}\\dfrac{4}{10}[\/latex] to show which numbers are multiplied together when cross-multiplying. These arrows are only useful visually. I would propose to change the arrows to an equal sign as the rest of the text explains what numbers are being cross-multiplied.\r\n
      \r\n

      Original<\/h2>\r\nReview cross products:\r\n\r\n[latex]\\dfrac{2}{5}\\rlap{\\nearrow}{\\searrow}\\dfrac{4}{10}[\/latex]\r\n\r\n[latex]\r\n\\begin{equation}\r\n\\begin{split}\r\n2\\times10 & =5\\times4 \\\\\r\n20 & =20\r\n\\end{split}\r\n\\end{equation}\r\n[\/latex]\r\n\r\n[latex]2\\times10=20[\/latex] and [latex]5\\times4=20[\/latex]\r\n\r\nTherefore: [latex]\\dfrac{2}{5}=\\dfrac{4}{10}[\/latex]\r\n\r\nRemember that when the cross products are the same, the fractions are equivalent.\r\n\r\nWhen finding the missing terms in a proportion, cross-multiplication can be used. Follow the examples carefully.\r\n\r\n<\/div>\r\n
      \r\n

      Proposed solution<\/h2>\r\nReview cross products:\r\n\r\n[latex]\\dfrac{2}{5} = \\dfrac{4}{10}[\/latex] ?\r\n\r\n[latex]\r\n\\begin{equation}\r\n\\begin{split}\r\n2\\times10 & =5\\times4 \\\\\r\n20 & =20\r\n\\end{split}\r\n\\end{equation}\r\n[\/latex]\r\n\r\n[latex]2\\times10=20[\/latex] and [latex]5\\times4=20[\/latex]\r\n\r\nTherefore: [latex]\\dfrac{2}{5}=\\dfrac{4}{10}[\/latex]\r\n\r\nRemember that when the cross products are the same, the fractions are equivalent.\r\n\r\nWhen finding the missing terms in a proportion, cross-multiplication can be used. Follow the examples carefully.\r\n\r\n<\/div>\r\n

      Unit 2, Topic A - 1<\/h2>\r\nThe author uses downward arrows that line up with the words fractions, decimals, and percents to show examples of what equivalent fractions, decimals, and percents look like. These are not read out correctly and is a purely visual shorthand. My proposed solution is to place it in a table after the text.\r\n
      \r\n

      Original<\/h2>\r\nWriting equivalent fractions is an important math skill.\r\n[latex]\\begin{equation}\\begin{split}\r\n\\text{Equivalent common } &\\text{fractions, } &\\text{decimals, and } &\\text{percents all represent the same amount} \\\\\r\n&\\downarrow &\\downarrow &\\downarrow \\\\\r\n&\\tfrac{1}{2} = &0.5 = &50\\% \\\\\r\n&\\tfrac{3}{10} = &0.3 = &30\\%\r\n\\end{split}\\end{equation}[\/latex]\r\n\r\n<\/div>\r\n
      \r\n

      Proposed solution<\/h2>\r\nWriting equivalent fractions is an important math skill.\r\n\r\nEquivalent common fractions, decimals, and percents all represent the same amount.\r\n\r\n\r\n\r\n\r\n
      Equivalent fractions, decimals, and percentages<\/caption>\r\n
      Fractions<\/th>\r\nDecimals<\/th>\r\nPercentages<\/th>\r\n<\/tr>\r\n
      [latex]\\frac{1}{2}[\/latex]<\/td>\r\n[latex]0.5[\/latex]<\/td>\r\n[latex]50\\%[\/latex]<\/td>\r\n<\/tr>\r\n
      [latex]\\frac{3}{10}[\/latex]<\/td>\r\n[latex]0.3[\/latex]<\/td>\r\n[latex]30\\%[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n

      Unit 2 Topic A - 2<\/h2>\r\nIn this case, both arrows and crosses are used. In this case, I would put the equations into a table along with text to better explain solution.\r\n
      \r\n

      Original<\/h2>\r\nIf the decimal point moves to the end of the number it is not necessary to write the decimal point. Remember that zeros at the beginning of a number are also not necessary.\r\n\r\n[latex]\r\n\\begin{equation}\\begin{split}\r\n&\\curvearrowright \\\\\r\n0.24=0&.24=\\cancel{0}24\\%=24\\%\r\n\\end{split}\\end{equation}[\/latex]\r\n\r\n[latex]\r\n\\begin{equation}\\begin{split}\r\n&\\curvearrowright \\\\\r\n0.05=0&.05=\\cancel{00}5\\%=5\\%\r\n\\end{split}\\end{equation}[\/latex]\r\n\r\n<\/div>\r\n
      \r\n

