1.basic of fractions

2
1. Changing whole numbers to fractions.
A smaller part of a whole number.C. FRACTIONS - A smaller part of a whole number.
Written with one number over the other, divided by a line.
3
8
11
16
or 3
8
11
16
Any number smaller than 1, must be a fraction.
Multiply the whole number times the number of parts being
considered.
Changing the whole number 4 to “sixths”:
4 = 4 x 6
6
=
24
6
or 24
6
Try thinking of the fraction as “so many of a specified number of parts”.
For example: Think of 3/8 as “three of eight parts” or...
Think of 11/16 as “eleven of sixteen parts”.

3
CHANGING WHOLE NUMBERS TO FRACTIONS EXERCISES
1. 49 to sevenths
2. 40 to eighths
3. 54 to ninths
4. 27 to thirds
5. 12 to fourths
6. 130 to fifths
49 x 7
7
= 343
7
or 343
7
=
40 x 8
8
= 320
8
or 320
8
=
54 x 9
9
= 486
9
or 486
9
=
27 x 3
3
= 81
3
or 81
3
=
12 x 4
4
= 48
4
or 48
4
=
130 x 5
5
= 650
5
or 650
5
=

4
3. Mixed numbers.
Combination of a whole number and a proper fraction.
4. Changing mixed numbers to fractions.
Change 3 7/8 into an improper fraction.
• Add both fractions together.
=24
8
7
8
+ 31
8
• Change whole number (3) to match fraction (eighths).
3 x 8
8
24
8
or
24
83 = =
2. Proper and improper fractions.
Proper Fraction - Numerator is smaller number than denominator.
Improper Fraction - Numerator is greater than or equal to denominator.
3/4
15/9

5
CHANGING MIXED NUMBERS TO FRACTIONS EXERCISES
1. 4 1/2
3. 19 7/16
5. 6 9/14
2. 8 3/4
4. 7 11/12
6. 5 1/64
1
2
4 x 2
2
8
2
= + = 9
2
19 x 16
16
304
16
= + 7
16
= 311
16
7 x 12
12
84
12
= + 11
12
= 95
12
6 x 14
14
84
14
= + 9
14
= 93
14
5 x 64
64
320
64
= + 1
64
= 321
64
8 x 4
4
24
4
= + 3
4
= 27
4
=
=
=
=
=
=

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5. Changing improper fractions to whole/mixed
numbers.
Change 19/3 into whole/mixed number..
19/3 = 19 3 = 6, remainder 1 = 6 1/3 (a mixed number)
= 37 7 = 5, remainder 2 = 5 2/7 (a mixed number)
= 44 4 = 11, no remainder = 11 (a whole number)
= 240 8 = 30, no remainder = 30 (a whole number)
CHANGING IMPROPER FRACTIONS TO WHOLE/MIXED NUMBERS EXERCISES
1. 37/7 =
2. 44/4 =
3. 23/5 =
4. 43/9 =
5. 240/8 =
6. 191/6 =

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6. Reducing Fractions
Terms - The name for numerator and denominator of a fraction.
Reducing - Changing to different terms.
Reducing does not change value of original fraction.
7. Reducing to Lower Terms
Divide both numerator and denominator by same number.
Example:
.
3 3 = 1
9 3 = 3
.
..
3
9 = 3
9 & 1
3 Have same value.
8. Reducing to Lowest Terms
Lowest Terms - 1 is only number which evenly divides both numerator
and denominator.
Example: 16
32 =
.
16 2 = 8
32 2 = 16
.
..
a.
.
8 2 = 4
16 2 = 8
.
..
b.
.
4 2 = 2
8 2 = 4
.
..
c.
.
2 2 = 1
4 2 = 2
.
..
d.

