Algebra 1 Common Core Student Edition, Grade 8-9

How do you

represent th e

problem w ith an

expression?

Start your expression

with zero to represent

sea level. Subtract for

dives, and add for rises.

A l l o f th e a d d i t i o n p r o p e r t ie s o f r e a l n u m b e r s t h a t y o u le a r n e d i n L e s s o n 1 -4 a p p ly

to b o th p o s itive a n d negative n u m b e rs. Y ou can use these p ro p e rtie s to re o rd e r and

s im p li f y e x p re s s io n s.

Adding and Subtracting Real Numbers

Scuba Diving A reef explorer dives 25 ft to photograph brain coral and then rises 16 ft to

travel over a ridge before diving 47 ft to survey the base of the reef. Then the diver rises 29 ft

to see an underwater cavern. What is the location of the cavern in relation to sea level?

Distance and direction for each

change in location

Location in relation to

sea level after changes

Represent the diver's

trip w ith an expression.

Reorder the values to make

calculations easier.

0 - 2 5 + 1 6 - 4 7 + 2 9 W rite an expression.

= 0 + ( - 2 5 ) + 16 + ( - 4 7 ) + 29 Use rule fo r subtracting real numbers.

= 0 + 16 + 29 + (-25) + (-47) Commutative Property of Addition

= 0 + (1 6 + 2 9 ) + [ ( - 2 5 ) + ( - 4 7 ) ] Group addends w ith the same sign.

= 0 + 4 5 + ( - 7 2 ) Add inside grouping symbols.

= 45 + (-72) Identity Property of Addition

= - 2 7 Use rule fo r adding numbers w ith different signs.

T h e c a v e r n is a t - 2 7 f t i n r e la t io n t o sea le v e l.

G o t It? 4. A r o b o t s u b m a r in e d iv e s 8 0 3 f t t o th e o c e a n flo o r. I t r is e s 2 1 5 f t as t h e w a t e r

g e ts s h a llo w e r. T h e n th e s u b m a r in e d iv e s 2 6 1 9 f t i n t o a d e e p c re v ic e. N e x t,

i t r is e s 7 3 4 f t t o p h o t o g r a p h a c r a c k i n th e w a ll o f th e c re v ic e. W h a t is th e

lo c a t io n o f th e c r a c k i n r e la t io n to sea le v e l?

9 Lesso n Ch eck

Do y o u k n o w H OW?

Use a number line to find each sum.

1. -5 + 2 2. —2 + ( —1)
   Find each sum or difference.


2. -1 2 + 9 4. -4 + (-3)


3. -3 -(-5 ) 6. 1.5-8.5

Do y o u UN DERSTAN D? l ^ P R A a f c ES

7. Vocabulary What is the sum of a number and its
   opposite?


8. C o m p a r e a n d C o n t r a s t How is subtraction related to
   addition?


9. Error Analysis Y o u r f r i e n d says t h a t s in c e -a is t h e
   opposite of a, th e o p p o s it e o f a n u m b e r is a lw a y s
   n e g a tiv e. D e s c r ib e a n d c o r r e c t t h e e r ro r.

c

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