28 Proposed ALF Math Book 6 Corrections
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This chapter details the issues and proposed changes from the Adult Literacy Fundamental Mathematics – Book 6.
The following solutions work with Apple’s screen reading software. Other screen readers have not been tested.
There are several examples as well as Exercises that use the format . 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.
Example A: Original
Express in higher terms.
is equivalent to
Example A: Proposed solution
Express in higher terms.
is equivalent to
Example A: Edited proposed solution
Express in higher terms.
is equivalent to
This issue is seen in Unit 1 (Topic A, B, C).
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
(1)
. The screenreader doesn’t acknowledge this strike through (\cancel command) and simply reads the number as normal.
Adding an extra equation
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.
Example B: Original
Cross multiply:
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Divide both sides by 6. The 6’s with the N will cancel (reduce), and the N will be alone.
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Check by cross-multiplying:
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Example B: Proposed solution
Cross multiply:
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Divide both sides by 6. The 6’s with the N will cancel (reduce), and the N will be alone.
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Check by cross-multiplying:
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This solution can be used in Units 1 Topic C, Unit 2 Topic A, Unit 3 Topic A, Unit 4 Topic A.
Adding an additional text explanation
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.
Example A: Original
*** QuickLaTeX cannot compile formula: \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*} *** Error message: Missing $ inserted. leading text: \end{split} Missing { inserted. leading text: \end{split} Missing { inserted. leading text: \end{split} Missing { inserted. leading text: \end{split} Missing { inserted. leading text: \end{split} Missing { inserted. leading text: \end{split} Missing $ inserted. leading text: \end{split} Missing { inserted. leading text: \end{split} Missing { inserted. leading text: \end{split} Missing { inserted. leading text: \end{split} Missing { inserted. leading text: \end{split} Missing { inserted. leading text: \end{split} Missing $ inserted. leading text: \end{split} Missing { inserted. leading text: \end{split} Missing { inserted. leading text: \end{split} Missing { inserted. leading text: \end{split} Missing { inserted.
Example A: Proposed solution
Multiply by 100% | |
Convert 100% to a fraction. | |
Divide 100 by 4. The 4 cancels and 100 is reduced to 25. | |
Multiply 3 by 25%. | |
Convert number to a fraction. | |
Multiply by 100%. | |
Convert 100% to a fraction. | |
Divide 100 by 5. The 5 cancels and 100 is reduced to 20. | |
Multiply 6 by 20%. | |
This solution can be used in Unit 2 Topic A.
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
(9)
. This symbol isn’t accessible as a screen reader does not pronounce it.
Removing the arrows and showing moved decimal point
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.
In this particular example, the following textbox is directly before the example:
Example B: Original
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Example B: Proposed solution
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This solution can be used in Unit 2 Topic A.
Removing the arrows and multiplying/dividing by 100%
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.
Exercise 4: Original
Change each percent to its decimal equivalent.
Percent | ÷ 100% Move decimal 2 places to left |
= Decimal | |
---|---|---|---|
A. |
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||
B. | |||
C. | |||
D. | |||
E. | |||
F. |
Answers to Exercise 4
Exercise 4: Proposed solution
Change each percent to its decimal equivalent.
Percent | ÷ 100% Move decimal 2 places to left |
= Decimal | |
---|---|---|---|
A. | |||
B. | |||
C. | |||
D. | |||
E. | |||
F. |
Answers to Exercise 4
This solution can be used in Unit 2 Topic A.
Unit 1 Topic C
The author uses 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.
Original
Review cross products:
(15)
and
Therefore:
Remember that when the cross products are the same, the fractions are equivalent.
When finding the missing terms in a proportion, cross-multiplication can be used. Follow the examples carefully.
Proposed solution
Review cross products:
?
(16)
and
Therefore:
Remember that when the cross products are the same, the fractions are equivalent.
When finding the missing terms in a proportion, cross-multiplication can be used. Follow the examples carefully.
Unit 2, Topic A – 1
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.
Original
Writing equivalent fractions is an important math skill.
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Proposed solution
Writing equivalent fractions is an important math skill.
Equivalent common fractions, decimals, and percents all represent the same amount.
Fractions | Decimals | Percentages |
---|---|---|
Unit 2 Topic A – 2
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.
Original
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.
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Proposed solution
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.
Move decimal point two places to the right and add percent sign. | |
Remove unnecessary zeros. |
Move decimal point two places to the right and add percent sign. | |
Remove unnecessary zeros. |
Unit 2, Topic A – 3
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.
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.
