Download 6th entering 7th grade Math - 6Y and 6X Mrs

Summer Math Packet
5Y
& 5X Knight
Will be 7th graders in Fall
Name
June 2OI5
Dear Parents and Students,
We all know that over the summer, mathematical skills are often weakened which may
result in a setback at the beginning of the school year. To avoid the need to play
"catch-up" in the fall, an assignment has been prepared to help the students maintain
their skills. This assignment is made up of concepts that have been taught in sixth
grade and will provide students a thorough review of skills needed for seventh grade. lt
is important that this packet be completed to the best of their ability. The objective of
this assignment is to help them succeed in the next school year.
All questions must have work to support the answers. Work can be done on the
question paper, if work space is available. lf not, work should be completed on loose
leaf and attached to question paper. Do not squeeze work into a tiny area. Any
assignment without work will be considered an incomplete assignment. This packet
along with any loose leaf used to show work is to be placed in a folder and submitted on
the first day of school.
Thank you for your cooperation. Have a great summer!
Sincerely,
,l?rs. trorzru
Mrs. Kwan
ltLL*
//rr,$tr
Mrs. Knight
Reducin
Reduce each ratio to its lowest form.
An swe rs
2)
42
54
s)
15
24
8)
3s
28
63
11)
27
36
10
60
L4\ 42 30
16) eo
10
L7) e:
le) 64
72
20)
Ex)
5o :35
1)
3)
t2 32
4) 4s
6)
t2
7) 2:
e)
20
36
10)
t4
rz)
70
l0
13)
ls)
48 42
18) 5:20
Name:
Ratios
4s 21
20
t6
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42
18
t2
Page 1 of
[Jnderstandin
Ratios
1
Narne:
Answers
Solve each problem.
1)
A recipe called forthe ratio of sugarto flourto be 5 : l. If you used 35 ounce of sugar, how
rnany ounces of flour would you need to use?
2)
A teacher had 21 red pens. If the ratio of red pens to blue pens she owned was 3 : l, how
many pens did she have total?
3)
A chess player played 20 games total. If he won 2 of the garnes, what is the ratio of garnes
he lost to games he won?
4)
At a pet store the ratio of cats to dogs sold was l0 : l. If there were 60 cats that were sold,
how nrany dogs were sold?
5) At a restaurant
the ratio of kids meals sold to adult nreals sold was 5:4.1f there were 20
kids meals sold. what is the combined arnount o{'kids and adult meals sold?
6)
A student bought 34 pencils fbr school. If he sharpened l6 of the pencils before school,
what is his ratio of unsharpened pencils to sharpened pencils?
7) A buffet offers ranch or caesar dressing. The ratio of ranch dressing
used is 8
they
:3. If the buffet
uses T2cases
of
used to caesar dressing
ranch dressing, how many cases of caesardo
use'?
8) A student finished 72 of her homework
problems in class. If the ratio of problems she
flnished to problems she still had left was 8 : l, how many homervork problerns did she
have total?
9)
At a carnival Cody bought l5 tickets. If he used 6 tickets trying to win the ring toss game,
what is the ratio of tickets he has to tickets he's used'/
10) At a farm
l0
Math
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the ratio of cows to horses was
many horses were there?
about:blank
: 3. If there were 20 cows at the fbrm, how
6l17 12014
Usin
Ratio
Name:
uations
Answers
Solve each problem.
l)
Every pint is 2 cups. This can be expressed using the equation y x 2: Z, where y is
equal to the number of pints and Z is equal to the total number of cups. Using this
equation find the total cups in 5 pints.
This can be expressed using the equation y x 1.000 : Z,
where y is equal to the number of liters and Z is equal to the total number of milliters.
Using this equation find the total milliters in l0 liters.
2) Every liter is 1,000 milliters.
3) E,very gallon is 4 quarts. This can be expressed using the equation y x 4: Z,wherey
is equal to the number of gallons and Z is equal to the total number of quarts. Using
this equation find the total quarts in 5 gallons.
4)
For each kilogram there are I,000 grams. This can be expressed using the equation y
1,000 Z, where y is equal to the number of kilogram and Z is equal to the total
number of grams. Using this equation find the total grams in 9 kilograms.
5)
E,very quarter is 5 nickels. This can be expressed using the equation y x 5 Z, where y
is equal to the number of quarters and Z is equal to the total number of nickels. Using
:
:
this equation find the total nickels in 7 quarters.
6)
7)
8)
9)
Every quarter is 25 pennies. This can be expressed using the equation y x 25
where y is equal to the number of quarters and Z is equal to the total number
pennies. Using this equation find the total pennies in 5 quarters.
: Z,
of
Every foot is l2 inches. This can be expressed using the equation y x 12 : Z, wherc y
is equal to the number of feet and Z is equal to the total number of inches. Using this
equation find the total inches in l0 feet.
l0:
can be expressed using the equation y x
Z, where y is equal to the number of centimeters and Z is equal to the total number
millimeters. Using this equation find the total millimeters in l0 centimeters.
