Transcript Ch 1-4 Adding Integers

1-4 Adding Integers
California
Evaluating
Algebraic Expressions
Standards
NS1.2 Add, subtract, multiply, and divide
rational numbers (integers, fractions, and
terminating decimals) and take positive rational
numbers to whole-number powers.
AF1.3 Simplify numerical
expressions by applying properties of rational
numbers (e.g. identity, inverse, distributive,
associative, commutative) and justify the
process used.
1-4 Adding Integers
Additional Example 1A: Using a Number Line to
Add Integers
Expressions
Use Evaluating
a number line Algebraic
to find the sum.
(–6) + 2
Start at 0. Move left 6
units. From –6, move
right 2 units.
–6
2
–6 –5 –4 –3 –2 –1
0
1
2
3
4
5
You finish at –4, so (–6) + 2 = –4.
Helpful Hint
To add a positive number move to the right.
To add a negative number move to the left.
1-4 Adding Integers
Additional Example 1B: Using a Number Line to
Add Integers
Expressions
Use Evaluating
a number line Algebraic
to find the sum.
Start at 0. Move left 3
units. From –3, move
left 6 units.
–3 + (–6)
–6
–3
–9 –8 –7 –6 –5 –4 –3 –2 –1 0
You finish at –9, so –3 + (–6) = –9.
1
2
1-4 Adding Integers
Check It Out! Example 1A
Use a number line to find the sum.
Evaluating Algebraic Expressions
(–3) + 7
Start at 0. Move left 3
units. From –3, move
right 7 units.
7
–3
–6 –5 –4 –3 –2 –1
0
1
2
You finish at 4, so (–3) + 7 = 4.
3
4
5
1-4 Adding Integers
Check It Out! Example 1B
Use a number line to find the sum.
Evaluating Algebraic Expressions
(–2) + 4
4
Start at 0. Move left 2
units. From –2, move
right 4 units.
–2
–6 –5 –4 –3 –2 –1
0
1
2
You finish at 2, so (–2) + 4 = 2.
3
4
5
1-4 Adding Integers
Another
way to add
integers is toExpressions
use absolute
Evaluating
Algebraic
value.
1-4 Adding Integers
Additional Example 2: Using Absolute Value to Add
Integers
Evaluating
Add.
Algebraic Expressions
A. 1 + (–2)
1 + (–2) Think: Find the difference of 1 and –2 .
–1
2 > 1; use the sign of 2.
B. (–8) + 5
(–8) + 5 Think: Find the difference of –8 and 5 .
–3
8 > 5; use the sign of 8.
1-4 Adding Integers
Additional Example 2: Using Absolute Value to
Add Integers
Evaluating Algebraic Expressions
Add.
C. (–2) + (–4)
(–2) + (–4)
–6
Think: Find the sum of –2 and –4 .
Same sign; use the sign of the
integers.
1-4 Adding Integers
Check It Out! Example 2
Add.
Evaluating
Algebraic Expressions
A. 3 + (–6)
3 + (–6) Think: Find the difference of 3 and –6 .
–3
6 > 3; use the sign of 6.
B. (–4) + 1
(–4) + 1 Think: Find the difference of –4 and 1 .
–3
4 > 1; use the sign of 4.
1-4 Adding Integers
Check It Out! Example 2
Add.
Evaluating
Algebraic Expressions
C. (–6) + (–7)
(–6) + (–7)
–13
Think: Find the sum of –6 and –7 .
Same sign; use the sign of the
integers.
1-4 Adding Integers
Additional Example 3: Evaluating Expressions with
Integers
Evaluating Algebraic Expressions
Evaluate c + 4 for c = –8.
c+4
(–8) + 4
Replace c with –8.
Think: Find the difference of –8 and 4 .
–8 + 4 = –4 8 > 4; use the sign of 8.
1-4 Adding Integers
Check It Out! Example 3
Evaluate
d + 7 forAlgebraic
d = –3.
Evaluating
Expressions
d+7
(–3) + 7 Replace d with –3.
Think: Find the difference of –3 and 7 .
–3 + 7 = 4
7 > 3; use the sign of 7.
1-4 Adding Integers
Additional Example 4: Application
Meka opened a new bank account. Find her account
balance
after the first
four transactions
listed below.
Evaluating
Algebraic
Expressions
Deposits: $200, $20
Withdrawals: $166, $38
200 + 20 + (–166) + (–38) Use a positive sign for
deposits and a negative
sign for withdrawals.
Group integers with the
(200 + 20) + (–166 + –38)
same signs.
220 + (–204)
Add integers within each
group.
220 > 204; use the sign
16
of 220.
Meka’s account balance after the first four transactions
is $16.