Fractions, Decimals, and Percents--Interrelationships in Mathematics, Applied to Test-Taking Strategy
By Alexandra Berube, bostontutoringservices.comBeing able to memorize the most common fractions, decimals, and percents, is key to performing well on standardized tests. I prepare students for the ISEE and SSAT tests regularly, and this is one of the most important concepts for them to mater. In many types of math, you need to be able to manipulate different forms of the same amount, such as 25% =1/4 = .25. Or, 10% =1/10=.1.
Understanding the interrelationship of these will make solving word problems so much easier. Many problems will ask them to find the percent of something, and they need to understand why the word 'of' in this case means 'times' (X). To solve 10% of 100, first I need to show them that 10% is 1/10, because a percent means the number over 100 (such as, 78% means 78/100, or 30% means 30/100)--so 10% means 10/100, which reduces to 1/10.
Then I show them why 1/10th of something means 1/10 times something. I draw a grid with 10 columns, and I show the student that 1/10 of those is one. So 1/10 of 10 is 1. I have to translate this into 1/10 times 10 is 1. I show this as: 1/10 X 10 is 1/10 X 10/1 (because any integer becomes a fraction if you put it over one--when you divide an integer by one, the result is the original number). 1/10 X 10/1= 10/10 which reduces to one. I do this in a number of ways with a number of percents that have been translated into fractions, until they understand that the percent of something means the percent times that number.
Furthermore, knowing certain concepts and the shortcuts you can use with them is crucial in test-taking strategy. Knowing that 10% of something means you are lopping off the last zero, or moving the decimal place over once to the left, such as in 10% of 80 equals eight. If they can do this in their head, they can save so much time.
In the same way, they should know that any percent of one hundred is that number (25% of 100 is 25). There are a million shortcuts like these that adults who have been using math for decades will not even think about. All adults have our own shortcuts that we apply on a daily basis, but explaining these to students is crucial, because we can never assume they will adopt these shortcuts on their own.
Yet it is extremely important to introduce the shortcuts at the appropriate times, once they already understand the longer way to solve a problem. I will show them that 25% means 25/100, which can be reduced to 1/4. 1/4 of 100 means 1/4 times 100, which is 100/4, which is 25. You can't skip any steps and assume that they will make these leaps on their own.
About Alexandra Berube
Alexandra is the Managing Director of Boston Tutoring Services, a tutoring company that offers one-to-one in-home tutoring in Massachusetts. She is also a former Kindergarten teacher who also tutors students in grades K-8, in all subject areas, including test preparation.