      Proposed solution<\/h2>\r\nIf the decimal point moves to the end of the number it is not necessary to write the decimal point. Remember that zeros at the beginning of a number are also not necessary.\r\n\r\n\r\n\r\n\r\n
      Convert 0.24 to a percentage<\/caption>\r\n
      [latex]0.24[\/latex]<\/td>\r\n<\/td>\r\n<\/tr>\r\n
      [latex]24.00\\%[\/latex]<\/td>\r\nMove decimal point two places to the right and add percent sign.<\/td>\r\n<\/tr>\r\n
      [latex]24\\%[\/latex]<\/td>\r\nRemove unnecessary zeros.<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n\r\n\r\n\r\n\r\n
      Convert 0.05 to a percentage<\/caption>\r\n
      [latex]0.05[\/latex]<\/td>\r\n<\/td>\r\n<\/tr>\r\n
      [latex]5.00\\%[\/latex]<\/td>\r\nMove decimal point two places to the right and add percent sign.<\/td>\r\n<\/tr>\r\n
      [latex]5\\%[\/latex]<\/td>\r\nRemove unnecessary zeros.<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n \r\n\r\n<\/div>\r\n

      Unit 2, Topic A - 3<\/h2>\r\nThe long division in this example does not show up in either the PDF version correctly nor is it accessible for screen readers. I am unsure of alternatives other than reinserting it as an image with alt text.\r\n\r\nAs for the rest of the equation, I would put everything into a table, adding text explanation where necessary. I'd also remove the arrow when moving the decimal point.\r\n
      \r\n

      Original<\/h2>\r\n[latex]\\begin{equation}\\begin{split}\r\n&\u00a0 & \\ \\ 0.375 &\\hspace{3.9cm}\\curvearrowright \\\\\r\n\\tfrac{3}{8} &= \\text{_____}\\% \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ 8&\\overline{\\smash{)}3.000} \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ 0&\\tfrac{3}{8}=0.375\\hspace{1.5cm}0.375=37.5\\% \\\\\r\n&\u00a0 & \\ \\ 2 \\ 4 \\smash{\\downarrow}\\smash{\\downarrow} \\\\\r\n&\u00a0 &\u00a0 \\ \\ \\ \\ \\ 60 \\smash{\\downarrow} \\\\\r\n&\u00a0 &\u00a0 \\ \\ \\ \\ \\ \\underline{56} \\smash{\\downarrow} \\\\\r\n&\u00a0 &\u00a0 \\ \\ \\ \\ \\ \\ \\ 40\r\n\\end{split}\\end{equation}[\/latex]\r\n\r\n \r\n\r\n[latex]\\begin{equation}\\begin{split}\r\n&\u00a0 & \\ \\ 0.33\\overline{3} &\\curvearrowright \\\\\r\n\\tfrac{1}{3} &= \\text{_____}\\% \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ 3&\\overline{\\smash{)}1.000} \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ 0&.33\\overline{3}=33.\\overline{3}\\% \\\\\r\n&\u00a0 &\u00a0 &\\text{also written as }33\\tfrac{1}{3}\\%\r\n\\end{split}\\end{equation}[\/latex]\r\n\r\n \r\n\r\n[latex]\\begin{equation}\\begin{split}\r\n&\u00a0 &\u00a0 \\ \\ \\ \\ 0.916\\overline{6} &\\curvearrowright \\\\\r\n\\tfrac{11}{12} &= \\text{_____}\\% \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ 12&\\overline{\\smash{)}11.000} \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ 0&.91\\overline{6}=91.\\overline{6}\\% \\\\\r\n&\u00a0 & \\ \\ 10 \\ 8 \\smash{\\downarrow}\\smash{\\downarrow} \\\\\r\n&\u00a0 &\u00a0 \\ \\ \\ \\ \\ \\ \\ 20 \\smash{\\downarrow} \\\\\r\n&\u00a0 &\u00a0 \\ \\ \\ \\ \\ \\ \\ 12 \\smash{\\downarrow} \\\\\r\n&\u00a0 &\u00a0 \\ \\ \\ \\ \\ \\ \\ \\ \\ 80 \\\\\r\n&\u00a0 &\u00a0 \\ \\ \\ \\ \\ \\ \\ \\ \\ \\underline{72} \\\\\r\n&\u00a0 &\u00a0 \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ 8\r\n\\end{split}\\end{equation}[\/latex]\r\n\r\n<\/div>\r\n
      \r\n

      Proposed solution<\/h2>\r\n\r\n\r\n\r\n\r\n\r\n
      Convert [latex]\\frac{3}{8}[\/latex] to a percentage<\/caption>\r\n
      [latex]\\frac{3}{8} = \\text{_____}\\%[\/latex]<\/td>\r\n<\/td>\r\n<\/tr>\r\n
      \"equation<\/td>\r\nUse long division to write fraction as a decimal.<\/td>\r\n<\/tr>\r\n
      [latex]\\frac{3}{8} = 0.375[\/latex]<\/td>\r\n<\/td>\r\n<\/tr>\r\n
      [latex]0.375 = 37.5\\%[\/latex]<\/td>\r\nMove the decimal point two places to the right and add the percent sign.<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n \r\n\r\n\r\n\r\n\r\n\r\n
      Convert [latex]\\frac{1}{3}[\/latex] to a percentage<\/caption>\r\n
      [latex]\\frac{1}{3} = \\text{_____}\\%[\/latex]<\/td>\r\n<\/td>\r\n<\/tr>\r\n
      \"equation<\/td>\r\nUse long division to write fraction as a decimal.<\/td>\r\n<\/tr>\r\n
      [latex]\\frac{1}{3} = 0.33\\overline{3}[\/latex]<\/td>\r\n<\/td>\r\n<\/tr>\r\n
      [latex]0.33\\overline{3}=33.\\overline{3}\\% \\text{ also written as } 33\\frac{1}{3}\\%[\/latex]<\/td>\r\nMove the decimal point two places to the right and add the percent sign.<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n \r\n\r\n\r\n\r\n\r\n\r\n
      Convert [latex]\\frac{11}{12}[\/latex] to a percentage<\/caption>\r\n
      [latex]\\frac{11}{12} = \\text{_____}\\%[\/latex]<\/td>\r\n<\/td>\r\n<\/tr>\r\n
      \"equation<\/td>\r\nUse long division to write fraction as a decimal.<\/td>\r\n<\/tr>\r\n
      [latex]\\frac{11}{12} = 0.91\\overline{6}[\/latex]<\/td>\r\n<\/td>\r\n<\/tr>\r\n
      [latex]0.916\\overline{6} = 91.\\overline{6}\\%[\/latex]<\/td>\r\n\u00a0Move the decimal point two places to the right and add the percent sign.<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n \r\n\r\n<\/div>\r\n

