RATIONAL NUMBERS
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RATIONAL NUMBERS
Fractions
INTEGERS• WHAT IS AN INTEGER?
• The integers consist of the positive natural numbers (1, 2, 3, …), their negatives (−1, −2, −3, ...) and the number zero.
RATIONAL NUMBERS• WHAT IS A RATIONAL NUMBER?
• In mathematics, a rational number (commonly called a fraction) is a ratio or quotient of two integers, usually written as a fraction a/b, where b is not zero.
RATIONAL NUMBERS• WHAT IS A RATIONAL NUMBER?
• In mathematics, a rational number (commonly called a fraction) is a ratio or quotient of two integers, usually written as a fraction a/b, where b is not zero.
• EXAMPLES:• , 0.25, , -0.125
14
-5 4
ADDING FRACTIONS
To add two fractions with the same denominator, add the numerators and place that sum over the common denominator
EXAMPLE:
35
+ 15
= 45
ADDING FRACTIONS
To Add Fractions with different denominators:
Find the Least Common Denominator (LCD) of the fractions
Rename the fractions to have the LCD Add the numerators of the fractions Simplify the Fraction
EXAMPLE
14
+13
To make the denominator of the first fraction 12, multiply both the numerator and denominator by 3.
Adding Fractions
14 +
13 ?=
x3
x3
?12
+ =
To make the denominator of the second fraction 12, multiply both the numerator and denominator by 4.
Adding Fractions
14 +
13 ?=
x4
x4
312
+ ?12
=
To make the denominator of the second fraction 12, multiply both the numerator and denominator by 4.
Adding Fractions
14
+ 13 ?=
x4
x4
312
+4
12 =
We can now add the two fractions.
Adding Fractions
14 +
13
?=
312
+ 412
=7
12
TRY THIS
13
+ 25
?=
TRY THIS
13
+ 25
?=
515
+ 615
?=
x5
x5
x3
x3
TRY THIS
13
+ 25
?=
515
+ 615
=
x5
x5
x3
x3
1115
SUBTRACTING FRACTIONS
To Subtract Fractions with different denominators:
Find the Lowest Common Denominator (LCD) of the fractions
Rename the fractions to have the LCD Subtract the numerators of the fractions The difference will be the numerator and the
LCD will be the denominator of the answer. Simplify the Fraction
TRY THIS
25
- 13
?=
TRY THIS
25
- 13
?=
615
- 515
?=
x3
x3
x5
x5
TRY THIS
25
- 13
?=
615
- 515
=
x3
x3
x5
x5
115
MULTIPLYING FRACTIONSTo Multiply Fractions: Multiply the numerators of the fractions Multiply the denominators of the fractions Place the product of the numerators over the product of the denominators Simplify the Fraction
To multiply fractions, simply multiply the two numerators
Multiplying Fractions
35
x 13
=
x =
??
Then simply multiply the two denominators.
35
x 13
=
x =
3?
Multiplying Fractions
Place the numerator over the denominator.
35
x 13
=
x =
315
Multiplying Fractions
State in simplest form.
35
x 13
= 315
= 15
Multiplying Fractions
DIVIDING FRACTIONS
To Divide Fractions: Multiply the reciprocal of the second term
( fraction) Multiply the numerators of the fractions Multiply the denominators of the fractions Place the product of the numerators over
the product of the denominators Simplify the Fraction
Example:
35
÷ 13
Dividing Fractions
=
35
x 31
=
Multiply by the reciprocal…
95
TRY THESE
1)
2)
23
x14 =
25
13
=÷
TRY THESE
1)
2)
23
x 14
=
25
13
=÷
212
TRY THESE
1)
2)
23
x 14 =
25
13
=÷
16
= 212
TRY THESE
1)
2)
23
x 14 =
25
13
=÷
16
= 212
25
31
x =
TRY THESE
1)
2)
23
x 14 =
25
13
=÷
16
= 212
25
31
x = 65
TRY THESE
1)
2)
23
x 14 =
25
13
=÷
16
= 212
25
31
x = 65
=151
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