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The position taken in this chapter is that fraction concepts and probably fraction symbolism are prior ideas to decimals. As a result, the most prominent idea pervading all of the content is that decimals are simply another way to write fractions. Nearly every decimal idea can be related to existing fraction ideas. If students can capitalize on this connection, existing ideas can be expanded rather than having to construct disconnected new concepts.

This set of the familiar fractions, along with tenths, means that no number between zero and one is more than five hundredths from a familiar fraction. For thinking about percentages, estimation of decimal computation, and mental computation, the use of a familiar fraction is frequently an incredible advantage over the decimal representation.

For example, estimating 74.23% of 145 is difficult, but 3/4 of 145 is close to 3 x 36 or about 108 - mentally and quickly. (The actual product of 0.7423 x 145 is 107.6335.) While you may not always use a fraction equivalent in a mental computation or estimate, the option expands the possibilities considerably. Further, the connection of decimals to familiar fraction concepts enhances our number sense with decimal numeration.

Students get bogged down with percent problems due to rules about shifting decimals and trying to decide if they should multiply or divide. The rules overcome intuition and there is no clear way to think through or analyze the situation. While there may be some merit to setting up proportions (covered in the next chapter), that approach is not helpful for mental computation or estimation. The percent problems that students get in school should, for a long time, involve percentages equivalent to the familiar fractions. The other quantities involved should be compatible with the fraction equivalents. All percent problems should be in the most realistic language possible, even taken from directly from newspapers and magazine articles or TV. Most importantly, students should be required to draw models to explain their analysis of the problem. The fraction connection to decimals makes all of this possible.

When the percents are not equivalent to a familiar fraction and/or the other quantities in the exercise are not numerically compatible, then estimates can be made by substituting a close familiar fraction. In that sense, 86% might be "rounded" to 7/8 or 87.5% - a whole new meaning to rounding that was earlier introduced with whole numbers. Exact computations come last and should get the least emphasis.