      Unit 2 Topic A - 4<\/h2>\r\nThe long division in this example does not show up in either the PDF version correctly nor is it accessible for screen readers. I am unsure of alternatives other than reinserting it as an image with alt text.\r\n\r\nAs for the rest of the equation, I would simply remove it from the {equation} and simply have it in simple LaTeX.\r\n
      \r\n

      Original<\/h2>\r\n[latex]\\begin{equation}\\begin{split}\r\n&\u00a0 \\ \\ \\ \\ \\ \\ 1 \\\\\r\n110\\%=\\tfrac{110}{100}=1\\tfrac{10}{100}=1\\tfrac{1}{10} \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ 100&\\overline{\\smash{)}110} \\\\\r\n&\u00a0 \\ \\ \\underline{100} \\\\\r\n&\u00a0 \\ \\ \\ \\ 10\r\n\\end{split}\\end{equation}[\/latex]\r\n\r\n[latex]\\begin{equation}\\begin{split}\r\n&\u00a0 \\ \\ \\ \\ \\ \\ 1 \\\\\r\n120\\%=\\tfrac{120}{100}=1\\tfrac{20}{100}=1\\tfrac{1}{5} \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ 100&\\overline{\\smash{)}120} \\\\\r\n&\u00a0 \\ \\ \\underline{100} \\\\\r\n&\u00a0 \\ \\ \\ \\ 20\r\n\\end{split}\\end{equation}[\/latex]\r\n\r\nRemember 100% is the whole thing. [latex]100\\%=1[\/latex].\r\n\r\n<\/div>\r\n
      \r\n

      Proposed Solution<\/h2>\r\n[latex]110\\%=\\tfrac{110}{100}=1\\tfrac{10}{100}=1\\tfrac{1}{10}[\/latex] \"equation\r\n\r\n[latex]120\\%=\\tfrac{120}{100}=1\\tfrac{20}{100}=1\\tfrac{1}{5}[\/latex] \"equation\r\n\r\nRemember 100% is the whole thing. [latex]100\\%=1[\/latex].\r\n\r\n<\/div>","rendered":"

      *Note: For this to chapter to display properly, QuickLaTeX plugin must be deactivated.<\/p>\n

      This chapter details the issues and proposed changes from the Adult Literacy Fundamental Mathematics \u2013 Book 6<\/a>.<\/p>\n

      The following solutions work with Apple’s screen reading software. Other screen readers have not been tested.<\/p>\n

      Operands within fractions<\/h1>\n

      There are several examples as well as Exercises that use the format [latex]\\dfrac{4}{5}\\left(\\dfrac{\\times2}{\\times2}\\right)[\/latex]. The two multiplication signs within the parenthesis are not read out correctly. The proposed change is to move the multiplication (or division sign in some cases) outside the parentheses.<\/p>\n

      \n
      \n

      Example A: Original<\/p>\n<\/header>\n

      \n

      Express [latex]4:5[\/latex] in higher terms.<\/p>\n

      [latex]4:5=\\dfrac{4}{5}\\longrightarrow\\dfrac{4}{5}\\times\\left(\\dfrac{\\times2}{\\times2}\\right)\\longrightarrow\\dfrac{8}{10}[\/latex]<\/p>\n

      [latex]4:5[\/latex] is equivalent to [latex]8:10[\/latex]<\/p>\n<\/div>\n<\/div>\n

      \n
      \n

      Example A: Proposed solution<\/p>\n<\/header>\n

      \n

      Express [latex]4:5[\/latex] in higher terms.<\/p>\n

      [latex]4:5=\\dfrac{4}{5}\\longrightarrow\\dfrac{4}{5}\\times\\left(\\dfrac{2}{2}\\right)\\longrightarrow\\dfrac{8}{10}[\/latex]<\/p>\n

      [latex]4:5[\/latex] is equivalent to [latex]8:10[\/latex]<\/p>\n<\/div>\n<\/div>\n

