Pg48
1.5
Rational Number Operations
The strategies and order of operations you used for calculations with integers, fractions, and
decimals can be extended to all rational numbers.
Calculations with rational number operations may be simpler to perform if you rename mixed
numbers as improper fractions, and rewrite negative fractions with the negative sign in the
numerator.
Example 1
Evaluate.
−4 + 2 − 2 1 ÷ ℎ = 5 1 = −1 7
5
−3
2
3
9
−12 10
−
15
15
−12 − 10
=
15
22
=−
15
=
1 1
7
= −2 "5 # ÷ "−1 #
2 3
9
−5 16
16
=
" # ÷ "− #
2 3
9
40
9
= − × "− #
3
16
15
=
2
Example 2
Matthew was chatting online with his friend Bruce, who lives in the United States. Bruce said
that the temperature outside was degrees Fahrenheit. Matthew was not sure how cold that
was because he was used to temperature readings measured in degrees Celsius. He found the
following conversion formula from a weather website: = − 32 where is the
temperature in degrees Celsius and is the temperature in degrees Fahrenheit. Determine the
Celsius temperature equivalent to −5.5 .
5
= −5.5 − 32
9
5
= −37.5
9
= −20.83! Example 3
These temperatures were recorded at noon on January 1 from 1998 to
2006 at Ottawa MacDonald-Cartier International Airport. Determine the
average noon temperature on January 1 for the years given.
−20.9 − 22.7 − 5.4 − 11.4 − 10.9 − 5 − 4.7 − 2.8 − 9.6
9
&'( = −10.37!
&'( =
Practice
Pg54 #10 ~ 12 & 14 ~ 15