Fractions
A fraction i one part of a whole number. The number 1 is the smallest whole number. Anything smaller
than 1 is a fraction and can be divided into any number of fractional parts. Fraction are written above
below or on both sides of a fraction bar. Fraction bars may be horizontal or inclined. The denominator
shows how many parts the whole number has been divided into. The denominator is the lower (or right
hand) number of the fraction. The numerator shows the number of parts in the fraction. The numerator
is the upper (or left hand side) number. A proper fraction has a denominator larger than its numerator.
An improper fraction has a numerator larger then the denominator. A mixed number is a combination of
a whole number and a fraction
Fractions may be added horizontally or vertically. Horizontal
placement is the most common, as identification of numerators
and denominators is easier. Fractions which may be added include proper fractions, improper fractions, mixed numbers, and
fractions with unlike denominators. There is a different rule for
each of these four combinations.
Proper Fractions: Fractions having the
same denominator are added by adding the numerators and
placing them over the denominator. For example, in the problem
1/3 + 1/3 = 2/3, the numerators (1+1) are added to produce 2.
The denominator (3) remains constant.
Improper Fraction: Adding Improper Fractions. Fractions
Which produce a sum in which the numerator is larger than the
denominator (improper fractions) are changed to a mixed number by dividing the numerator by the denominator, recording the
quotient obtained, and treating the remainder as a numerator
placed over the original denominator. For example, in the problem 3/8 + 3/8 + 3/8 = 9/8, the improper fraction 9/8 is changed to
1 1/8 by dividing 9 by 8.
Adding mixed Numbers:
To add fractions containing mixed numbers, add the whole numbers, add the numerators, and carry the denominator. For example, in the problem 1 1/4 + 3 1/4 + 4 1/4 = 8 3/4, the whole number 1,3,4 are added tp produce 8. The numerators 1+1+1 are
added to produce 3, which is placed over the denominator.
Subtraction of fractions is similar to addition of fractions. Fractions may be subtracted horizontally or vertically. Horizontal
placement is the most common, as identification of numerators
and denominators is easier. All fractions must have a common
denominator before one can be subtracted from another. Fractions which may be subtracted include fractions with like denominators, fractions with unlike denominators, and mixed numbers.
There is a different rule for each of these three combinations.
Subtracting Fractions with Like Denominators:
To subtract fractions having the same denominators, subtract
one numerator from the other numerator and place over the denominator. For example, to subtract 7/16 from 11/16 subtract the
numerator 7 from the numerator 11 to get 4. Place the 4 over the
denominator 16. Then reduce.
Subtracting Fractions with Unlike Denominators:
To subtract fractions having unlike denominators, reduce the
fractions to their LCD and subtract one numerator from the other.
For example, to subtract 7/16 from 3/4, reduce 3/4 to 12/16 and
subtract 7/16 to 5/16.
Subtracting Mixed Numbers:
Subtracting Mixed Numbers. To subtract fractions having mixed
numbers, follow the applicable procedure for denominators, subtract the numerators, subtract the whole numbers, and if necessary, reduce the fraction to its lowest common denominator.
Fractions may be multiplied horizontally or vertically. Horizontal
placement of fractions is the most common, as identification of numerators and denominators is easier. Fractions which may be multiplied include two fractions, fractions and a whole number, a mixed
number and a whole number, and two mixed numbers. There is a
different rule for each of these four combinations.
Multiplying Two Fraction:
To multiply two fractions, multiply the numerator of one fraction by
the numerator of the other fraction. Do the same with the denominators. Reduce the answer as required.
Multiplying Fractions and a Whole Number:
To multiply a fraction and a whole number, multiply the numerator
of the fraction by the whole number and place over the denominator. Reduce the answer as required.
Multiplying a Mixed Number and a Whole Number:
Multiplying a Mixed Number and a Whole Number. To multiply a
mixed number and a whole number, multiply the fraction of the
mixed number by the whole number, multiply the whole numbers,
and add the two products.
Multiplying Two Mixed numbers:
Multiplying Two Mixed Numbers. To multiply two mixed numbers,
change both mixed numbers to improper fractions and multiply.
Fractions are divided horizontally. Fractions which may be divided include a fraction by a whole number, a mixed number by a whole number, two fractions, a whole number by a fraction, and two mixed numbers. There is a different rule for each of these five combinations.
Dividing a Fraction by a Whole Number:
To divide a fraction by a whole number, multiply the denominator of
the fraction by the whole number.
Dividing a Mixed Number by a Whole number:
To divide a mixed number by a whole number, change the mixed number to an improper fraction and multiply the denominator of the improper fraction by the whole number.
Dividing Two Fractions:
To divide two fractions, invert the divisor fraction and multiply the numerator by the numerator and the denominator by the denominator.
Dividing a whole Number By a Fraction:
To divide a whole number by a fraction, change the whole number into
fraction form, invert the divisor fraction, and multiply the numerator by
the numerator and the denominator by the denominator.
Dividing two Mixed Numbers:
To divide two mixed numbers, change both mixed numbers to improper fractions, invert the divisor fraction, and multiply the numerator
by the numerator and the denominator by the denominator.