      \n
      \n

      Example A: Edited proposed solution<\/p>\n<\/header>\n

      \n

      Express [latex]4:5[\/latex] in higher terms.<\/p>\n

      [latex]4:5=\\dfrac{4}{5}\\longrightarrow\\dfrac{4}{5}\\times\\left(\\dfrac{2}{2}\\right)\\longrightarrow \\dfrac{4\\times2}{5\\times2}\\longrightarrow\\dfrac{8}{10}[\/latex]<\/p>\n

      [latex]4:5[\/latex] is equivalent to [latex]8:10[\/latex]<\/p>\n<\/div>\n<\/div>\n

      This issue is seen in Unit 1 (Topic A, B, C).<\/p>\n

      Crossed-off numbers when simplifying equations<\/h1>\n

      Frequently, the book shows numbers or variables being struck through as a visual shorthand to show the number being reduced through simplification of fractions, such as [latex]\\begin{equation}\\begin{split} \\dfrac{\\cancel{6}\\textit{N}}{\\cancel{6}}\\end{split}\\end{equation}[\/latex]. The screenreader doesn’t acknowledge this strike through (\\cancel command) and simply reads the number as normal.<\/p>\n

      Adding an extra equation<\/h2>\n

      In most cases, the surrounding text provides enough context that we can simply add an extra equation that shows the equation before and after simplification, like the example below.<\/p>\n

      \n
      \n

      Example B: Original<\/p>\n<\/header>\n

      \n

      [latex]\\dfrac{6}{7}=\\dfrac{24}{\\textit{N}}[\/latex]<\/p>\n

      Cross multiply:
      \n[latex]\\begin{equation}\\begin{split} 6\\times\\textit{N} &= 7\\times24 \\\\ 6\\textit{N} &= 168 \\end{split}\\end{equation}[\/latex]
      \nDivide both sides by 6. The 6’s with the N<\/em> will cancel (reduce), and the N<\/em> will be alone.
      \n[latex]\\begin{equation}\\begin{split} \\dfrac{\\cancel{6}\\textit{N}}{\\cancel{6}} &= \\dfrac{168}{6} \\\\ \\\\ \\textit{N} &= 168\\div6 \\\\ \\\\ \\textit{N} &= 28 \\\\ \\\\ \\dfrac{6}{7} &= \\dfrac{24}{28} \\end{split}\\end{equation}[\/latex]
      \nCheck by cross-multiplying:
      \n[latex]\\begin{equation}\\begin{split} \\text{Is }6\\times28 &= 7\\times24? \\\\ 6\\times28 &= 168 \\\\ 7\\times24 &= 168 \\\\ \\text{the cross-product }168 &= \\text{the cross-product }168 \\\\ \\text{Yes - }6:7 &= 24:28 \\end{split}\\end{equation}[\/latex]<\/p>\n<\/div>\n<\/div>\n

      \n
      \n

      Example B: Proposed solution<\/p>\n<\/header>\n

      \n

      [latex]\\dfrac{6}{7}=\\dfrac{24}{\\textit{N}}[\/latex]<\/p>\n

      Cross multiply:
      \n[latex]\\begin{equation}\\begin{split} 6\\times\\textit{N} &= 7\\times24 \\\\ 6\\textit{N} &= 168 \\end{split}\\end{equation}[\/latex]
      \nDivide both sides by 6. The 6’s with the N<\/em> will cancel (reduce), and the N<\/em> will be alone.
      \n[latex]\\begin{equation}\\begin{split} \\dfrac{{6}\\textit{N}}{{6}} &= \\dfrac{168}{6} \\\\ \\\\ N &=\\dfrac{168}{6} \\\\ \\\\ \\textit{N} &= 168\\div6 \\\\ \\\\ \\textit{N} &= 28 \\\\ \\\\ \\dfrac{6}{7} &= \\dfrac{24}{28} \\end{split}\\end{equation}[\/latex]
      \nCheck by cross-multiplying:
      \n[latex]\\begin{equation}\\begin{split} \\text{Is }6\\times28 &= 7\\times24? \\\\ 6\\times28 &= 168 \\\\ 7\\times24 &= 168 \\\\ \\text{the cross-product }168 &= \\text{the cross-product }168 \\\\ \\text{Yes - }6:7 &= 24:28 \\end{split}\\end{equation}[\/latex]<\/p>\n<\/div>\n<\/div>\n

      This solution can be used in Units 1 Topic C, Unit 2 Topic A, Unit 3 Topic A, Unit 4 Topic A.<\/p>\n

      Adding an additional text explanation<\/h2>\n

      In other cases, more explanation may be necessary. In this case, we’ll opt to put the equation into a table so we can provide more of an explanation when we remove the strike-throughs.<\/p>\n

      \n
      \n

      Example A: Original<\/p>\n<\/header>\n

      [latex]\\begin{equation}\\begin{split} \\frac{3}{4} &= \\text{_____}\\% \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ &\\frac{3}{4} &\\times 100\\% \\ &= \\frac{3}{\\cancel{4} 1} &\\times \\frac{\\cancel{100} 25}{1} \\ &= 75\\% \\\\ 1\\frac{1}{5} &= \\text{_____}\\% \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ 1&\\frac{1}{5} &\\times 100\\% \\ &= \\frac{6}{\\cancel{5} 1} &\\times \\frac{\\cancel{120} 20}{1} \\ &= 120\\% \\end{split}\\end{equation}[\/latex]<\/div>\n<\/div>\n
      \n
      \n

