Transcript Adding and Subtracting Rational Numbers

Adding and Subtracting
Rational Numbers
Rational Numbers
• The term, Rational Numbers, refers to any number that can
be written as a fraction.
• This includes fractions that are reduced, fractions that can
be reduced, mixed numbers, improper fractions, and even
integers and whole numbers.
• An integer, like 4, can be written as a fraction by putting the
number 1 under it.
4
4=
1
Types of Rational Numbers
• Reduced Fractions:
2
3
4
• Not Reduced Fractions:
6
1
• Mixed Numbers: 5
4
• Improper Fractions: 6
4
6
• Integers and Whole Numbers:
1
Simplifying Fractions
• Simplifying fractions by dividing the numerator (top
number) and denominator (bottom number) by the
same value.
• Repeat this until there are no more numbers that
divide into both the numerator & denominator.
• Example:
• Example:
• Example:
4 ¸2 2
=
6 ¸2 3
15 ¸5 3
=
10 ¸5 2
36 ¸6 6
=
42 ¸6 7
Simplifying Fractions
• Example: 15 is already simplified.
14
• Example: 3 2 = 3×5 + 2 = 17 is already simplified.
5
5
5
(Rewrite mixed numbers as improper fractions before
you simplify.)
36 ¸2 18 ¸3 6
=
=
• Example:
42 ¸2 21 ¸3 7
(If after you divide, the fraction can still be
simplified, keep going.)
Adding Rational Numbers
• First they must have a common denominator.
• Next, look at the signs. If they have the same signs you
add the absolute values and keep the sign.
• If they have different signs subtract the absolute values
keep the sign of the larger absolute value.
Use the song to help remind you if you need to:
http://www.teachertube.com/viewVideo.php?video_id=286228
Subtracting Rational Numbers
• First they must have a common denominator.
• Next, rewrite subtraction as addition – keep-changechange.
• Follow the rules for adding rational numbers.
Use the song to help remind you if you need to:
http://www.teachertube.com/viewVideo.php?video_id=286228
Getting a Common Denominator
• Use this formula to get two fractions to have a
common denominator:
2 4
+
3 5
Common Denominator = 3•5=15.
2 4 2 ×5 + 4 ×3
+ =
3 5
15
2 4 2 × 5+ 4 × 3 22
7
+ =
=
=1
3 5
15
15 15
Simplify if possible.
More Examples
{
22
22 ¸2 11
3 1 18 4
=
=
=
1) + = +
24 ¸2 12
4 6 24 24 24
Common Denominator
Divide to Simplify.
5 3 5× 2 + 3×8 34 34 ¸2 17
2)
+ =
=
=
=
8 2
8 ×2
16 16 ¸2 8
More Examples
6 10 6 -10 Change Subtraction to Addition.
3) = +
(Keep-Change_Change.)
5 3 5
3
-32
6 × 3 -10 × 5 18 + ( -50)
=
=
+
=
15
5× 3 3× 5
15
Note: A fraction with a negative numerator
or denominator is a negative fraction.
-32 32
32
=
=15
-15
15
More Examples
Change Subtraction to Addition
(Keep-Change-Change.).
1
5
13 11
-13 -11
4) - 3 - 1
=- =
+
4
6
4 6
4
6
Change Mixed Numbers to Improper Fractions.
-13 -11 (-13)× 6 (-11)× 4 -78 -44 -122 -61
+
=
+
=
+
=
=
4
6
4×6
6×4
24 24
24 12
Get Common Denominator
Simplify.
You Try It!
Find each sum or difference.
3 4
1) +
5 3
2
1
3) 5 + (-2 )
5
4
1 7
2)
8 10
1 1
4) - 3 2 5
Solutions
3 4 3 ×3 + 4× 5 29
1) + =
=
5 3
5 ×3
15
1 7 1 -7 1×10 + (-7) ×8 -46
23
2) - = +
=
=
=8 10 8 10
8 ×10
80
40
2
1 27 9 27× 4 9×5 108 45 63 3
3) 5 +(-2 ) = +(- ) =
+(- ) = +(- ) = = 3
5
4 5
4 5× 4
4×5 20
20 20 20
1 1
7 1 -7 -1 (-7)5 + (-1)2
37
4) - 3 - = - - =
+
=
=2 5
2 5 2
5
2 ×5
10