Original
*** QuickLaTeX cannot compile formula: \begin{equation*}\begin{split} & & \ \ 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\% \\ & & \ \ 2 \ 4 \smash{\downarrow}\smash{\downarrow} \\ & & \ \ \ \ \ 60 \smash{\downarrow} \\ & & \ \ \ \ \ \underline{56} \smash{\downarrow} \\ & & \ \ \ \ \ \ \ 40 \end{split}\end{equation*} *** Error message: Extra alignment tab has been changed to \cr. leading text: \end{split} Missing $ inserted. leading text: \end{split} Missing { inserted. leading text: \end{split} Missing { inserted. leading text: \end{split} Missing { inserted. leading text: \end{split} Missing { inserted. leading text: \end{split} Missing { inserted. leading text: \end{split} Missing $ inserted. leading text: \end{split} Missing { inserted. leading text: \end{split} Missing { inserted. leading text: \end{split} Missing { inserted. leading text: \end{split} Missing { inserted. leading text: \end{split} Missing { inserted. leading text: \end{split} Missing $ inserted. leading text: \end{split} Missing { inserted. leading text: \end{split} Missing { inserted. leading text: \end{split}
*** QuickLaTeX cannot compile formula: \begin{equation*}\begin{split} & & \ \ 0.33\overline{3} &\curvearrowright \\ \tfrac{1}{3} &= \text{_____}\% \ \ \ \ \ \ \ \ \ \ \ 3&\overline{\smash{)}1.000} \ \ \ \ \ \ \ \ \ \ \ 0&.33\overline{3}=33.\overline{3}\% \\ & & &\text{also written as }33\tfrac{1}{3}\% \end{split}\end{equation*} *** Error message: Extra alignment tab has been changed to \cr. leading text: \end{split} Missing $ inserted. leading text: \end{split} Missing { inserted. leading text: \end{split} Missing { inserted. leading text: \end{split} Missing { inserted. leading text: \end{split} Missing { inserted. leading text: \end{split} Missing { inserted. leading text: \end{split} Missing $ inserted. leading text: \end{split} Missing { inserted. leading text: \end{split} Missing { inserted. leading text: \end{split} Missing { inserted. leading text: \end{split} Missing { inserted. leading text: \end{split} Missing { inserted. leading text: \end{split} Missing $ inserted. leading text: \end{split} Missing { inserted. leading text: \end{split} Missing { inserted. leading text: \end{split}
*** QuickLaTeX cannot compile formula: \begin{equation*}\begin{split} & & \ \ \ \ 0.916\overline{6} &\curvearrowright \\ \tfrac{11}{12} &= \text{_____}\% \ \ \ \ \ \ \ \ \ \ \ 12&\overline{\smash{)}11.000} \ \ \ \ \ \ \ \ \ \ \ \ 0&.91\overline{6}=91.\overline{6}\% \\ & & \ \ 10 \ 8 \smash{\downarrow}\smash{\downarrow} \\ & & \ \ \ \ \ \ \ 20 \smash{\downarrow} \\ & & \ \ \ \ \ \ \ 12 \smash{\downarrow} \\ & & \ \ \ \ \ \ \ \ \ 80 \\ & & \ \ \ \ \ \ \ \ \ \underline{72} \\ & & \ \ \ \ \ \ \ \ \ \ \ 8 \end{split}\end{equation*} *** Error message: Extra alignment tab has been changed to \cr. leading text: \end{split} Missing $ inserted. leading text: \end{split} Missing { inserted. leading text: \end{split} Missing { inserted. leading text: \end{split} Missing { inserted. leading text: \end{split} Missing { inserted. leading text: \end{split} Missing { inserted. leading text: \end{split} Missing $ inserted. leading text: \end{split} Missing { inserted. leading text: \end{split} Missing { inserted. leading text: \end{split} Missing { inserted. leading text: \end{split} Missing { inserted. leading text: \end{split} Missing { inserted. leading text: \end{split} Missing $ inserted. leading text: \end{split} Missing { inserted. leading text: \end{split} Missing { inserted. leading text: \end{split}
Proposed solution
![]() |
Use long division to write fraction as a decimal. |
Move the decimal point two places to the right and add the percent sign. |
![]() |
Use long division to write fraction as a decimal. |
Move the decimal point two places to the right and add the percent sign. |
![]() |
Use long division to write fraction as a decimal. |
Move the decimal point two places to the right and add the percent sign. |
Unit 2 Topic A – 4
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.
As for the rest of the equation, I would simply remove it from the {equation} and simply have it in simple LaTeX.
Original
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Remember 100% is the whole thing. .
Proposed Solution
Remember 100% is the whole thing. .