      Example A: Proposed solution<\/p>\n<\/header>\n

      [latex]\\frac{3}{4} = \\text{_____}\\%[\/latex]<\/div>\n
      \n\n\n\n\n\n\n\n\n
      [latex]\\frac{3}{4}[\/latex]<\/td>\n<\/td>\n<\/tr>\n
      [latex]\\frac{3}{4} \\times 100\\%[\/latex]<\/td>\nMultiply by 100%<\/td>\n<\/tr>\n
      [latex]\\frac{3}{4} \\times \\frac{100}{1}\\%[\/latex]<\/td>\nConvert 100% to a fraction.<\/td>\n<\/tr>\n
      [latex]\\frac{3}{1} \\times \\frac{25}{1}\\%[\/latex]<\/td>\nDivide 100 by 4. The 4 cancels and 100 is reduced to 25.<\/td>\n<\/tr>\n
      [latex]3 \\times 25\\%[\/latex]<\/td>\nMultiply 3 by 25%.<\/td>\n<\/tr>\n
      [latex]75\\%[\/latex]<\/td>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n
      <\/div>\n
      [latex]1\\frac{1}{5} = \\text{_____}\\%[\/latex]<\/div>\n
      \n\n\n\n\n\n\n\n\n\n
      [latex]1\\frac{1}{5}[\/latex]<\/td>\n<\/td>\n<\/tr>\n
      [latex]\\frac{6}{5}[\/latex]<\/td>\nConvert number to a fraction.<\/td>\n<\/tr>\n
      [latex]\\frac{6}{5} \\times 100\\%[\/latex]<\/td>\nMultiply by 100%.<\/td>\n<\/tr>\n
      [latex]\\frac{6}{5} \\times \\frac{100}{1}\\%[\/latex]<\/td>\nConvert 100% to a fraction.<\/td>\n<\/tr>\n
      [latex]\\frac{6}{1} \\times \\frac{20}{1}\\%[\/latex]<\/td>\nDivide 100 by 5. The 5 cancels and 100 is reduced to 20.<\/td>\n<\/tr>\n
      [latex]6 \\times 20\\%[\/latex]<\/td>\nMultiply 6 by 20%.<\/td>\n<\/tr>\n
      [latex]120\\%[\/latex]<\/td>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n

      This solution can be used in Unit 2 Topic A.<\/p>\n

      Arrows<\/h1>\n

      This author uses arrows to indicate when the student should move the decimal point to the left or right while converting between decimals and percentages, which looks like [latex]\\begin{equation}\\begin{split} &\\curvearrowright \\\\ 0&.125 \\end{split}\\end{equation}[\/latex]. This symbol isn’t accessible as a screen reader does not pronounce it.<\/p>\n

      Removing the arrows and showing moved decimal point<\/h2>\n

      In some cases, the surrounding text gives us adequate instructions or explanations so that we are able to simply remove the number with the arrow.<\/p>\n

      In this particular example, the following textbox is directly before the example:<\/p>\n

      To change a decimal to a percent, move the decimal point two places to the right and then write the percent sign after the number.<\/div>\n
      \n
      \n

      Example B: Original<\/p>\n<\/header>\n

      Change each decimal to a percent.<\/div>\n
      [latex]\\begin{equation}\\begin{split} &\\curvearrowright \\\\ 0.125=0&.125=12.5\\% \\end{split}\\end{equation}[\/latex]<\/div>\n
      [latex]\\begin{equation}\\begin{split} &\\curvearrowright \\\\ 1.375=1&.375=137.5\\% \\end{split}\\end{equation}[\/latex]<\/div>\n<\/div>\n
      \n
      \n

      Example B: Proposed solution<\/p>\n<\/header>\n

      Change each decimal to a percent.<\/div>\n
      <\/div>\n
      [latex]\\begin{equation}\\begin{split} 0.125=12.5\\% \\end{split}\\end{equation}[\/latex]<\/div>\n
      [latex]\\begin{equation}\\begin{split} 1.375=137.5\\% \\end{split}\\end{equation}[\/latex]<\/div>\n<\/div>\n

      This solution can be used in Unit 2 Topic A.<\/p>\n

      Removing the arrows and multiplying\/dividing by 100%<\/h2>\n

      In some cases, it is simply enough to remove the arrows and show that the number or percentage is being multiplied or divided by 100%, respectively, since the surrounding text is enough to explain what is happening.<\/p>\n

      \n
      \n

      Exercise 4: Original<\/p>\n<\/header>\n

      \n

      Change each percent to its decimal equivalent.<\/p>\n\n\n\n\n\n\n\n\n\n
      <\/th>\nPercent<\/th>\n\u00f7 100%
      \nMove decimal 2 places to left<\/th>\n      		= Decimal<\/th>\n<\/tr>\n
      A.<\/th>\n[latex]23\\%[\/latex]<\/td>\n[latex]\\begin{equation}\\begin{split} &\\curvearrowleft \\\\ & \\ 23. \\end{split}\\end{equation}[\/latex]<\/td>\n[latex]=0.23[\/latex]<\/td>\n<\/tr>\n
      B.<\/th>\n[latex]1\\%[\/latex]<\/td>\n<\/td>\n<\/td>\n<\/tr>\n
      C.<\/th>\n[latex]112\\%[\/latex]<\/td>\n<\/td>\n<\/td>\n<\/tr>\n
      D.<\/th>\n[latex]10.3\\%[\/latex]<\/td>\n<\/td>\n<\/td>\n<\/tr>\n
      E.<\/th>\n[latex]36\\%[\/latex]<\/td>\n<\/td>\n<\/td>\n<\/tr>\n
      F.<\/th>\n[latex]147\\%[\/latex]<\/td>\n<\/td>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

