**Fractions, Decimals, and Percents--Interrelationships
in Mathematics, Applied to Test-Taking Strategy**

Being 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.