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1 0 A 1 0 B 1 0 C 1 0 D 1 0 E 1 0 F
ChingQuizz
:
9
exercises
a v ailable
for
Quizz
assessmen t
:
1.
Reminders :
multiples,
divisors,
fr actions
E.6193
1
Complete
the
blanks
with
the
w ords
ˇ
factors
ı
and
ˇ
mul- tiples
ı
:
a
25
admits
the
in teger
5
as
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
b
21
is
a
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
of
the
in teger
7
.
c
24
is
not
a
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
of
the
in teger
8
.
d
8
is
a
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
of
the
in teger
24
.
2
F or
eac h
question,
circle
the
correct
answ ers
from
the
suggestions
:
a
The
in teger
32
admits
as
factors
:
2
4
8
12
b
The
in tegers
16
and
24
admit
as
common
factors
:
2
4
8
12
c
The
in teger
6
admits
for
m ultiples
:
6
12
26
36
d
The
in tegers
8
and
12
admit
as
common
m ultiples
:
8
12
24
96
E.5725
In
this
exer cise,
any
evidenc e
of
even
inc omplete
r ese ar ch
or
even
unsuc c essful
initiative
wil l
b e
c onsider e d
in
the
assessment.
We
consider
the
six
iden tical
test
tub es
but
filled
to
differen t
lev els.
1
F or
eac h
of
the
test
tub es,
giv e
the
fraction
of
the
sp eci- men
sho wn
in
gra y .
2
Whic h
test
tub es
m ust
b e
com bined
to
obtain
a
new
test
tub e
filled
to
unit y?
E.5696
In
middle
sc ho ol,
Lise
eats
1
4
from
the
pac k age
of
cak es
she
just
op ened.
Bac k
from
college,
her
sister
Agathe
eats
the
2
3
of
the
cak es
remaining
in
the
pac k age
Lise
started.
This
lea v es
5
cakes.
What
w as
the
original
n um b er
of
cak es
in
the
pac k age?
If
the
w ork
is
not
completed,
still
lea v e
a
searc h
record.
It
will
b e
considered
in
the
assessmen t.
E.2915
Fill
in
the
blanks
with
the
appropri- ate
fraction
simplified
:
a
3
×
=
5
b
15
×
=
35
c
2
×
=
9
d
18
×
=
27
e
16
×
=
2
f
77
×
=
7
2.
Reminders :
simplific ation
E.1633
Simplify
eac h
of
the
follo wing
frac- tions
as
far
as
p ossible
:
a
18
30
b
45
63
c
24
36
d
10
5
Indication
:
we
will
follo w
a
w ording
iden tical
to
that
pre- sen ted
b elo w
:
E.1634
Simplify
the
follo wing
fractions
as
m uc h
as
p ossible
:
a
14
42
b
120
180
c
18
42
d
224
84
E.4666
Whic h
of
the
follo wing
are
simplifi- cations
of
fractions?
a
30
20
=
3
2
b
12
21
=
4
7
c
24
18
=
8
9
d
19
20
=
18
19
e
18
32
=
9
16
f
49
21
=
7
3
3.
Reminders :
addition,
subtr action
with
the
same
denominator
E.8716
Addition
and
subtraction
rule
:
For
an y
in teger
a
,
b
,
c
,
with
c
=0
,
w e
ha v e
:
a
c
+
b
c
=
a
+
b
c
;
a
c
−
b
c
=
a
−
b
c
Note:
so
adding
or
subtracting
t w o
fractions
requires
the
same
denominator.
https:/ /c hingmath.fr
chapExoCorrec/6193 sacados/6193
chapExoCorrec/5725 sacados/5725 1 0 A 1 0 B 1 0 C 1 0 D 1 0 E 1 0 F chapExoCorrec/5696 sacados/5696 chapExoCorrec/2915 sacados/2915 chapExoCorrec/1633 sacados/1633 chapExoCorrec/1634 sacados/1634 chapExoCorrec/4666 sacados/4666 chapExoCorrec/8716 sacados/8716
−
−
Translate
eac h
of
the
graphs
b elo w
b y
a
calculation
on
frac- tional
n um b ers
:
1
2
3
E.4661
P erform
the
calculations
b elo w
:
a
2
3
+
8
3
b
7
5
+
9
5
c
13
7
+
3
7
d
12
5
−
6
5
e
13
7
−
5
7
f
17
15
−
3
15
E.8717
P erform
the
follo wing
calculations
and
giv e
the
result
as
a
simplified
fraction
:
a
5
12
+
13
12
b
2
7
+
17
7
c
4
10
+
1
10
d
15
12
−
1
12
e
7
2
−
4
2
f
22
15
−
7
15
E.8725
P erform
the
follo wing
calculations
and
giv e
the
results
as
simplified
fractions
:
a
2
10
+
3
10
b
5
3
+
12
3
c
15
4
−
11
4
E.8726
P erform
the
calculations
b elo w
and
giv e
their
result
as
a
simplified
fraction
:
a
5
6
+
11
6
b
54
3
−
27
3
c
3
15
+
7
15
4.