Every centimeter is
l0 rnillirneters. This
:
Every dollar is l0 dimes. This can be expressed using the equation y x l0 Z, where y
is equal to the number of dollars and Z is equal to the total number of dimes. Using
this equation find the total dimes in 7 dollars.
:
10)
Every yard is 3 fbet. This can be expressed using the equation y x 3 Z, where y is
equal to the number of yards and Z is equal to the total number of feet. Using this
equation find the total feet in 6 yards.
11)
Every meter is 100 centimeters. This can be expressed using the equation y x 100
where y is equal to the number of meters and Z is equal to the total number of
centimeters. Using this equation find the total centimeters in 4 meters.
t2)
of
: Z,
Every cup is 8 ounces. This can be expressed using the equation y x 8 : Z, where y is
equal to the number of cups and Z is equal to the total number of ounces. Using this
equation find the total ounces in 7 cups.
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Name:
Dividing Fractions
Solve each problem. Write your answer as a mixed number (if possible).
2)4r
l)r
4
+J_:
4
4\3
3)t7
+-
23
I
+
A-
s)
E __
53
a
J
4
6)
I
4-:2
7)z
l4
8)
5:
6
e)22
10)35
..L /t--
11)
t2)
7
2
Math
+
62
36
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l3
5-
Answers
tive Number Location on Numberline
Solve each problem.
1)
An swe rs
Which letter best shows
A
-ll2?
-89
2) Which letter best shows -43?
A
3)
-95
Which letter best shows -84?
A
4)
-56
Which letter best shows -105?
A
5)
-80
Which letter best shows -102?
A
6)
-76
Which letter best shows -25?
A
-55
7\ Which letter best shows -10?
A
8)
-58
Which letter best shows -116?
A
-96
e) Which letter best shows -52?
A
-88
10) Which letter best shows -123?
A
Name:
-100
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with Absolute Value
Use<rlor-tocompare.
1)
l-6ll
lsl
l.
2)
87
95
2.
3)
l40l
144l
4)
-33
l-201
s)
l2rl
l-e0l
6)
-28
-42
7)
-13
42
8)
64
_-8e
e) l-231-l-t7l
10)
27
ls4l
11)
l-731
-49
t2)
161l
-5
13)
ls
lsel
t4)
ls)
An swe rs
l-e
1
I
lsll
22
99
16) 3e
-1
t7)
47
l-271
t8)
lssl
l27l
1e)
l-esl
l50l
20)
-4e
lsl
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Name:
Understandin Absolute Value
Use the numberlines to find the ahsolute value.
1)
a. What is the value of 'A'?
b. How far
is'A'from
Answers
-20
-10
0
l0
20
-20
-r0
0
r0
20
-20
-10
0
l0
-20
-10
0
l0
20
-20
-10
0
l0
20
-20
-10
0
l0
20
-20
-10
0
(absolute value)?
2)
a. What is the value of 'A'?
b. How far
is'A' frotn 0
(absolr"rte value)?
3)
a. What is the value of 'A'?
b. How far
is'A' from 0
<liii lii,
litrilai til .iiliritlii
20
il'iirl>
(absolute value)?
4)
a. What is the value of 'A'?
b. How far
is'A' fiotn 0
(absolute value)'/
s) a. What is the value of 'A'?
b. How far is'A' from 0
(absolute value)?
6) a. What is the value of 'A'?
b. How far
is'A' from 0
(absolute value)?
7',1
a. What is the value of 'A'?
b. How far
is'A' fiotn
0
<liir,lar iil
irl,riil
0
l0
r lr tilii
il't
20
l>
A
(absolute valr"re)?
8)
a. What is the value of 'A'?
b. How far
is'A' fiom
0
-20
<lrii,li
-r0
0
t0
r,liri+l,Or rl ili;+lti
iliti
20
l>
A
(absolute value)?
9) a. What is the value of 'A'?
b. How far
is'A' fiorn
0
-20
<liir,li
-10
i,fiiiilor
0
r0
til ,t li iil t il
20
,l>
(absolute value)?
10)
a. What is the value of 'A'?
b. How far
is'A' from 0
-10
-20
<liitiliitilt+rl
(absolute value)?
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0
r0
ii lo i,li,iilrt,iliiiil>
20
Distance on a Grid
Find the distance between points.
Answers
1*
Math
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Nome
Solving Addition and
Subtraction Equations
in each equation'
Explain how to get the variable alone
1.
10: 100
n * 10 - 10: 100 -
2,
n+
10
x-75:49
x-75+_-:49+-_
answer'
Solve each equation and check your
3, g - B:25
4.25+Y:42
6.30: m-18
7'
5, r + 82:97
8, a-51:12
150: e + 42
15 - s
Al $t S. She had $t S left' Solve the equation
she made the loan'
to find how much money Jo had before
9. Jo loaned
-
15
A$o
B $ts
,
c $so
D $60
:
what isthe varue of the
10. criticar Thinking rf n + 10 40, then
exPression n - 25?