      Answers to Exercise 4<\/strong><\/p>\n

        \n
      1. [latex]0.01[\/latex]<\/li>\n
      2. [latex]1.12[\/latex]<\/li>\n
      3. [latex]0.103[\/latex]<\/li>\n
      4. [latex]0.36[\/latex]<\/li>\n
      5. [latex]1.47[\/latex]<\/li>\n<\/ol>\n<\/div>\n<\/div>\n
        \n
        \n

        Exercise 4: Proposed solution<\/p>\n<\/header>\n

        \n

        Change each percent to its decimal equivalent.<\/p>\n\n\n\n\n\n\n\n\n\n
        <\/th>\nPercent<\/th>\n\u00f7 100%
        \nMove decimal 2 places to left<\/th>\n        		= Decimal<\/th>\n<\/tr>\n
        A.<\/th>\n[latex]23\\%[\/latex]<\/td>\n[latex]23. \\div 100\\%[\/latex]<\/td>\n[latex]=0.23[\/latex]<\/td>\n<\/tr>\n
        B.<\/th>\n[latex]1\\%[\/latex]<\/td>\n<\/td>\n<\/td>\n<\/tr>\n
        C.<\/th>\n[latex]112\\%[\/latex]<\/td>\n<\/td>\n<\/td>\n<\/tr>\n
        D.<\/th>\n[latex]10.3\\%[\/latex]<\/td>\n<\/td>\n<\/td>\n<\/tr>\n
        E.<\/th>\n[latex]36\\%[\/latex]<\/td>\n<\/td>\n<\/td>\n<\/tr>\n
        F.<\/th>\n[latex]147\\%[\/latex]<\/td>\n<\/td>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

        Answers to Exercise 4<\/strong><\/p>\n

          \n
        1. [latex]0.01[\/latex]<\/li>\n
        2. [latex]1.12[\/latex]<\/li>\n
        3. [latex]0.103[\/latex]<\/li>\n
        4. [latex]0.36[\/latex]<\/li>\n
        5. [latex]1.47[\/latex]<\/li>\n<\/ol>\n<\/div>\n<\/div>\n

          This solution can be used in Unit 2 Topic A.<\/p>\n

          Specific changes<\/h1>\n

          Unit 1 Topic C<\/h2>\n

          The author uses [latex]\\dfrac{2}{5}\\rlap{\\nearrow}{\\searrow}\\dfrac{4}{10}[\/latex] to show which numbers are multiplied together when cross-multiplying. These arrows are only useful visually. I would propose to change the arrows to an equal sign as the rest of the text explains what numbers are being cross-multiplied.<\/p>\n

          \n

          Original<\/h2>\n

          Review cross products:<\/p>\n

          [latex]\\dfrac{2}{5}\\rlap{\\nearrow}{\\searrow}\\dfrac{4}{10}[\/latex]<\/p>\n

          [latex]\\begin{equation} \\begin{split} 2\\times10 & =5\\times4 \\\\ 20 & =20 \\end{split} \\end{equation}[\/latex]<\/p>\n

          [latex]2\\times10=20[\/latex] and [latex]5\\times4=20[\/latex]<\/p>\n

          Therefore: [latex]\\dfrac{2}{5}=\\dfrac{4}{10}[\/latex]<\/p>\n

          Remember that when the cross products are the same, the fractions are equivalent.<\/p>\n

          When finding the missing terms in a proportion, cross-multiplication can be used. Follow the examples carefully.<\/p>\n<\/div>\n

          \n

          Proposed solution<\/h2>\n

          Review cross products:<\/p>\n

          [latex]\\dfrac{2}{5} = \\dfrac{4}{10}[\/latex] ?<\/p>\n

          [latex]\\begin{equation} \\begin{split} 2\\times10 & =5\\times4 \\\\ 20 & =20 \\end{split} \\end{equation}[\/latex]<\/p>\n

          [latex]2\\times10=20[\/latex] and [latex]5\\times4=20[\/latex]<\/p>\n

          Therefore: [latex]\\dfrac{2}{5}=\\dfrac{4}{10}[\/latex]<\/p>\n

          Remember that when the cross products are the same, the fractions are equivalent.<\/p>\n

          When finding the missing terms in a proportion, cross-multiplication can be used. Follow the examples carefully.<\/p>\n<\/div>\n

          Unit 2, Topic A – 1<\/h2>\n

          The author uses downward arrows that line up with the words fractions, decimals, and percents to show examples of what equivalent fractions, decimals, and percents look like. These are not read out correctly and is a purely visual shorthand. My proposed solution is to place it in a table after the text.<\/p>\n

