L ESSON 13 - P OLYNOMIAL E QUATIONS & C OMPLEX N UMBERS PreCalculus - Santowski.
A DDING AND S UBTRACTING R ATIONAL N UMBERS. R ATIONAL N UMBER :
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Transcript of A DDING AND S UBTRACTING R ATIONAL N UMBERS. R ATIONAL N UMBER :
ADDING AND SUBTRACTING RATIONAL NUMBERS
RATIONAL NUMBER:Any number that can be written
as a fraction of two integersCan be positive or negative Includes decimals and whole
numbers!
Examples:½, ¾, 2.5, 8.25, 1, 976
ADDING AND SUBTRACTING
We can use the same rules we found for integers for rational numbers
Adding Rule 1: If the signs are the same Add and keep the same sign
Adding Rule 2: Different signs Subtract and use larger sign
Subtracting Rule: Keep-Change-Change
FRACTIONSLet’s review
Example 1:
Try this one:
25+16=¿2×65×6
+1×56×5
=¿1230
+530
=¿1730
23−17=¿2×73×7
−1×37×3
=¿1421−321
=¿1121
OR I could useKeep-Change-Change!
1421
+−321
=¿1121
MORE FRACTIONSProblem 1:
−25
+34=¿−(2×4 )5×4
+ 3×54×5
=¿−820
+1520
=¿720
Which fraction has a bigger
absolute value?
So the sign of our
answer is positive!
Remember: We subtract to find our
answer because we are battling
our zero pairs!15−8=7
TRY THIS ONE:Problem 2:
13+(−79 )=¿1×3
3×3+(−79 )=¿3
9+(−79 )=¿
−49
Remember we want to wait until we have a common denominator before we
decide which fraction has a bigger absolute value.
A COUPLE MORE:Problem 3: Subtraction
Problem 4:
−1320
−15=¿−1320
−1×45×4
=¿−1320
−420
=¿
23−(−727 )=¿2×9
3×9−(−727 )=¿18
27−(−727 )=¿
Keep-Change-Change!−1720
2527Keep-Change-Change!
¿ −1320
+(−420 )=¿
1827
+(+727 )=¿
MIXED NUMBERSProblem 1:
Problem 2:
1+15=¿1×51×5
+15=¿55+15=65¿115
Whoa! That looks easy! Let’s think about pizza…
−2−12=¿−(2×2)1×2
−12=¿−42−12=¿
¿−52or −2
12
Remember this only works when they have the SAME SIGN!
−42
+(−12 )=¿
MORE MIXED NUMBERS Try going backwards: Rewrite the
following mixed numbers as a sum of two numbers.
8+1112
−9+(−58 )
−15+(−49 )
LET’S TALK ABOUT DECIMALS
They work the same way as integers and fractions! Just follow your adding and subtracting integer rules!
3.8
0 .8
Addition Rule 2:
−4 .3
7.6+ (+4.3 )=¿11.9Keep-Change-Change
−2.9+ (−3.9 )=¿−6 .8
PROPERTIES Commutative Property of Addition: Numbers
can be added in any order.Example: 5+3=3+5
Associative Property of Addition: Numbers can be grouped in any way.Example: (7+3) + 5 = 7 + (3+5)
Identity Property of Addition: The sum of any number and zero is that number.Example: 18 + 0 = 18
MORE WITH PROPERTIES Write the property used for each example:
1.
2.
3.
Commutative Property of Addition
Associative Property of Addition
Identity Property of Addition
ADDING AND SUBTRACTING
RATIONAL NUMBERS PRACTICE