Transcript 11 2 - applebymath

11. 2
Adding Integers
In the Real World
Football During a high school football game,
your team gained 6 yards on the first play,
lost 8 yards on the second, and gained 11
yards on the third play. Did your team gain
the 10 yards needed for a first down?
11. 2
EXAMPLE
Adding Integers
1
Modeling Integer Addition
To
understand
the problem
read to
and
organizegains
the information.
Start
at 0 on a number
line. above,
Use arrows
represent
and losses.
Move right to add a positive number and left to add a negative number.
First play:
First play gained 6 yards: 0 + 6 = 6
6 means a gain of 6 yards.
Second play lost 8 yards:
6 + (–8) = –2
Second play:
–8
means
loss of118 yards:
yards. –2 + 11 = 9
Third
play agained
11
Third play:
11 means a gain of 11 yards.
–8
6
–3 –2 –1
ANSWER
0
31
2
3
4
5
6
7
8
9 10
Your team gained only 9 yards during the first three plays,
which was not enough for a first down.
11. 2
Adding Integers
Absolute Value The absolute value of a number is its distance from 0 on a
number line. The absolute value of a number a is written | a |.
3 units
–4
–3
–2
–1
3 units
0
1
2
3
4
The absolute value of –3 is 3.
| –3 | = | 3 | = 3
11. 2
Adding Integers
Adding Integers
Words
Numbers
Same Signs To add two integers
with the same sign, add their
absolute values and write their
common sign.
3+5=8
Different Signs To add two
integers with different signs, first
subtract the lesser absolute value
from the greater absolute value.
Then write the sign of the number
with the greater absolute value.
–7 + 10 = 3
–3 + (–5) = –8
7 + (–10) = –3
Adding Integers
11. 2
EXAMPLE
2
Adding Integers
In the sum – 4 + (–7), both numbers have a negative sign. To find the sum,
find | – 4 | + | –7 | and write a negative sign.
– 4 + (–7) = –11
In the sum –8 + 3, the numbers have different signs and – 8 has the greater
absolute value. To find the sum, find | – 8 | – | 3 | and write a negative sign.
– 8 + 3 = –5
In the sum – 6 + 9, the numbers have different signs and 9 has the
greater absolute value. To find the sum, find | 9 | – | – 6 |.
–6 + 9 = 3