# [Blindmath] Basic Math

Bill Dengler codeofdusk at gmail.com
Tue Oct 11 18:07:03 UTC 2016

```Okay, I'll explain some of this as best as I can. If you have questions or something is unclear, feel free to ask and I'll try to help.

In order to understand decimals, fractions and percents, you first need to understand place value. Each digit of a number has a certain value, depending on its position in the number. For example, the number 11 is made of a ten and a one (10+1=11).
The number twelve is made of a ten and 2 ones.
20 is made of two tens and zero ones (10+10+0=20).
101 is made of one 100, 0 tens and 1 one (100+0+1=101).
1,000 is made of 1 thousand, 0 hundreds, 0 tens and 0 ones (1000+0+0+0=1000).
This pattern continues for hundred thousands, millions, ten millions, etc.
Each digit of a number in the decimal system, or base 10 (that's the number system we normally use for counting) is based on the number 10 being multiplied by itself an infinite number of times (10 times 10 is 100, 100 times 10 is 1,000, 1,000 times 10 is 10,000, etc).

Fractions are more precise than whole numbers. They represent quantities less than 1. The top number (or numerator) shows how many parts you have, and the bottom number (or denominator) shows the number of parts in the whole. For example, the fraction 1 over 2 is one half. You have 1 part of the whole, which is made of two parts; if you had both (2 over 2) you'd have exactly one whole. In the fraction 1 over 4, you have one part out of a total of 4. In the fraction 3 over 5, you have 3 parts out of the total of 5, etc.

Mixed numbers are, as their name implies, mixed; they have both a whole part and a fractional part. For example, 1 and 1 over 4 has a whole part, 1, and a fractional part, 1 over 4.

Decimals are mixed numbers that use the place value system described above for the denominator of their fractional part. The decimal point separates the whole part from the fractional part. In a decimal, the whole part can be (and often is) 0 or omitted; this means there is no whole part and the number is simply a fraction. For example, the decimal 0.5 is 5 over 10. The decimal 0.25 is 25 over 100. The decimal .0001 is 1 over 10,000. The decimal 1.5 is 1 and 1 over 2.

Percent literally means "for each 100." This means that they are fractions where the denominator is always 100. For example, 50% is simply the fraction 50 over 100. 25% is the fraction 25 over 100. 150% is the fraction 150 over 100. .5% is the fraction .5 over 100, in other words the fraction who's numerator is 5 over 10, and who's denominator is 100.

There is more than one way to represent the same fractional quantity. For example, what's the difference between 1 over 2 and 5 over 10? Or 1 over 2 and 4 over 8? Or 1 over 2 and 5,000 over 10,000? These "equivalent fractions" need to be "simplified", or reduced to lowest terms, for your final answer. This means the denominator must be the smallest possible value it can be that is still an equivalent fraction. For example, the fraction 25 over 100 (the decimal 0.25) "simplifies" to 1 over 4.

Hope this helps,
Bill
> On Oct 11, 2016, at 4:22 PM, Lanie Molinar via Blindmath <blindmath at nfbnet.org> wrote:
>
> I am using hard copy Braille on a Perkins, but I also have an abacus available, although I am not sure how to set these kinds of problems up on an abacus.
>
>
> On 10/11/2016 11:15 AM, Lewicki, Maureen via Blindmath wrote:
>> Tell us how you are answering: hard copy braille on a Perkins? Using a calculator? using an abacus? Using a refreshable braille device?
>>
>> Maureen Murphy Lewicki
>> Teacher of the Visually Impaired
>> Bethlehem Central School District
>> Bethlehem High School
>> 700 Delaware Ave
>> Delmar, NY 12054
>> http://www.bethlehemschools.org
>> Keep on beginning and failing. Each time you fail, start all over again, and you will grow stronger until you have accomplished a purpose - not the one you began with perhaps, but one you'll be glad to remember. Anne Sullivan
>>
>> -----Original Message-----
>> From: Blindmath [mailto:blindmath-bounces at nfbnet.org] On Behalf Of Lanie Molinar via Blindmath
>> Sent: Tuesday, October 11, 2016 12:09 PM
>> To: Blind Math <blindmath at nfbnet.org>
>> Cc: Lanie Molinar <laniemolinar91 at gmail.com>
>> Subject: [Blindmath] Basic Math
>> Importance: High
>>
>> Hi. I'm taking a basic math class online where I don't have an accessible textbook available yet. Unfortunately, since it's been several years since I've taken math like this and I have health issues now that have made it very hard to remember how to do the work, I'm really struggling with learning how to do it. I was wondering if anyone might be able to give me tips on how to handle problems like the ones I'm including below. I have a few friends who are trying to help me, but they're sighted, and without the textbook, I'm finding it difficult to understand what they're telling me. They do these problems in a very visual way, so I know they're having a hard time, too. Here are a few examples of problems I'm working on.
>>
>> 1. 538.9*2892.07    2. 82*0.00000789
>>
>> The next few problems involve changing fractions into decimals.
>>
>> 3. 1/20  I know the answer to this one, but I couldn't tell you how I
>> know it or show my work.    4. 4/9    5. 2/3
>>
>> These problems are division problems.
>>
>> 6. 434/8    7. 185/6    8. 689/14    9. 56.347/0.02    10. 553/6    11.
>> 175.12/31
>>
>> The next problems involve changing fractions into percents.
>>
>> 12. 37/40    13. 27/25
>>
>> The instructions for the next few are to find the following.
>>
>> 14. Price: \$75.37    Tax rate: 6%    Tax:
>>
>> 15. Attendees: 2,413    Percent men: 39%    Men:
>>
>> 16. Students: 15    Number of B‟s: 11    Percent of B‟s:
>>
>> Those are examples of the questions I'm having trouble with. I would really appreciate any help learning how to do these. Thanks.
>>
>>
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