Transcript Addition and Subtraction of Rational Numbers

Addition and
Subtraction of
Rational Numbers
Foundations of Algebra
Rational Numbers
• A rational number is a real number that can be written as a
simple fraction (i.e. as a ratio.)
• Example: 1.5 is a rational number because 1.5 = 3/2
(it can be written as a fraction).
• Here are some more examples
Number
As a
Fraction
Rational?
5
5/1
Yes
1.75
7/4
Yes
.001
1/1000
Yes
0.111...
1/9
Yes
√2
(square
root of 2)
?
NO !
Oops! The square root of 2
cannot be written as a
simple fraction. And there
are many more such
numbers, and because they
are not rational they are
called irrational.
Be Careful With "Mixed Fractions"
You may be tempted to write an Improper
Fraction (a fraction that is "top-heavy", i.e.
where the top number is bigger then the
bottom number) as a Mixed Fraction:
For example 7/4 = 1 3/4, shown here:
Improper Fraction
Mixed Fraction
7/
1 3 /4
4
=
But for mathematics the "Improper" form (such as
7/ ) is actually better.
4
Adding and Subtracting
Rational Numbers
• Adding and Subtracting Rational Numbers may require
you to combine numbers that are integers, decimals, and
fractions.
• The rules for adding and subtracting positive and
negatives numbers are the same for rational numbers.
• When you add or subtract fractions you must have a
common denominator.
• Since the decimal system involves tenths, hundredths,
thousandths, etc, the place-values used already represent
common denominators.
• To add 15.89 + 7.643, we only need to be sure the decimal
points are lined up so that the place-values are also lined
up.
Find the sum.
1) -2.304 + (-0.26) = -2.564
Line up the decimals and add (same signs).
2)
5 æ -3ö
+è ø
8
4 Get a common
5 æ -6 ö
+è ø
8
8
-1
=
8
denominator and
subtract.
Find the difference.
3)
-5 æ -3 ö
-ç ÷
9 è 5 ø
Change subtraction to
adding the opposite.
-5 æ 3 ö
+ç+ ÷
9 è 5ø
Get a common
denominator.
-25 æ 27 ö
+è ø
45
45
Subtract and keep sign of
the larger number.
2
45
Find the difference.
4)
1 6
2 7
1 æ -6 ö
+ç ÷
2 è 7 ø
7 æ -12 ö
+è
14
14 ø
-5
14
Change subtraction to
adding the opposite.
Get a common
denominator and
subtract.
5) Solve 6.32 – y if y = -3.42
Substitute for y:
6.32 - (-3.42)
6.32 + 3.42
9.74
Extra Practice
Extra Practice 2
Extra Practice 3