Download Lesson 2.2, 2.3, 2.4, 2.6

Lesson 2.2, 2.3, 2.4, 2.6: Rational Number Operations
Goal: To find the sum, difference, product or quotient.
ADDING REAL NUMBERS
To add real numbers, use the following rule (can be sung to the tune of “Row, Row, Row
Your Boat”):
Same signs add and keep, different signs subtract
Take the sign of the larger number, than you’ll be exact!


When adding decimals, make sure you line up the decimal points before doing
any adding of your numbers.
When adding fractions, convert fractions into an improper fraction before
proceeding to add them.
o Converting from a mixed number to an improper fraction:
2nd step: add the numerator to your multiplication answer
-5 ¼ = -21/4
1st step: multiply denominator by whole number
SUBTRACTING REAL NUMBERS
To subtract real numbers, change your subtraction sign to addition, and change the sign
of the number after the subtraction sign:
-8 – 17  -8 + -17
Once you have changed subtraction to addition and changed the sign of the number after
the subtraction sign, you may now follow the exact same rules as adding real numbers.
MULTIPLYING REAL NUMBERS
To multiply real numbers, use the following rules:
Problem
(+)(+)
(-)(-)
(-)(+)
(+)(-)

Answer
(+)
(+)
(-)
(-)
*same signs, answer is positive
*different signs, answer is negative
When multiplying decimals, multiply regularly, ignoring the decimal
points. Once you have your answer, put the decimal back into your
answer by moving it to the left as many places as there are digits behind
the decimal points in your problem.
o 5.74
x 3.4
19.516
3 total numbers behind the
decimal points
moved 3 places


When multiplying fractions, you multiply straight across…multiply
numerator by numerator and denominator by denominator…simplify
fraction if possible
When multiplying with a variable, multiply the numbers together as
normal and attach the variable at the end of your answer
DIVIDING REAL NUMBERS
To divide real numbers, follow the same rules as multiplying real numbers…
same signs  answer + ; different signs  answer –

When dividing fractions, you can never divide by a fraction, so you must
change your division into multiplication and flip (reciprocal) the fraction
after the division sign.
5
-4

9
3

5
3

9 -4
When dividing an expression by a number, divide each part of the
expression by the number, leaving you a simplified expression.

16x + 48
8

2x + 6
***THE BEST PART OF ALL OF THIS IS THAT YOU MAY USE A
CALCULATOR TO SOLVE THESE PROBLEMS RATHER THAN WORK
THEM OUT BY HAND…HOWEVER, DO MAKE SURE YOU DO
UNDERSTAND THE RULES OF ADDING, SUBTRACTING, MULTIPLYING
AND DIVIDING REAL NUMBERS!!
You Try…
Find the sum, difference, product, or quotient for each problem.
38. –7 + (-3)
39. 9.6 + (-2.1)
40. –4 – 8
41. 9 – 18
42. 6 – (-8)
43. –2.4 – (-1.8)
44. In the morning, the temperature is –30 F. In the afternoon, the temperature was 210 F.
What was the change in temperature?
45. –4(-6)
46. –3(-2)(-7)
47. – ½ (2)(3y)
48. (-2)(a)(-5)
49. 25  5
50. –40  (2/3)
51. ½  ¾
52. 12x – 8
4
~This concludes Sections 2.2, 2.3, 2.4, and
2.6…if you have any questions over this
material, make sure to bring them to class
tomorrow!