Learn Fractions
A fraction , in general, is the expression of a number
divided by another and aproper fraction represents the parties took
a whole.
The classic example is a cheese that we break
into portions. In the drawing, we made 8 servings, 3 Roses and 5 green.
 Taking 3 roses represent 3 servings of
eight which have divided the cheese, that is 3/8
of the cheese,
and if we take the 5 green, representing 5 servings of eight which have
divided the cheese is say 5/8 of the cheese.
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The parts that we (3 or 5) are called the
numerator and the parties that we divide the
cheese (8) denominator . To read a fraction, the
numerator is read normally but, as discussed below, the denominator is a
special form of read .
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Denominator
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Reading
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Examples
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2
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media
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5/2 = five half
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3
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thirds
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2/3 = two-thirds
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4
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Quarter
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3/4 = three quarters
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5
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fifths
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4/5 = four-fifths
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6
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sixths
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5/6 = five sixths
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7
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sevenths
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6/7 = six sevenths
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8
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knockout
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7/8 = seven eighths
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9
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Ninth
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8/9 = eight-ninths
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10
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tenths
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9/10 = nine tenths
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greater than 10
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Number is added to
the end avos
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10/11 = ten eleven avos
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Sorting Fractions
Fractions can be classified in different
ways; in the table below the characteristics of the most important is.
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Type
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Features
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Examples
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Own
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The numerator is smaller than the denominator
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1/2, 7/9
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Improper
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The numerator is greater than the denominator
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4/3, 5/2
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Homogeneous
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Have the same
denominator
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2/5, 4/5
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Heterogeneous
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They have
different denominators
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3/7, 2/8
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Full
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The numerator equals the denominator
represent an integer
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6/6 = 1
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Equivalents
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When they have the same value.
Two fractions are equivalent
if their cross products are equal
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2/3 and 4/6
2 x 6 = 3 x 4
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If a fraction multiply or divide the numerator
and denominator by the same number, we get an equivalent fraction to the first,
as both have the same value. For example:
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1
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(1 x 4)
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4
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3
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(3: 3)
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1
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-
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=
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---
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=
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-
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=
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0.5;
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-
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=
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---
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=
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-
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=
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0.2
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2
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(2 x 4)
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8
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15
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(15: 3)
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5
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Simplify or Reduce a fraction is to find the smallest possible
fraction equivalent;for this, the first thing we do is find the largest number
that divides evenly (remainder = 0) the numerator and denominator (greatest
common divisor) and then divide the numerator and denominator by the greatest
common divisor, since as we have seen before dividing the numerator and
denominator of a fraction by the same number we get an equivalent fraction (of
equal value). Example: Simplify 30/42numbers that divide exactly 30
(splitters) are: 2, 3, 5, 6 ., 10 and 15 which divide numbers exactly 42
(dividers) are:. 2, 3, 6, 7, 14 and 21 The common divisors .
both are 2, 3 and 6 The greatest common divisor is 6, therefore , divide
numerator and denominator by 6.
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30
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30/6
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5
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-
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=
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---
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=
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-
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42
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42/6
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7
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When a fraction, the numerator and denominator
have no common divisor, is said to be an irreducible fraction.
Adding and Subtracting
Fractions If the fractions have
the same denominator (homogeneous), add or subtract the numerators and put the
same denominator.
Example:
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3
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2
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(3 + 2)
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5
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5
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2
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(5-2)
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3
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-
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+
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-
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=
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---
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=
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-
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;
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-
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-
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-
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=
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---
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=
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-
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6
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6
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6
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6
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7
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7
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7
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7
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If the fractions have different denominators
(heterogeneous), the first thing you have to do is match the
denominators. To achieve this, we look at the given two equivalent
fractions multiplying the numerator and denominator of each of them by the denominator
of the other. Once obtained the same denominator, we proceed as in the
previous case, we add the numerators and put the common denominator.Example:
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2
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3
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(2 x 7)
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(3 x 5)
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14
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15
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29
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-
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+
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-
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=
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---
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+
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---
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=
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-
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+
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-
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=
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-
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5
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7
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(5 x 7)
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(7 x 5)
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35
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35
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35
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Fractions Multiplication
The product of several fractions is equal to
another fraction whose numerator is the product of the numerators and
denominator the product of the denominators.
Example:
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3
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4
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2
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(3 x 4 x 2)
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24
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2
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-
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x
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-
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x
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-
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=
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----
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=
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-
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simplifying
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=
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-
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4
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5
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3
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(4 x 5 x 3)
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60
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5
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Fraction Of A Number
Calculate the fraction of a number is the same
as multiplying the fraction by that number. Example: Calculate
the 2/3 of 60 :
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2
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2
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(2 x 60)
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120
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-
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of
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60
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=
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-
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x
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60
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=
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---
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=
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-
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=
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40
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3
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3
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3
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3
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Division of Fractions
The quotient of two fractions is another
fraction whose numerator is the product of the first numerator by the
denominator of the second, and the denominator denominator the product of the
first by the numerator of the second. Example:
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4
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3
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(4 x 5)
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20
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-
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:
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-
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=
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---
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=
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-
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9
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5
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(9 x 3)
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27
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