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Number & Operations for Teachers Copyright David & Cynthia Thomas, 2009 |
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The Meaning of “60%
of 30%” In Chapter Five, you learned to represent the operation this written notation with the spoken language “one-half of one-third”. Similar circumstances occasionally arise involving percents. For instance, the expression “60% of 30%” may be represented using an area model like that shown in Figure 6.7. In this model, the unit square is divided both vertically and horizontally into ten rows and columns. Three of the rows are shaded to represent 30% of the whole. Six columns are shaded to represent 60% of the whole. The dark region models the quantity 60% of 30%. By inspection, this area constitutes 18% of the whole. Expressed as a decimal, this quantity is written 0.18. The same result may be obtained by § Converting both percents to decimals and finding their product:
§ Converting
both percents to fractions and finding their product:
60% Figure 6.7: Modeling 60% of 30% Being able to convert between equivalent written representations (i.e., fraction, decimal, and percent) is itself an important skill. Figure 6.8 and Table 6.10 illustrate the conversions between the written representations 1/4, 0.25, and 25%. Naturally, some conversions are more complicated than others (e.g., Example 6.4). But all students should understand the fundamental relationships between fraction, decimal, and percent representations.
Figure 6.8: Sample Conversions
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