A5
825
c30
D50
the equation
11. writing to Explain Explain how to solve
35 + P
-
92. Then solve'
,:
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Nome
Solving Addition and
SubtraLtion Equations
alone in each equation'
Explain how to get the variable
-2,
n + 1.1 :22'3
1,
n + 1.1 - 1.1
:22'3
-
1'1
x-6.7 :28.8
:28.8 +
x-6.7+
.7 + Y - 54'4
3. g - 3-2:20
4.
6. 3.9: m-22'1
7. 100: e + 91 '8
g.
31
5. r+16.9:88'2
8. a-31 :12'6
He drove more in the afternoon'
Tom drove 11.g miles in the morning.
how far
equation courd you use to find
He drov e 32.4 mires in all" which
Tom drove in the afternoon?
A 11.8 + 32.4 - m
B 11.8 +m:32'4
G 11.8 -m:32'4
D m - 32.4: 11'8
: 45'5,then what is the value of the
10. critical Thinking lf n + 10
*
expression n 25?
A 10.5
825
c
25-5
D
45.5
ll.WritingtoExplainExplainhowtosolvetheequation
4.8 + P
-
12-2'Then solve'
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Nome
solving Multiplication and
Division Equations
get the variable alone in each equation'
For 1 through 3, explain how to
2,
1" rx7 - 42
rx7 +7 - 42+7
m+6:12
m+6x.-:12x-
Check your answer'
For 4 through 9, solve the equation.
4.9n -72
7. w + 7 :15
3. 44:2k
5. yx5:60
6. v + 13:2
8. 216 -
9. 17:t+3
36P
get the variable m alone on
)/Youtd
10. writing to Explain Tell how you
:
one side of the equation 15m
45'
problem that can be solved with the
11, Write a Problem Write a
equationr+6-
14.
can you use to
12. Number sense which equation
solve this Problem?
will bought 84 muffins'
There are 12 muffins in a package.
How many Packages did he buY?
A 12xP:84
B 84x12:P
G 12+p--84
D 84:12+P
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Nome
Solving Equations with Decimals
in each equation'
Explain how to get the variable alone
1. 7n -
2.
6.3
3. 67.3 -
x+5.2:8
3.2Q
Check your answers'
For 4through 9, solve each equation'
7, 56:
4. x + 8:5.6
8. n.2.1 :12
5. pX3.4:7'48
6.
4z
-
1.4t
9.5_s+3.7
50.8
a
pens that cost 65 cents each. she spent
10. sonja purchased some
totalof$9.10'Howmanypensdidshepurchase?Writeanequation
to describe the situation and solve'
11. Griticar Thinking n
A 3.1
32n
:
B 12.4
gg.2,then what is the value of the expression 8n?
solution as m
12" which equation has the same
+ 2'6 :
3'5?
C 2.6m: 3.5
D 3.5m :2-6
A,m+3.5:2,6
B yn + 9,1 :2,6
ig.
D32
G 24,8
get the variable p alone on one side
writing to Explain Tell how you would
of the equationS2'4
-
4P'
6
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Name
#omrnon Core Standards Pnactice
O.ruS.C.S Understand that positive and negative numbers are used together to describe quantities having
opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level,
positive/negative electric charge); use positive and negative numbers to represent quantities in real-world
explaining the meaning of O in each
creditydebits,
context",
situation.
2.
1. Which of the following
represents
a negative number? Circle all that
apply.
A
B
C
D
li,,
l'
rri
Temperature can be measured in
these temperatures is the coldest?
A 1O.F
deposit of $75
an increase of 2 inches in
height
a debt of $2
a loss of 5 pounds in weight
B
O"F
c
5"F
D 10"F
3.
Write an integer to represent 25 feet underground. Explain your answer.
4.
Write an integer to represent a rise of 150 feet. Explain your answer.
5. During a football
game, Howard's team gained 14 yards in one play and lost
12 yards in the next play. Write integers to represent the two plays.
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:
i
Wf ich of the following can be represented with -B? Circle all that apply.
A A loss of $B
B A rise of 8 feet uP to sea level
C A temperature 8 degrees below zero
D An oil drill digging 8 miles below the surface
E
F
A deposit of $g in a bank account
A change in temperature from 56"F to 64"F
T.
net income
Last week, Cy earned slightly more money than he spent. ls his
represented Oy , positive number or a negative number? Explain'
g.
be
A submarine travels 875 feet below sea level. Should the depth
represented by a positive number or a negative number? Explain.
9.
During the day, the temperature changes from -5"F to *5'F'
a,
Does the temperature become Warmer or cooler?
b. was the temperature that day ever 0'F? Explain how you know.
6
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