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REDUCING TO LOWER/LOWEST TERMS EXERCISES
.15 5 = 3
20 5 = 4
.
..
1. Reduce the following fractions to LOWER terms:
15
20 =a. to 4ths
• Divide the original denominator (20) by the desired denominator (4) = 5..
• Then divide both parts of original fraction by that number (5).
36
40 =b. to 10ths
24
36 =c. to 6ths
12
36 =d. to 9ths
16
76 =f. to 19ths
30
45 =e. to 15ths
.36 4 = 9
40 4 = 10
.
..
.
24 6 = 4
36 6 = 6
.
..
.12 4 = 3
36 4 = 9
.
..
.30 3 = 10
45 3 = 15
.
..
.16 4 = 4
76 4 = 19
.
..

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REDUCING TO LOWER/LOWEST TERMS EXERCISES (con’t)
2. Reduce the following fractions to LOWEST terms:
6
10a.
3
9 =b.
6
64 =c.
13
32 =d.
16
76 =f.
32
48 =e.
= 6 2 = 3
10 2 = 5
..a. ..
3 3 = 1
9 3 = 3
..a. ..
6 2 = 3
64 2 = 32
..a. ..
Cannot be reduced.
32 2 = 16
64 2 = 32
..a. ..
16 2 = 8
32 2 = 16
..b. ..
8 8 = 1
16 8 = 2
..c. ..
16 2 = 8
76 2 = 38
..a. ..
8 2 = 4
38 2 = 19
..b. ..

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9. Common Denominator
Two or more fractions with the same denominator.
1
8
2
8
6
8
7
8
When denominators are not the same, a common denominator is
found by multiplying each denominator together.
1
6
3
8
2
9
5
12
5
18
7
24
1
36
6 x 8 x 9 x 12 x 18 x 24 x 36 = 80,621,568
80,621,568 is only one possible common denominator ...
but certainly not the best, or easiest to work with.
10. Least Common Denominator (LCD)
Smallest number into which denominators of a group of two or
more fractions will divide evenly.

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The most number of times any single factors appears in a set is
multiplied by the most number of time any other factor appears.
10. Least Common Denominator (LCD) con’t.
To find the LCD, find the “lowest prime factors” of each denominator.
2 x 3 2 x 2 x 2 3 x 3 2 x 3 x 2 2 x 3 x 3 3 x 2 x 2 x 2 2 x 2 x 3 x 3
(2 x 2 x 2) x (3 x 3) = 72
Remember: If a denominator is a “prime number”, it can’t be
factored except by itself and 1.
LCD Exercises (Find the LCD’s)
3
8
2
9
5
12
5
18
7
24
1
361
6
1
6
1
8
1
12
2 x 3 2 x 2 x 2 2 x 3 x 2
2 x 2 x 2 x 3 = 24
1
12
1
16
1
24
2 x 2 x 2 x 2 x 3 = 48
3
10
4
15
7
20
2 x 5 3 x 5 2 x 2 x 5
2 x 2 x 3 x 5 = 60
2 x 2 x3 2 x 2 x 2 x 2 3 x 2 x 2 x 2

12
Divide the LCD by each of the other denominators, then multiply both
the numerator and denominator of the fraction by that result.
11. Reducing to LCD
Reducing to LCD can only be done after the LCD itself is known.
3
8
2
9
5
12
5
18
7
24
1
361
6
2 x 3 2 x 2 x 2 3 x 3 2 x 3 x 2 2 x 3 x 3 3 x 2 x 2 x 2 2 x 2 x 3 x 3
LCD = 72
1
6
72 6 = 12..
1 x 12 = 12
6 x 12 = 72
3
8
72 8 = 9..
3 x 9 = 27
8 x 9 = 72
2
9
72 9 = 8..
2 x 8 = 16
9 x 8 = 72
5
12
72 12 = 6..
5 x 6 = 30
12 x 6 = 72
Remaining fractions are handled in same way.

