Fractions Made Simple ...................
Fractions are not difficult if you remember several simple rules.
I will present only one technique. If you know others that work
for you, please use thos= e.
Because I am using "Notepad" and building= only text files, I need
present the symbols bein= g used for addition, subtraction, division,
multiplication, and grou= ping (if needed).
Addition symbol: +
Subtraction symbol: -
Division symbols: / and ÷
Multiply symbol: &tim= es;
Equal symbol: = =3D
Grouping symbols: ( )
Examples of each symbol being used with equals:
Addition: 2 + 14 =3D 16
Subtraction: 8 - 3 =3D 5
Division: 12/3 =3D 4 and 12 ÷ 3 =3D 4
Multipication: 17 × 9 =3D 153
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There is a correct order in which the different mathematical
operations are done. Some operations are equal in prior= ity.
This is the order in which operations are done:
1.
2.
4 + 6/3 =3D 4 + 2 =3D 6<= /p>
8 - 10/5 + 4 =3D 8 - 2 += 4 =3D 10
Use of Grouping symbols = may override the order. That is t= o say,
if grouping symbols are = used, always do the action inside the
grouping symbols first.<= /p>
(8 - 5)/(2 + 1) =3D 3/3 =3D 1
(2 + 5) × 4 =3D 7 = × 4 =3D 28
(8 - 2) × (3 + 4) = =3D 6 × 7 =3D 42
(8 - 12/3) ÷ (3 -= 1) =3D (8 - 4) ÷ (3 - 1) =3D 4 ÷ 2 =3D 2
In more complex grouping, the inner-most group is d= one first.
(2 × (3 - 1) + 2)<= span class=3DGramE>/(5 - 3) =3D (2 × 2 + 2)/2 =3D (4 + 2)/2 =3D 6/2= =3D 3
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Fractions use the division symbol as follows:
2/4<= span style=3D'mso-spacerun:yes'> or 17/3 or 1/6 but may be seen wr= itten as
2 17 1
——— or ———— or ———
4 3 6 &nbs= p;
The number on "top" is called the numerat= or.
The number on the "bottom" is called the denominator.
If the numerator is larger than the denominator, the fraction
is called an "impro= per fraction". This term will become
important when we cover converting "mixed numbers" to and from
improper fractions.
A mixed number has a whole number followed by a fra= ction:
3 1/= 2 or 12 5/7
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General rules:
1. Multiplying or dividing the numerator and the denominator by
= the same number same number will not change the value = of the
= Fraction. For example:
1/2 =3D 3/6 (multiplied = both by 3)
3/4 =3D 12/16 (multiplie= d both by 4)
10/14 =3D 5/7 (divided b= oth by 2)
24/30 =3D 4/5 (divided b= oth by 6)
2. Co= nvert a mixed number to an improper fraction by multiplying
= the whole number by the denominator and adding the numerator.
For example:
3 1/2 =3D 7/2 (3 times 2= and then add 1)
12 5/7 =3D 89/7 (12 time= s 7 and then add 5)
3. Co= nvert an improper fraction to a mixed number by dividing
= numerator by the denominator. The quotient will be the whole
= number and the remainder will by the fractional part's=
= numerator. Denominators remain the same. For example:
32/3 =3D 10 2/3 (a quoti= ent of 10, a remainder of 2)
18/5 =3D 3 3/5 (a quotie= nt of 3, a remainder of 3)
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Addition and subtraction rules for fractions:
If mixed numbers are involved, convert the mixed nu= mbers to
improper fractions before applying rules.
1. Fi= nd a common denominator for the fractions used.
2. Ad= d or subtract the numerators only.
3. Th= e common denominator will be in the answer.
4. If possible, reduce result to the smallest numbers.
Examples:
2/3 + 3/4 =3D 8/12 + 9/1= 2 =3D 17/12
1/6 + 1/2 =3D 1/6 + 3/6 = =3D 4/6 =3D 2/3 (divided both by 2)
14/5 - 5/2 =3D 28/10 - 2= 5/10 =3D 3/10
13/3 - 4/5 =3D 65/15 - 1= 2/15 =3D 53/15
Mixed number examples:
20 1/5 - 3/4 =3D 21/5 - = 3/4 [convert to improper]
21/5 - 3/4 =3D 84/20 - 1= 5/20 [apply rule 1]
84/20 - 15/20 =3D 69/20 = [apply rule 2]
69/20 =3D 3 9/20 [conver= t back to mixed number]
3 1/2 + 4 1/3 =3D 7/2 + = 13/3 [convert to improper]
7/2 + 13/3 =3D 21/6 + 26= /6 [apply rule 1]
21/6 + 26/6 =3D 47/6 [ap= ply rule 2]
47/6 =3D 7 5/6 [convert = back to mixed number]
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Multiplication and division rules for fractions:
If mixed numbers are involved, convert the mixed nu= mbers to
improper fractions before applying rules.
1. For division only, invert (or flip) the divisor.
2. Mu= ltiply the numerators.
3. Mu= ltiply the denominators.
4. If possible, reduce result to smallest numbers.
Examples:
2/3 × 1/4 =3D 2/12= =3D 1/6 (divide both by 2)
4/7 × 1/2 =3D 4/14= =3D 2/7 (divide both by 2)
6 2/3 ÷ 2/3 =3D 2= 0/3 ÷ 2/3 [convert to improper]
20/3 ÷ 2/3 =3D 20= /3 × 3/2 [apply rule 1]
20/3 × 3/2 =3D 60/= 6 =3D 10/1 (divide both by 6)
10/1 =3D 10 [convert to = mixed number]
Note: any number divided by = 1 is that number
2 1/4 × 1/6 =3D 9/= 4 × 1/6 [convert to improper]
9/4 × 1/6 =3D 9/24= =3D 3/8 (divide both by 3)
12 3/5 ÷ 5 2/3 = =3D 63/5 ÷ 17/3 [convert to improper]
63/5 ÷ 17/3 =3D 6= 3/5 × 3/17 [apply rule 1]
63/5 × 3/17 =3D 18= 9/85 (cannot be simplified)
189/85 =3D 2 19/85 [conv= ert to mixed number]
5/9 ÷ 2/3 =3D 5/9= × 3/2 [apply rule 1]
5/9 × 3/2 =3D 15/1= 8 =3D 5/6 (divide both by 3)
Hope this helps!!