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