Transcript j 15

Week 6, Day Three
HW # 23- Rational Numbers worksheet
Study for QUIZ 2-1 to 2-6 (review last night’s HW)
Warm up
Is the statement below true or false? Explain how
you arrived at your conclusion.
My number and your number are both divisible
by 8. Therefore, the sum of our numbers will be
divisible by 4.
Warm Up Response
1. If my number is divisible by 8, then 8 is a factor
of my number.
2. Since 4 is a factor of 8, my number would also
be divisible by 4.
3. The same would be true for your number.
4. Therefore, even if I add the numbers together,
4 would remain a factor of the sum.
EX: 16 + 32 = 48 which is divisible by 4 (and 8)
Homework Check
You should have checked your answers online last night.
PLEASE be sure that you do this. If you did not get a
majority of the problems correct, fill out a Hall Pass in your
Panther Planner and come see me! There is a quiz on Day
Four!
• Mystery Numbers
• Solving Equations
(both single and multi-step)
Mystery Numbers
Each group has a different statement. Decide if
the statement is TRUE or FALSE.
Prove your answer.
Be sure to use complete sentences and math
vocabulary.
2-7 Lesson Quiz
Solve.
1. x – 23.3 = 17.8
3. 9y =
3
5
y=
x = 41.1
1
15
5
j = –15
12
2
3
2. j +
= –14
3
4
d = 2 3 d=9 1
4.
4
2
8
Include an explanation of
why you did what you did
for #4.
2
5. Tamara can mow 5 acre in one hour. If her yard is 2 acres,
how many hours will it take her to mow the entire yard?
5 hours
2-7 EXTRA PRACTICE EXAMPLES
Additional Examples 1A: Solving Equations with
Decimals
Solve.
m + 4.6 = 9
m + 4.6 = 9
– 4.6
– 4.6
4.4
m =
Since 4.6 is added to m,
subtract 4.6 from both
sides to undo the
addition.
Remember!
Once you have solved an equation, it is a good idea to check
your answer. To check your answer, substitute your answer
for the variable in the original equation.
Additional Examples 1B: Solving Equations with
Decimals
Solve.
8.2p = –32.8
8.2p = –32.8
8.2
8.2
p = –4
Since p is multiplied by 8.2,
divide both sides by 8.2.
Additional Examples 1C: Solving Equations with
Decimals
Solve.
x 1.2
1.2 •
= 15
x 1.2
= 1.2 • 15
x = 18
Since x is divided by 1.2, multiply
both sides by 1.2.
Check It Out! Example 1
Solve.
A.
m + 9.1 = 3
Since 9.1 is added to m, subtract 9.1
from both sides to undo the addition.
m + 9.1 = 3
–9.1
m
=
–9.1
=
–6.1
B. 5.5b = 75.9
5.5 5.5
b
=
75.9 5.5
b = 13.8
Since b is multiplied by 5.5, divide both sides
by 5.5.
Check It Out! Example 1C
Solve.
C.
4.5 •
y 4.5= 90
y 4.5
= 4.5 • 90
y = 405
Since y is divided by 4.5, multiply
both sides by 4.5.
Additional Example 2A: Solving Equations with
Fractions
Solve.
n+
n+
2
=–
7
2 = –2 –
7
7
–
n=–
3
7
3
7
5
7
2
7
2
Since is added to n, subtract
7
2
7from both sides.
Additional Example 2B: Solving Equations with
Fractions
Solve.
1
2
3
1
6
1
1
Since is subtracted from y, add
6
y–
= 2 + 1 1
+
6
3
6 to both sides.
6
6
4 1
y =
+
Find a common denominator, 6.
6 6
5
y =
6
y–
=
Additional Example 2C: Solving Equations with
Fractions
Solve.
5
5x
=
8
6
5x
5
5
÷ = ÷
8
6
6
1
1
1
6
5
5
x• 5 = 8 •
6
4
1
1
3
x =
4
5
6
3
6
5
1
Since x is multiplied by ,
5
6
5
divide both sides by .
6
Multiply by the reciprocal. Simplify.
Check It Out! Example 2A
Solve.
5
1
=–
9
9
n+
n+
1 = –1 –
9
9
–
5
9
n=–
6
9
n=–
2
3
1
9
1
Since is added to n, subtract
9
1
9from both sides.
Simplify.
Check It Out! Example 2B
Solve.
1 =
2
1
1
y–
=
+
2
2
y–
3
4
3
+ 1
4
2
3 2
y =
+
4 4
5
y =
4
1
y =1
4
1
Since is subtracted from y, add
2
1
2 to both sides.
Find a common denominator, 4.
Simplify.
Check It Out! Example 2C
Solve.
3
3x
=
4
8
3x
3
3
÷ = ÷
4
8
8
1
18 1
3
3
x• 3 = 4 •
8
1
1
1
x=2
3
8
82
3 1
Since x is multiplied by ,
3
8
3
divide both sides by .
8
Multiply by the reciprocal. Simplify.
Check It Out! Example 3
2
Rick’s car holds
3 the amount of gasoline as his
wife’s van. If the car’s gas tank can hold 24
gallons of gasoline, how much gasoline can the tank in the minivan
hold?
Write an equation:
Capacity of
minivan’s tank
g
•
2/3
=
Capacity of
car’s tank
•
2
3
=
24