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Reducing to LCD Exercises
Reduce each set of fractions to their LCD.
1
6
1
8
1
12
2 x 3 2 x 2 x 2 2 x 3 x 2
2 x 2 x 2 x 3 = 24
1
12
1
16
1
24
3
10
4
15
7
20
2 x 5 3 x 5 2 x 2 x 5
2 x 2 x 3 x 5 = 602 x 2 x 2 x 2 x 3 = 48
2 x 2 x3 2 x 2 x 2 x 2 3 x 2 x 2 x 2
1
6
24 6 = 4
.
.
1 x 4 = 4
6 x 4 = 24
1
8
24 8 = 3
.
.
1 x 3 = 3
8 x 3 = 24
1
12
24 12 = 2
.
.
1 x 2 = 2
12 x 2 = 24
1
12
48 12 = 4
.
.
1 x 4 = 4
12 x 4 = 48
1
16
48 16 = 3
.
.
1 x 3 = 3
16 x 3 = 48
1
24
48 24 = 2
.
.
1 x 2 = 2
24 x 2 = 48
3
10
60 10 = 6
.
.
3 x 6 = 18
10 x 6 = 60
4
15
60 15 = 4
.
.
4 x 4 = 16
15 x 4 = 60
7
20
60 20 = 3
.
.
7 x 3 = 21
20 x 3 = 60

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12. Addition of Fractions
All fractions must have same denominator.
Determine common denominator according to previous process.
Then add fractions.
1
4
2
4
3
4
= 6
4+ + = 1
21
Always reduce to lowest terms.
13. Addition of Mixed Numbers
Mixed number consists of a whole number and a fraction. (3 1/3)
• Whole numbers are added together first.
• Then determine LCD for fractions.
• Reduce fractions to their LCD.
• Add numerators together and reduce answer to lowest terms.
• Add sum of fractions to the sum of whole numbers.

15
Adding Fractions and Mixed Numbers Exercises
Add the following fractions and mixed numbers, reducing answers to lowest terms.
1. =
3
4+
3
4
2. 7
10+
2
5
=
3. 15
16+
9
32 = 14. 3
4+
2
55 =
= 1
2
6
4 1 4
10
7
10+
1
10
=
1
11
10
=
39
32
30
32+
9
32 =
7
321=
5 + 1 = 6
8
20
15
20+ =
23
20
3
201= + 6
3
207=

16
14. Subtraction of Fractions
Similar to adding, in that a common denominator must be found first.
Then subtract one numerator from the other.
20
24
14
24
- =
6
24
To subtract fractions with different denominators: ( )
5
16
1
4
-
• Find the LCD...
5
16
1
4
-
2 x 2 x 2 x 2 2 x 2
2 x 2 x 2 x 2 = 16
• Change the fractions to the LCD...
5
16
4
16
-
• Subtract the numerators...
5
16
4
16
- =
1
16

17
15. Subtraction of Mixed Numbers
• Subtract the fractions first. (Determine LCD)
1
2
2
310 - 4
3 x 2 = 6 (LCD)
• Divide the LCD by denominator of each fraction.
6 3 = 2 6 2 = 3
.. ..
2
2
• Multiply numerator and denominator by their respective numbers.
2
3 x = 4
6
3
3
1
2 x = 3
6
• Subtract the fractions.
3
6
4
6 - = 1
6
• Subtract the whole numbers.
10 - 4 = 6
• Add whole number and fraction together to form complete answer.
6 +
1
6 = 6
1
6

18
15. Subtraction of Mixed Numbers (con’t)
• Subtract the fractions.
6
16
17
16
- = 11
16
• Subtract the whole numbers.
4 - 3 = 1
• Add whole number and fraction together to form complete answer.
1 +
11
16 = 1
11
16
Borrowing
• Subtract the fractions first. (Determine LCD)
3
8
1
165 - 3
(LCD) = 16
becomes 6
16
1
165 - 3
• Six-sixteenths cannot be subtracted from one-sixteenth, so
1 unit ( ) is borrowed from the 5 units, leaving 4.16
16
• Add to and problem becomes:16
16
1
16
6
16
17
164 - 3