          \n

          Original<\/h2>\n

          Writing equivalent fractions is an important math skill.
          \n[latex]\\begin{equation}\\begin{split} \\text{Equivalent common } &\\text{fractions, } &\\text{decimals, and } &\\text{percents all represent the same amount} \\\\ &\\downarrow &\\downarrow &\\downarrow \\\\ &\\tfrac{1}{2} = &0.5 = &50\\% \\\\ &\\tfrac{3}{10} = &0.3 = &30\\% \\end{split}\\end{equation}[\/latex]<\/p>\n<\/div>\n

          \n

          Proposed solution<\/h2>\n

          Writing equivalent fractions is an important math skill.<\/p>\n

          Equivalent common fractions, decimals, and percents all represent the same amount.<\/p>\n\n\n\n\n\n
          Equivalent fractions, decimals, and percentages<\/caption>\n
          Fractions<\/th>\nDecimals<\/th>\nPercentages<\/th>\n<\/tr>\n
          [latex]\\frac{1}{2}[\/latex]<\/td>\n[latex]0.5[\/latex]<\/td>\n[latex]50\\%[\/latex]<\/td>\n<\/tr>\n
          [latex]\\frac{3}{10}[\/latex]<\/td>\n[latex]0.3[\/latex]<\/td>\n[latex]30\\%[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n

          Unit 2 Topic A – 2<\/h2>\n

          In this case, both arrows and crosses are used. In this case, I would put the equations into a table along with text to better explain solution.<\/p>\n

          \n

          Original<\/h2>\n

          If the decimal point moves to the end of the number it is not necessary to write the decimal point. Remember that zeros at the beginning of a number are also not necessary.<\/p>\n

          [latex]\\begin{equation}\\begin{split} &\\curvearrowright \\\\ 0.24=0&.24=\\cancel{0}24\\%=24\\% \\end{split}\\end{equation}[\/latex]<\/p>\n

          [latex]\\begin{equation}\\begin{split} &\\curvearrowright \\\\ 0.05=0&.05=\\cancel{00}5\\%=5\\% \\end{split}\\end{equation}[\/latex]<\/p>\n<\/div>\n

          \n

          Proposed solution<\/h2>\n

          If the decimal point moves to the end of the number it is not necessary to write the decimal point. Remember that zeros at the beginning of a number are also not necessary.<\/p>\n\n\n\n\n\n
          Convert 0.24 to a percentage<\/caption>\n
          [latex]0.24[\/latex]<\/td>\n<\/td>\n<\/tr>\n
          [latex]24.00\\%[\/latex]<\/td>\nMove decimal point two places to the right and add percent sign.<\/td>\n<\/tr>\n
          [latex]24\\%[\/latex]<\/td>\nRemove unnecessary zeros.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n\n\n\n\n\n
          Convert 0.05 to a percentage<\/caption>\n
          [latex]0.05[\/latex]<\/td>\n<\/td>\n<\/tr>\n
          [latex]5.00\\%[\/latex]<\/td>\nMove decimal point two places to the right and add percent sign.<\/td>\n<\/tr>\n
          [latex]5\\%[\/latex]<\/td>\nRemove unnecessary zeros.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

           <\/p>\n<\/div>\n

          Unit 2, Topic A – 3<\/h2>\n

          The long division in this example does not show up in either the PDF version correctly nor is it accessible for screen readers. I am unsure of alternatives other than reinserting it as an image with alt text.<\/p>\n

          As for the rest of the equation, I would put everything into a table, adding text explanation where necessary. I’d also remove the arrow when moving the decimal point.<\/p>\n

          \n

          Original<\/h2>\n

          [latex]\\begin{equation}\\begin{split} &\u00a0 & \\ \\ 0.375 &\\hspace{3.9cm}\\curvearrowright \\\\ \\tfrac{3}{8} &= \\text{_____}\\% \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ 8&\\overline{\\smash{)}3.000} \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ 0&\\tfrac{3}{8}=0.375\\hspace{1.5cm}0.375=37.5\\% \\\\ &\u00a0 & \\ \\ 2 \\ 4 \\smash{\\downarrow}\\smash{\\downarrow} \\\\ &\u00a0 &\u00a0 \\ \\ \\ \\ \\ 60 \\smash{\\downarrow} \\\\ &\u00a0 &\u00a0 \\ \\ \\ \\ \\ \\underline{56} \\smash{\\downarrow} \\\\ &\u00a0 &\u00a0 \\ \\ \\ \\ \\ \\ \\ 40 \\end{split}\\end{equation}[\/latex]<\/p>\n

           <\/p>\n

          [latex]\\begin{equation}\\begin{split} &\u00a0 & \\ \\ 0.33\\overline{3} &\\curvearrowright \\\\ \\tfrac{1}{3} &= \\text{_____}\\% \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ 3&\\overline{\\smash{)}1.000} \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ 0&.33\\overline{3}=33.\\overline{3}\\% \\\\ &\u00a0 &\u00a0 &\\text{also written as }33\\tfrac{1}{3}\\% \\end{split}\\end{equation}[\/latex]<\/p>\n

