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Many students don't have a secure understanding of percentages. This is a problem, for several reasons. Percentages pervade our lives, and so it's important to have a good "feel" for them. On-the-fly estimates involving money, medicine, politics, and the like often require their calculation. Percent questions also frequently appear on the SAT/ACT. In a nutshell, percents are fractions with denominator 100. The “50-25-10” rule enables use of simple unit fractions as guides in estimating percentages: 50% = 1/2. 25% = 1/4. 10% = 1/10. Example 1 To estimate 62% of 48,300, first, round 62% to 60%, and 48,300 to 48,000, for convenience. 60% is 10% more than half. Half of $48,000 is 24,000, and 10% of 48,000 is 4,800. Altogether, this makes $28,800. Since we rounded down, adjust the answer up a little, to perhaps 30,000. The correct answer is 29,760. To work out tricky SAT/ACT percent problems, it’s sometime best to pick a sample value to work with, and see what happens. In ...

Many students don't have a secure understanding of percentages. This is a problem, for several reasons. Percentages pervade our lives, and so it's important to have a good "feel" for them. On-the-fly estimates involving money, medicine, politics, and the like often require their calculation. Percent questions also frequently appear on the SAT/ACT. In a nutshell, percents are fractions with denominator 100. The “50-25-10” rule enables use of simple unit fractions as guides in estimating percentages: 50% = 1/2. 25% = 1/4. 10% = 1/10. Example 1 To estimate 62% of 48,300, first, round 62% to 60%, and 48,300 to 48,000, for convenience. 60% is 10% more than half. Half of $48,000 is 24,000, and 10% of 48,000 is 4,800. Altogether, this makes $28,800. Since we rounded down, adjust the answer up a little, to perhaps 30,000. The correct answer is 29,760. To work out tricky SAT/ACT percent problems, it’s sometime best to pick a sample value to work with, and see what happens. In ...

The reason I've always been captivated by the Trivium and Quadrivium is almost certainly that these ancient western educational models happen to coincide with six main interests of mine: math, music, astronomy/cosmology, logic, writing, and debate.  Moreover, philosophy, another one of my main interests, was considered such an obvious part of classic liberal arts training that it wasn't included in the list of subjects for either the Quadrivium or Trivium. From the Wikipedia article on Quadrivium : " From the time of Plato through the Middle Ages, the quadrivium (plural: quadrivia[1]) was a grouping of four subjects or arts—arithmetic, geometry, music, and astronomy—that formed a second curricular stage following preparatory work in the trivium, consisting of grammar, logic, and rhetoric. Together, the trivium and the quadrivium comprised the seven liberal arts,[2] and formed the basis of a liberal arts education in Western society until gradually displaced as a curricular...

The reason I've always been captivated by the Trivium and Quadrivium is almost certainly that these ancient western educational models happen to coincide with six main interests of mine: math, music, astronomy/cosmology, logic, writing, and debate.  Moreover, philosophy, another one of my main interests, was considered such an obvious part of classic liberal arts training that it wasn't included in the list of subjects for either the Quadrivium or Trivium. From the Wikipedia article on Quadrivium : " From the time of Plato through the Middle Ages, the quadrivium (plural: quadrivia[1]) was a grouping of four subjects or arts—arithmetic, geometry, music, and astronomy—that formed a second curricular stage following preparatory work in the trivium, consisting of grammar, logic, and rhetoric. Together, the trivium and the quadrivium comprised the seven liberal arts,[2] and formed the basis of a liberal arts education in Western society until gradually displaced as a curricular...

The reason I've always been captivated by the Trivium and Quadrivium is almost certainly that these ancient western educational models happen to coincide with six main interests of mine: math, music, astronomy/cosmology, logic, writing, and debate.  Moreover, philosophy, another one of my main interests, was considered such an obvious part of classic liberal arts training that it wasn't included in the list of subjects for either the Quadrivium or Trivium. From the Wikipedia article on Quadrivium : " From the time of Plato through the Middle Ages, the quadrivium (plural: quadrivia[1]) was a grouping of four subjects or arts—arithmetic, geometry, music, and astronomy—that formed a second curricular stage following preparatory work in the trivium, consisting of grammar, logic, and rhetoric. Together, the trivium and the quadrivium comprised the seven liberal arts,[2] and formed the basis of a liberal arts education in Western society until gradually displaced as a curricular...