19
Subtracting Fractions and Mixed Numbers Exercises
Subtract the following fractions and mixed numbers, reducing answers to lowest
terms.
1. =
1
3-
2
5
1
15
- 5
15
6
15
=
4. =
2
5-
1
333 15
14
15
=
6
15-
5
1533 15
=
6
15-
20
1532 15 17
2. =
3
12-
5
8
9
24
- 6
24
15
24
= = 3
8
3. =
1
3-2
547 28
1
15=
5
15-
6
1547 28 19
5. =
15
16-1
4101 57
5
16
=
15
16-
4
16101 57
=
15
16-
20
16100 57 43
6. =5
12-3
414 10
=
5
12-
9
1214 10
4
124 1
34=

20
16. MULTIPLYING FRACTIONS
• Common denominator not required for multiplication.
4
16
3
4 X
1. First, multiply the numerators.
2. Then, multiply the denominators.
3. Reduce answer to its lowest terms.
4
16
3
4 X = 12
=
4
16
3
4 X = 12
=64
4
4
12
64 = 3
16
..

21
17. Multiplying Fractions & Whole/Mixed Numbers
• Change to an improper fraction before multiplication.
1. First, the whole number (4) is changed to improper fraction.
2. Then, multiply the numerators and denominators.
3. Reduce answer to its lowest terms.
4
1
4
1
3
4 X = 12
4
3
4 X 4
4
4
12
4 = 3
1
.. = 3

22
18. Cancellation
• Makes multiplying fractions easier.
• If numerator of one of fractions and denominator of other
fraction can be evenly divided by the same number, they can be
reduced, or cancelled.
Example:
5
16
8
3 X = 5
16
8
3 X =
1
2
5
2
1
3 X = 5
6
Cancellation can be done on both parts of a fraction.
3
24
12
21
X =
1
7 2
1
1
2
1
7 X =
1
14

23
Multiply the following fraction, whole & mixed numbers.
Reduce to lowest terms.
Multiplying Fractions and Mixed Numbers Exercises
1. 2.
3. 4.
5. 6.
7. 8.
9.
1
26X =
4
5 X = 2
3
9
5 X =
4
16
3
4 X =
4
35
35
4 X =
7
12
1
6 X =
3
5
9
10 X =
5
11
2
3 X =
77
15X =
26
3
5
3
16
1
2 2
5 1 1
5
1 27
50
7
72
10
33
25 2
3

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19. Division of Fractions
• Actually done by multiplication, by inverting divisors.
• The sign “ “ means “divided by” and the fraction to the
right of the sign is always the divisor.
Example:
1
5
3
4 becomes 5
1
3
4 X =
15
4 = 3 3
4
20. Division of Fractions and Whole/Mixed Numbers
• Whole and mixed numbers must be changed to improper fractions.
Example:
1
8
becomes3 3
16 2 16 3 + 3
16
=
51
16 and
2 X 8 + 1
8
=
17
8
X
X
51
16
17
8 Inverts to 51
16
8
17 = X
51
16
8
17
1
2 1
3
= 1
1
3
2 X
1
1
3
2 X = 3
2 = 1
2
1 Double
Cancellation

25
Divide the following fraction, whole & mixed numbers. Reduce
to lowest terms.
Dividing Fractions,Whole/Mixed Numbers Exercises
1. 2.
3. 4.
5.
3
8
=
= =
3
6
5
8 =
7
4
14
3 =
18 144
51
16
1
8 15 7
12
1
41
1
28
5
725
2
32

26
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for Female Education”
Help us in bringing a change in a girl life, because
“When someone takes away your pens you
realize quite how important education is”.
Just Click on any advertisement on the page, your
one click can make her smile.
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1.basic of fractions

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