 Teacher resources and professional development across the curriculum

Teacher professional development and classroom resources across the curriculum            Session 9, Part B:
Decimals and Percents

In This Part: Percent as Proportion | Percents as Fractions and Decimals | Percent Models

As we've mentioned, percents can also be expressed as fractions and decimals. In this case, all three representations are used to indicate some part of a whole.

 • What percent and decimal are represented by the fraction 1/8? Using cross-multiplication (that is, multiplying both sides of the equation first by 100 and then by 8), we get 1 • 100 = 8x, so x = (1 • 100) 8. One hundred divided by 8 is 12.5, so x = 12.5%, or 0.125 (i.e., 12.5/100). • What fraction and decimal are represented by 35%? You can use the same process as above, but in this case it is easier to remember the definition of percent. Thirty-five percent means 35 out of 100, which is the fraction 35/100 (which reduces to 7/20) and the decimal 0.35 (35 hundredths). • What percent and fraction are represented by the decimal 1.8? This decimal is 1 8/10, or 18/10: Since the denominator of this fraction is 10, it's easiest just to multiply both the top and bottom by 10, which gives us 180/100, or 180%. Problem B4 What percent and decimal are represented by the fraction 1/200? Problem B5 What fraction and decimal are represented by 0.2%? Problem B6 What fraction and decimal are represented by 170%? Problem B7 What fraction and percent are represented by the decimal 0.004? Knowing some fraction, decimal, and percent equivalents allows you to estimate the answers for percent problems or conversions. Some critical values are shown in the following table:  Percent Decimal Reduced Fraction      0.5% 1% 10% 12.5% 20% 25% 33.33% 50% 66.67% 75% 80% 100% 150% 0.005 0.01 0.1 0.125 0.2 0.25 0.5 0.75 0.8 1.0 1.5 1/200 1/100 1/10 1/8 1/5 1/4 1/3 1/2 2/3 3/4 4/5 1 3/2  Problem B8 If you have \$12,000, how would you use this table to compute 25%? Problem B9 Twenty percent of an 80-meter bridge has been built. Using fractions, calculate how many more meters remain to be completed.   Session 9: Index | Notes | Solutions | Video