Reminders :
addition,
subtr action
with
the
denominator
multiple
of
e ach
other
E.8718
Note:
To
add
t w o
fractions,
b oth
denominators
must
be
equal.
In
the
questions
b elo w,
w e
transform
one
of
the
fractions
in to
an
equal
fraction
but
with
a
denominator
iden tical
to
the
other
fraction.
Th us,
w e
can
apply
the
rules
previously
giv en
Each
of
the
graphs
b elo w
represen ts
an
addition
of
fractions.
Cop y
and
complete
the
blanks
to
obtain
the
desired
equalit y :
1
1
:
:
:
+
3
:
:
:
=
:
:
:
:
:
:
+
:
:
:
:
:
:
=
:
:
:
+
:
:
:
:
:
:
=
5
8
2
5
:
:
:
−
1
:
:
:
=
:
:
:
:
:
:
−
:
:
:
:
:
:
=
:
:
:
−
:
:
:
:
:
:
=
3
10
E.8728
P erform
the
calculations
b elo w
and
give
the
results
as
simplified
fractions
:
A
3
10
+
2
100
b
2
10
+
7
100
c
0.25
+
1
10
E.1040
P erform
the
follo wing
op erations
:
a
3
100
+
7
10
b
1
10
+
27
100
c
5
10
−
2
10
d
3
10
−
7
100
e
17
10
−
19
100
f
1
10
−
1
1000
E.4662
P erform
the
calculations
b elo w.
The
results
will
b e
giv en
as
a
simplified
fraction.
a
4
7
−
3
14
b
19
12
−
5
4
c
37
16
−
9
4
d
13
10
+
6
5
e
6
21
+
1
7
f
5
6
+
7
24
E.1354
1
Simplify
the
follo wing
fractions
:
12
60
;
30
60
2
P erform
the
follo wing
op eration :
1
5
+
1
2
And
giv e
the
result
as
a
maximally
simplified
fraction.
E.8724
P erform
the
follo wing
calculations.
The
results
will
b e
giv en
as
a
simplified
fraction.
a
1
+
5
6
+
3
10
b
2
+
5
12
−
7
15
c
1
5
+
3
10
−
3
14
5.
Finding
the
c ommon
denominator
and
c omp aring
fr actions
https:/ /c hingmath.fr
− chapExoCorrec/4661 sacados/4661 chapExoCorrec/8717 sacados/8717 chapExoCorrec/8725 sacados/8725 chapExoCorrec/8726 sacados/8726 chapExoCorrec/8718 sacados/8718 − chapExoCorrec/8728 sacados/8728 chapExoCorrec/1040 sacados/1040 chapExoCorrec/4662 sacados/4662 chapExoCorrec/1354 sacados/1354 chapExoCorrec/8724 sacados/8724
et et
E.8719
Proposition :
Let
a
,
b
,
c
be
three
strictly
p ositiv e
in tegers
:
If
t w o
fractions
ha v e
the
same
denominator
then
the
largest
fraction
is
the
one
with
the
largest
n umerator
:
if
a< b
then
a
c
<
b
c
Example:
for
comparison
3
5
<
4
5
If
t w o
fractions
ha v e
the
same
n umerator
then
the
largest
fraction
is
the
one
with
the
smallest
denomina- tor :
if
b< c
then
a
b
>
a
c
Example:
are
compared
to
2
5
<
2
7
1
a
Giv e
all
m ultiples
of
6
that
are
strictly
less
than
30
.
b
Complete
the
dotted
lines
:
5
6
=
:
:
:
12
=
:
:
:
18
=
:
:
:
24
2
Complete
the
dotted
lines
:
3
4
=
:
:
:
8
=
:
:
:
12
=
:
:
:
16
=
:
:
:
20
=
:
:
:
24
=
:
:
:
28
3
Compare
the
t w o
fractions
of
5
6
and
3
4
.
E.4700
1
Determine
the
least
common
m ultiple
of
4
and
6
.
2
Compare
the
t w o
fractions
:
7
4
and
11
6
6.
Addition
and
subtr action
E.2542
Consider
the
t w o
n um b ers
written
as
fractions
:
A
=
5
6
;
B
=
1
4
.