           <\/p>\n

          [latex]\\begin{equation}\\begin{split} &\u00a0 &\u00a0 \\ \\ \\ \\ 0.916\\overline{6} &\\curvearrowright \\\\ \\tfrac{11}{12} &= \\text{_____}\\% \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ 12&\\overline{\\smash{)}11.000} \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ 0&.91\\overline{6}=91.\\overline{6}\\% \\\\ &\u00a0 & \\ \\ 10 \\ 8 \\smash{\\downarrow}\\smash{\\downarrow} \\\\ &\u00a0 &\u00a0 \\ \\ \\ \\ \\ \\ \\ 20 \\smash{\\downarrow} \\\\ &\u00a0 &\u00a0 \\ \\ \\ \\ \\ \\ \\ 12 \\smash{\\downarrow} \\\\ &\u00a0 &\u00a0 \\ \\ \\ \\ \\ \\ \\ \\ \\ 80 \\\\ &\u00a0 &\u00a0 \\ \\ \\ \\ \\ \\ \\ \\ \\ \\underline{72} \\\\ &\u00a0 &\u00a0 \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ 8 \\end{split}\\end{equation}[\/latex]<\/p>\n<\/div>\n

          \n

          Proposed solution<\/h2>\n\n\n\n\n\n\n
          Convert [latex]\\frac{3}{8}[\/latex] to a percentage<\/caption>\n
          [latex]\\frac{3}{8} = \\text{_____}\\%[\/latex]<\/td>\n<\/td>\n<\/tr>\n
          \"equation<\/td>\nUse long division to write fraction as a decimal.<\/td>\n<\/tr>\n
          [latex]\\frac{3}{8} = 0.375[\/latex]<\/td>\n<\/td>\n<\/tr>\n
          [latex]0.375 = 37.5\\%[\/latex]<\/td>\nMove the decimal point two places to the right and add the percent sign.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

           <\/p>\n\n\n\n\n\n\n
          Convert [latex]\\frac{1}{3}[\/latex] to a percentage<\/caption>\n
          [latex]\\frac{1}{3} = \\text{_____}\\%[\/latex]<\/td>\n<\/td>\n<\/tr>\n
          \"equation<\/td>\nUse long division to write fraction as a decimal.<\/td>\n<\/tr>\n
          [latex]\\frac{1}{3} = 0.33\\overline{3}[\/latex]<\/td>\n<\/td>\n<\/tr>\n
          [latex]0.33\\overline{3}=33.\\overline{3}\\% \\text{ also written as } 33\\frac{1}{3}\\%[\/latex]<\/td>\nMove the decimal point two places to the right and add the percent sign.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

           <\/p>\n\n\n\n\n\n\n
          Convert [latex]\\frac{11}{12}[\/latex] to a percentage<\/caption>\n
          [latex]\\frac{11}{12} = \\text{_____}\\%[\/latex]<\/td>\n<\/td>\n<\/tr>\n
          \"equation<\/td>\nUse long division to write fraction as a decimal.<\/td>\n<\/tr>\n
          [latex]\\frac{11}{12} = 0.91\\overline{6}[\/latex]<\/td>\n<\/td>\n<\/tr>\n
          [latex]0.916\\overline{6} = 91.\\overline{6}\\%[\/latex]<\/td>\n\u00a0Move the decimal point two places to the right and add the percent sign.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

           <\/p>\n<\/div>\n

          Unit 2 Topic A – 4<\/h2>\n

          The long division in this example does not show up in either the PDF version correctly nor is it accessible for screen readers. I am unsure of alternatives other than reinserting it as an image with alt text.<\/p>\n

          As for the rest of the equation, I would simply remove it from the {equation} and simply have it in simple LaTeX.<\/p>\n

          \n

          Original<\/h2>\n

          [latex]\\begin{equation}\\begin{split} &\u00a0 \\ \\ \\ \\ \\ \\ 1 \\\\ 110\\%=\\tfrac{110}{100}=1\\tfrac{10}{100}=1\\tfrac{1}{10} \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ 100&\\overline{\\smash{)}110} \\\\ &\u00a0 \\ \\ \\underline{100} \\\\ &\u00a0 \\ \\ \\ \\ 10 \\end{split}\\end{equation}[\/latex]<\/p>\n

          [latex]\\begin{equation}\\begin{split} &\u00a0 \\ \\ \\ \\ \\ \\ 1 \\\\ 120\\%=\\tfrac{120}{100}=1\\tfrac{20}{100}=1\\tfrac{1}{5} \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ 100&\\overline{\\smash{)}120} \\\\ &\u00a0 \\ \\ \\underline{100} \\\\ &\u00a0 \\ \\ \\ \\ 20 \\end{split}\\end{equation}[\/latex]<\/p>\n

          Remember 100% is the whole thing. [latex]100\\%=1[\/latex].<\/p>\n<\/div>\n

          \n

          Proposed Solution<\/h2>\n

          [latex]110\\%=\\tfrac{110}{100}=1\\tfrac{10}{100}=1\\tfrac{1}{10}[\/latex] \"equation<\/p>\n

          [latex]120\\%=\\tfrac{120}{100}=1\\tfrac{20}{100}=1\\tfrac{1}{5}[\/latex] \"equation<\/p>\n

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