Transcript 1-3 Add and Subtract Real Numbers

Add and Subtract
Real Numbers
Honors Math – Grade 8
Get ready for the Lesson
An oil well has been dug to a depth of 1.7 miles. Additional drilling
makes the well 1.2 miles deeper. What signed number expresses
the final depth of the well?
What operation?
Addition
A number line can be used
to add signed numbers.
What are the addends?
 1.7  1.2
The well has been dug
into the earth.
Start at 0 and move to the left for negative #’s and to
the right for positive #’s.
KEY CONCEPT
Adding Signed Numbers
To add signed numbers with like signs:
1. Add their absolute values.
2. Use the sign of the addends for the sum.
 1 .7
 1.7
1 .7
 1.2
  1.2
 1 .2
 2.9
KEY CONCEPT
Adding Signed Numbers
To add signed numbers with unlike signs:
1. Subtract the lesser absolute value from the greater absolute value
greater  lesser
2. Use the sign of the addend with the greater absolute value.
2
40
2
3
 3 16
3
24
7
 1  1 21
8
24
19
 1 24
7  2
1  3 
8  3
Use the sign of the
rational number with
the greater absolute
value.
2
7
3  1
3
8
Simplify the absolute
values.
Subtract the Mixed
Numbers. What is the
LCD?
Make equivalents.
Borrow and subtract.
8.4  12.63
Subtract the lesser
absolute value from the
greater absolute value.
Simplify the absolute
values.
Subtract the Decimals.
Use the sign of the
rational number with the
greater absolute value.
 12.63  8.4
12.63  8.4
12.63
 8 .4
4.23
Unlike Signs!
Add the absolute values!
Simplify the absolute
values.
Add the mixed numbers.
What is the LCD?
Add the Mixed Numbers.
Use the sign of the
addends for the sum.
1  1
 2   7 
9  3
1
1
2  7
9
3
1
1
2 2
9
9
1
3
7 7
9
3
Like Signs!
4
9
9
Subtract the lesser
absolute value from the
greater absolute value.
Simplify the absolute
values.
Subtract the Decimals.
Use the sign of the
rational number with the
greater absolute value.
1
 4.93 
4
 4.93  0.25
4.93  0.25
4.93
 0.25
4.68
Unlike Signs!
Fraction &
Decimal
Change the
fraction to a
decimal!
KEY CONCEPT
Subtracting Signed Numbers
To subtract signed numbers:
1. Add its opposite.
2. Follow rules for adding signed numbers.
 20.2   7.33
Align the Decimal Points
Add the opposite of the
subtrahend.
 20.2  20.2
  7.33  7.33
Apply the rule for adding
unlike signs.
20.2
 7.33
 12.87
5  1
2  4 
6  3
Add the opposite of the
subtrahend.
5
1
2 4
6
3
Apply the rule for adding
like signs.
Add the mixed numbers.
What is the LCD?
Add the Mixed Numbers.
Rename the sum.
5  25
2
6
6
1
2
4 4
6
3
7
1
6 7
6
6
Both addends
are positive. The
sum is positive!
 6.34   10.4
Align the Decimal Points
Add the opposite of the
subtrahend.
 6.34
  10.4
 6.34
 10.4
Simplify the absolute values.
Subtract the
decimals.
10.4
 6.34
4.06
Apply the rule for adding
unlike signs.
Subtract the greater
absolute value from the
lesser absolute value.
10.4   6.34
Use the sign of the
rational number with the
greater absolute value.