1
Giv e
the
least
common
m ultiple
of
the
denominators
of
these
t w o
fractions.
2
W rite
the
t w o
n um b ers
A
and
B
in
fractional
writing
so
that
they
ha v e
the
same
denominator.
3
A dd
the
n um b ers
A
and
B
E.2544
Cop y
and
p erform
the
follo wing
ad- ditions,
completing
the
in termediate
step
b eforehand
:
a
1
3
+
1
2
=
:
:
:
6
+
:
:
:
6
=
:
:
:
+
:
:
:
6
=
:
:
:
6
b
3
5
+
7
10
=
:
:
:
10
+
:
:
:
10
=
:
:
:
+
:
:
:
10
=
:
:
:
10
c
5
6
+
3
4
=
:
:
:
12
+
:
:
:
12
=
:
:
:
+
:
:
:
12
=
:
:
:
12
d
8
7
+
8
3
=
:
:
:
21
+
:
:
:
21
=
:
:
:
+
:
:
:
21
=
:
:
:
21
e
2
15
+
1
10
=
:
:
:
30
+
:
:
:
30
=
:
:
:
+
:
:
:
30
=
:
:
:
30
f
5
6
+
10
9
=
:
:
:
18
+
:
:
:
18
=
:
:
:
+
:
:
:
18
=
:
:
:
18
E.8736
P erform
the
follo wing
sums
:
a
1
6
+
1
9
b
3
10
−
1
4
c
3
4
−
1
6
d
5
9
+
1
12
e
5
8
−
1
10
f
1
10
+
5
12
Hint :
To
p erform
these
sums,
w e
will
fo cus
on
the
smallest
common
denominator
and
use
a
similar
format
:
E.8720
P erform
the
follo wing
op erations
and
giv e
the
result
in
simplified
form
:
a
7
6
+
9
10
b
3
20
+
7
12
c
7
15
+
7
10
Note:
Use
a
format
similar
to
the
one
b e- lo w
:
E.8721
1
a
Complete
the
blanks
:
120
=
12
×
:
:
:
;
120
=
15
×
:
:
:
b
Determine
the
least
common
m ultiple
of
the
n um b ers
12
and
15
.
2
P erform
the
follo wing
sum
:
1
12
+
1
15
.
Giv e
the
simplified
form
of
the
result.
https:/ /c hingmath.fr
chapExoCorrec/8719 sacados/8719
et
et chapExoCorrec/4700 sacados/4700 chapExoCorrec/2542 sacados/2542 chapExoCorrec/2544 sacados/2544 chapExoCorrec/8736 sacados/8736 chapExoCorrec/8720 sacados/8720 chapExoCorrec/8721 sacados/8721
A B M N 5 3 15 7 4 28 ... 6 18 11 6 66 13 8 52 104 15 10 ... 17 12 51 68
A B C D
E.8774
Belo w
is
sho wn
a
segmen t
[
AB
]
where
t w o
p oin ts
M
and
N
are
placed
suc h
that
:
segmen t
[
AM
]
is
one-third
of
segmen t
[
AB
]
;
segmen t
[
BN
]
represents
t w o-sev en ths
of
segmen t
[
AB
]
.
Determine
the
fraction
of
segmen t
[
AB
]
that
separates
p oin ts
M
and
N
.
E.2132
Three
p oin ts
A
,
B
and
C
of
a
graduated
line
ha v e
abscissa
:
1
4
;
1
3
;
5
12
Are
these
three
p oin ts
ev enly
spaced
on
the
graduated
line?
E.8755
The
Egyptians
used
only
1
numerator
fractions,
with
the
exception
of
the
2
3
fraction.
T o
find
the
double
of
their
n umerator
fractions
1
,
tables
w ere
a v ailable,
one
of
whic h
is
sho wn
b elo w
:
whose
use
of
the
first
ro w
of
the
table
tells
us
:
The
double
1
5
is
the
sum
of
1
3
and
1
15
1
Complete
the
table
with
the
correct
v alues
replacing
the
blanks.
2
Chec k
the
relationship
induced
b y
the
last
ro w
of
this
table.
E.8714
Consider
the
square
sho wn
opp o- site,
whic h
has
b een
decomp osed
in to
4
equal
squares.
Some
of
these
squares
ha v e
b een
sub divided
in to
squares
of
the
same
dimension.
What
fraction
of
the
square
ABC D
is
shaded?
7.
