It appears that many students are struggling with fractions, decimals and percents. While I would like to answer each inquiry I receive with a personally directed response, time is simply not available to do so. Accordingly, I have prepared this lesson covering these subjects, which I believe will answer most of your questions. It is not intended to be the
most thorough and complete dissertation on the subject, but rather a simplified, and (hopefully understandable) treatment. If you still need further help after you have studied this lesson, e-mail me. I'll respond as quickly as I can.
FRACTIONS
DECIMALS
PERCENTS
FRACTIONS
FRACTION - A term consisting of a top number (numerator) and a bottom number
(denominator). A fraction whose numerator is smaller than its denominator
(3/4) is called a Proper Fraction, and a fraction whose numerator is greater
than its denominator (5/4) is called an Improper Fraction.
MIXED NUMBER - A term consisting of an integer (6) followed by a fraction
(3/4), written as 6¾
LOWEST COMMON DENOMINATOR (LCD) - The smallest number in a problem involving
the addition or subtraction of fractions that the denominator of each term
can be divided into with no remainder. For example : 2/3 + 4/5 - 1/2, The LCD
is 30, or 5/6 - 1/3 + 7/9, The LCD is 18.
NEVER attempt to solve a problem using a mixed number . ALWAYS convert it to
an improper fraction. For example: 3 4/5 = 19/5. (multiply 5 by 3 and add 4 =
19), 6 2/3 = 20/3 (multiply 3 by 6 and add 2 = 20).
AFTER you have completed solving a fraction problem you can then express the
answer as a mixed number if that is required.
WARNING!!
WHEN ADDING OR SUBTRACTING FRACTIONS , convert each fraction so that its
denominator is equal to the LCD. This means multiplying BOTH the numerator
and denominator by the SAME term. For example, say the LCD is 18 and one
fraction in the problem is 2/3 , then to convert that fraction to denominator
of 18 you must multiply numerator and denominator by 6, so the fraction
becomes 12/18. You follow this same procedure for each term , add or subtract
as indicated by the sign of each term and divide the total by the LCD. For
example, 5/6 - 1/3 + 7/9 . the LCD is 18 , and the numerator becomes (3*5 -
6*1 + 2*7) or 23, and the denominator, of course, is 18, so the fraction is
23/18 or 1 5/18
MULTIPLICATION OF FRACTIONS is straightforward. You just multiply the
numerators and multiply the denominators and then reduce the fraction to its
lowest term, if possible. For example, 2/3* 4/7 = 8/21,
or 5/6*2/3 = 10/18 = 5/9. If you are multiplying a whole number by a
fraction, just pretend that the denominator of the whole number is 1 (which
it is), and proceed as above .
For example, 4*2/3 = 4/1*2/3 = 8/3.
WHEN YOU DIVIDE FRACTIONS, you actually multiply the numerator by the
reciprocal of the denominator. A reciprocal is a fraction turned upside down.
For example, 2/3 divided by 5/6 = 2/3*6/5 = 12/15 = 4/5
TOP
DECIMALS
A DECIMAL FRACTION is a number whose denominator is some power of ten
(10;100;1000;etc), and is named by a numeral in which the denominator is not
written as in a common fraction, but it is expressed by place value. Places
following the decimal point are 1 place = tenths, 2 places = hundredths, 3
places = thousandths
For example: 7 tenths is written .7, 75 hundredths is written .75, 752
thousandths is written .752
TO CONVERT A FRACTION TO ITS DECIMAL EQUIVALENT, just divide the numerator by
the denominator . For example, 3/8 = .375 (or three hundred seventy five
thousandths), 1/2 = .5 (or five tenths), 3/4 = .75 (or seventy five hundredths)
TO CONVERT DECIMALS TO FRACTIONS, write the decimal as a fraction and reduce
the fraction to its lowest term. For example, .6 = 6 tenths = 6/10 = 3/5,
.64 = 64 hundredths = 64/100 = 16/25, .750 = 750 thousandths = 3/4
TOP
PERCENTS
Cent means hundred! For example, there are 100 years in a century , a
centipede has 100 legs, etc.
TO CHANGE A FRACTION TO A PERCENT, just multiply the numerator by 100 and
divide that answer by the denominator. For example, 6/8 = how many percent?,
or 6 is what percent of 8? Multiply 6 by 100 and divide by 8 and the answer
is 75. So 6 is 75% of 8.
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