Project Math Access

### Addition of Fractions and Mixed Numbers

Following the procedures outlined below, it is possible to use the braillewriter to add, subtract, multiply, and divide simple fractions and mixed numbers. Once again, the strict format transcribing rules for writing fractions and mixed numbers in braille are changed radically.

Immediately to the right of the problem identifier, the first addend is written. It begins with the opening fraction indicator (dots 1-4-5-6) followed by the numerator. Following that is the simple fraction horizontal bar (dots 3-4). The denominator is brailled immediately after the horizontal bar. The final portion of the addend is the closing simple fraction indicator (dots 3-4-5-6). The paper advance key is tapped once.

The carriage is positioned immediately under the opening fraction indicator of the first addend. The opening simple fraction indicator for the second addend is brailled in that space (lined up in the same column as the first). The same procedure is then followed for brailling the second addend. The opening fraction indicators should always be brailled in the same braille column.

The numerators and/or the denominators of either the first addend or subsequent addends may have varying numbers of digits. For example, the numerator of the first addend might be a single digit while the numerator of the second addend may be a two-digit numeral. Therefore, the horizontal bars of the addends and the closing fraction indicators cannot be brailled in the same columns without leaving appropriate spaces. Strict transcribing rules require leaving appropriate spaces so that the horizontal bars and closing fraction indicators "line up". However, it is recommended that these spaces are not used in calculation exercises, in order to simplify the process and permit the student to focus on the actual computation.

After the problem has been written, the student needs to determined if lowest common denominators must be found. If the denominators are the same, a simple adding of the numerators should take place. In that case, the paper is advanced twice, leaving a blank line under the final addend. The braillewriter carriage is positioned in the column in which the opening fraction indicators are located. The opening fraction indicator is brailled.

The carriage has now moved to the numerator portion of the answer. The student reads the numerators of the addends and adds them. He or she then brailles that answer, followed by the horizontal bar. The denominator is then written, followed by the closing fraction indicator.

The next step is to reduce the fraction to lowest terms, and then to determine if the numerator is larger than the denominator. If it is, then the fraction must be transformed into a mixed number. This is done by dividing the denominator into the numerator. The result of that division is the whole number portion of the resulting mixed number. The remainder is the numerator of the fraction portion of the mixed number.

The following process should be used to write the various steps in the above procedures in braille. The unaltered answer should be followed by a space and an equals sign (dots 4-6, 1-3). If the answer requires being reduced to lowest terms, an opening fraction indicator should be written. The new numerator is written followed by the horizontal bar. The new denominator is written followed by the closing fraction indicator. If this does not result in a mixed number, the final answer can be indicated by advancing two lines, moving the carriage to the left, and writing ans. = followed by the fraction.

If the fraction, reduced to lowest terms, can be changed into a mixed number, then the improper fraction (numerator larger than denominator) should be followed by a space and an equals sign. The procedures to change the improper fraction to a mixed number should be used. The resultant mixed number should be written following the equals sign. The whole number of the portion need not be written with a numeric indicator preceding it. It should be followed by the opening mixed number indicator (dots 4-5-6, 1-4-5-6), followed by the numerator.

The horizontal bar is brailled next, followed by the denominator. The final symbol is the closing mixed number indicator (dots 4-5-6, 3-4-5-6). To indicate the final answer, the paper should be advanced two lines. The carriage should be moved to the far left and the abbreviation, ans., should be brailled followed by the equals sign. The equals sign should be followed by a space, and the mixed number is brailled following it. In this instance, the whole number portion of the answer should be preceded by a numeric indicator. The remaining portion of the answer is brailled as indicated above, using the proper mixed number indicators.

```#11.  2/3  = 20/30
9/10 = 27/30

47/30

47/30 = 1 17/30

ans. = 1 17/30
```

Addition of mixed numbers follows a similar pattern. The mixed number addends are brailled using mixed number indicators. No numeric indicators should be used. If the fraction portions of the addends require no alteration, the whole numbers can be added, as well as the numerators of the fractional portions. The answer is brailled under after blank line, under the final addend. The correct procedure for adding the fractional portion is carried out. If it requires reduction to lowest terms, the procedures described above should be followed. Lastly, the final answer should be written beginning at the left as described in previous paragraphs. If the fractional portions of the mixed number addends require the finding of common denominators, the procedures for accomplishing that should be followed, as outlined above.

```#12.  1 1/2 = 3/2
3 4/5 = 19/5

3/2   = 15/10
19/5  = 38/10

53/10 = 5 3/10

ans. = 5 3/10
```