Relative
numb ers :
simplific ation
of
fr actions
E.4663
Complete
the
blanks
to
v erify
the
follo wing
equations
:
a
5
:
:
:
=
−
5
7
b
−
3
4
=
3
:
:
:
c
−
3
:
:
:
=
3
4
d
12
−
15
=
−
:
:
:
5
e
27
:
:
:
=
−
3
−
2
f
36
24
=
−
15
:
:
:
E.4664
Complete
the
blanks
b elo w
to
v erify
the
equalities :
a
8
−
5
=
:
:
:
20
b
−
15
:
:
:
=
−
3
7
c
−
4
11
=
−
16
:
:
:
d
36
81
=
−
:
:
:
9
e
−
7
−
10
=
:
:
:
40
f
12
20
=
−
15
:
:
:
8.
Relative
numb ers :
addition
and
subtr action
E.1056
P erform
the
follo wing
additions
and
subtractions,
giving
the
result
as
a
fraction
simplified
as
far
as
p ossible
:
a
2
4
+
2
−
4
b
5
3
+
−
17
6
c
−
5
12
−
−
2
3
d
2
+
−
3
2
E.8737
P erform
the
follo wing
additions
and
subtractions,
giving
the
result
as
a
fraction
simplified
to
the
maxim um
:
a
2
7
+
3
11
b
5
8
+
2
c
−
3
11
+
−
4
5
E.4761
P erform
the
follo wing
op erations.
The
result
will
b e
giv en
as
a
simplified
fraction
:
a
−
1
6
+
1
−
14
b
3
10
−
7
15
c
−
3
15
−
−
4
25
d
5
6
+
9
−
10
E.8738
P erform
the
follo wing
additions
and
subtractions,
giving
the
result
as
a
fraction
simplified
to
the
maxim um
:
a
−
7
10
+
5
6
b
−
1
15
+
−
1
12
9.
Problem
https:/ /c hingmath.fr
chapExoCorrec/8774 sacados/8774
A B M N chapExoCorrec/2132 sacados/2132 chapExoCorrec/8755 sacados/8755 5 3 15 7 4 28 ... 6 18 11 6 66 13 8 52 104 15 10 ... 17 12 51 68 chapExoCorrec/8714 sacados/8714 A B C D chapExoCorrec/4663 sacados/4663 chapExoCorrec/4664 sacados/4664 chapExoCorrec/1056 sacados/1056 chapExoCorrec/8737 sacados/8737 chapExoCorrec/4761 sacados/4761 chapExoCorrec/8738 sacados/8738
Etape n o 1 Etape n o 2 Etape n o 3
E.4630
Successiv e
figures
are
constructed
b y
adding
a
new
square
;
more
precisely ,
the
new
square
added
to
a
side
measuring
half
of
the
previous
square
:
It
is
assumed
that
the
first
square
had
a
side
measuring
1
cm
.
1
Sho w
that
the
area
of
the
figure
in
step
2
measures
:
A
2
=
5
4
2
Determine
as
an
irreducible
fraction,
the
area
A
3
of
this
figure
made
in
step
3
.
3
Determine
the
area
A
4
of
this
figure
in
step
four.
E.4765
1
T est
the
iden tit y
b elo w
for
in tegers
b et w een
1
and
9
:
1
n
(
n
+
1)
=
1
n
−
1
n
+
1
2
Use
the
previous
question
to
easily
determine
the
v alue
of
A
où
:
A
=
1
+
1
2
+
1
6
+
1
12
+
1
20
+
1
30
+
1
42
+
1
56
+
1
72
+
1
90
10.
Share
E.8778
P erform
the
follo wing
calculations
and
giv e
the
results
as
simplified
fractions
:
a
5
3
+
2
9
b
2
3
−
5
4
c
3
10
−
7
6
d
15
16
×
24
75
E.8779
P erform
the
calculations
b elo w
and
giv e
their
results
as
simplified
fractions
:
a
2
3
−
3
2
×
4
9
b
10
9
×
6
25
+
1
3
×
1
5
c
1
3
1
−
5
2
E.8780
P erform
the
follo wing
calculations
and
giv e
the
results
as
simplified
fractions
:
a
1
2
3
a
1
+
3
÷
3
2
×
5
−
5
11.
Unclassified
exer cises
E.3326
Simplify
the
fraction
1404
3465
by
3.
Is
the
resulting
fraction
irreducible?
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chapExoCorrec/4630 sacados/4630 Etape n o 1 Etape n o 2 Etape n o 3 chapExoCorrec/4765 sacados/4765 chapExoCorrec/8778 sacados/8778 chapExoCorrec/8779 sacados/8779 chapExoCorrec/8780 sacados/8780 chapExoCorrec/3326 sacados/3326