Using Equal Ratios
to Find Missing Values
6.RP.A.3
Using Equal Ratios to Find Missing Values
X
1
2
3
4
5
6
7
8
9
10
1
1
2
3
4
5
6
7
8
9
10
2
2
4
6
8
10
12
14
16
18
20
3
3
6
9
12
15
18
21
24
27
30
4
4
8
12
16
20
24
28
32
36
40
5
5
10
15
20
25
30
35
40
45
50
6
6
12
18
24
30
36
42
48
54
60
7
7
14
21
28
35
42
49
56
63
70
8
8
16
24
32
40
48
56
64
72
80
9
9
18
27
36
45
54
63
72
81
90
10
10
20
30
40
50
60
70
80
90
100
Here is
Let’s
look
a multiplication
at the multiples
table.
of 1 and the multiples of 6.
Using Equal Ratios to Find Missing Values
1
1
2
3
4
5
6
7
8
9
10
1
1
2
3
4
5
6
7
8
9
10
6
6
12
18
24
30
36
42
48
54
60
When we bring them together, we can see many equal ratios.
Using Equal Ratios to Find Missing Values
1:6
cubes
faces
1
1
2
3
4
5
6
7
8
9
10
6
6
12
18
24
30
36
42
48
54
60
The
This
Here
They
If
42
there
first
is
are
have
the
are
ratio
2 cubes.
3
a
ratio
7 total
cubes,
weofsee
ofcubes
12
18
how
isfaces.
1:6.
many
to faces,
faces
because
are there?
for every cube, there are 6 faces.
Using Equal Ratios to Find Missing Values
5:7
students
5
10 15 20 25 30
desks
7
14 21 28 35 42
Let’s
If
…
For
And,
athen
for
classroom
every
for
use
every
the
every
this
10ratio
15
20
25
7students,
desks
table
30
has
ofstudents,
5students
to…
students
find
there
more
there
to
will
…
desks
equal
be
will
14be
21
28
35
is
ratios.
desks.
5:7.
42 desks.
Using Equal Ratios to Find Missing Values
5:7
students
5
10× ?4 15 20 25 30
desks
7
14× 4 21 28 35 42
Now,
If
5
Let’s
So,
28
times
x
there
4for
=
also
let’s
20
every
are
what
multiply
use
5 students
number
20
this
students,
ratio
7 by
isfor
4.
equal
toevery
What
there
findtoais
7
must
20?
missing
desks,
7 x be
4? 28
how
value
desks.
many
in the
desks
table.must there be if there are 20 students?
Using Equal Ratios to Find Missing Values
4:11
pencils
pens
4
8
12 16 20 24
11 22 33 44 55 66
Let’s
If
…
For
And,
there
for
then
every
for
use
every
are
the
every
another
8
12
16
20
4
ratio
pencils,
11
pencils,
pencils
24
pens
ofpencils,
table
pencils
there
…
…
there
to will
find
there
to
willpens
be
more
be
will
22
44
33
55
isbe
pens.
equal
pens.
4:11.
66 pens.
ratios.
Using Equal Ratios to Find Missing Values
4:11
pencils
pens
4
6
×?
24
11
×6
66
Now,
If
4
Let’s
So,
66
times
x
there
6for
=
also
let’s
24
every
are
what
multiply
use
4 pencils
number
24
this
pencils,
ratio
11 for
is
byequal
to
6.
there
every
find
What
to
must
a
1124?
missing
ispens,
11
bex66
6?
how
value
pens.
many
in the
pens
table.
must there be if there are 24 pencils?
Using Equal Ratios to Find Missing Values
4:11
pencils
pens
4
×5
20
11
×?
5
55
How
11
Let’s
So,
20
times
x
for
5many
also
=every
55
what
multiply
pencils
55
number
pens,
4
would
bythere
is5.equal
there
What
must
to
be
is 55?
be
the
if there
20
product?
pencils.
were 55 pens?
Using Equal Ratios to Find Missing Values
4:11
pencils
pens
4
×8
32
11
×8
88
If x
11
4
So,
there
x8for
8==32
every
were
88 88
88 pens,
pens, how
theremany
would
pencils
be 32 would
pencils.
there be?
Using Equal Ratios to Find Missing Values
4:11
pencils
pens
4
×9
36
11
×9
99
If x
11
4
So,
there
x9for
9==36
every
were
99 99
99 pens,
pens, how
theremany
would
pencils
be 36 would
pencils.
there be?
Using Equal Ratios to Find Missing Values
4:11
pencils
pens
4
× 10
40
11
× 10
110
If x
4
What
110.
there
10
So,
is
=were
11
40
forxevery
10?
40 pencils,
40 pencils,
how many
there would
pens would
be 110there
pens.
be?
Using Equal Ratios to Find Missing Values
4:11
pencils
pens
4
8
24 32 40 400
11 22 66 88 110 1,100
22there were 8
66
88
If
110
1,100
24pencils,
32
40
400
pencils,
pencils,
how
how
how
many
many
many
pens
pens
pens
would
would
would
there
there
there
be?
be?
be?
Using Equal Ratios to Find Missing Values
5:4
cars
5
×3
15
trucks
4
×3
12
If x
5
4
Now,
For
…
So,
there
there
3the
for
every
=let’s
15
12
every
were
ratio
are
5look
cars
4of
15
15
trucks.
at
cars
cars,
cars,
inanother
ato
parking
how
there
trucks
ratio.
many
would
lot
in the
…
trucks
beparking
12would
trucks.
lotthere
is 5:4.
be?
Using Equal Ratios to Find Missing Values
5:4
cars
5
×7
35
trucks
4
×7
28
If x
4
5
So,
there
7for
= 35
every
were
28 28
28 trucks,
trucks, how
theremany
would
cars
be 35
would
cars.
there be?
Using Equal Ratios to Find Missing Values
5:4
cars
5
× 11
55
trucks
4
× 11
44
If x
4
5
So,
there
11
for=every
were
55
44 44
44 trucks,
trucks, how
theremany
would
cars
be 55
would
cars.
there be?
Using Equal Ratios to Find Missing Values
5:4
cars
5
× 30
150
trucks
4
× 30
120
If x
5
4
So,
there
30
for=every
were
150 150
120
150 cars,
cars, how
theremany
would
trucks
be 120
would
trucks.
there be?
Using Equal Ratios to Find Missing Values
Lightning Round
Using Equal Ratios to Find Missing Values
8:3
pencils
8
16 56 72 88 800
students
3
6
21 27 33 300
Using Equal Ratios to Find Missing Values
7:20
apples
bananas
7
14 28 35 63 70
20 40 80 100 180 200
Using Equal Ratios to Find Missing Values
2:5
weekend
days
2
6
weekdays
5
15 50 100 250 500
20 40 100 200
Using Equal Ratios to Find Missing Values
12:7
letters
mailboxes
12 24 36 60 84 132
7
14 21 35 49 77
Using Equal Ratios to Find Missing Values
shoes
socks
3:8
3 ×× 14? 42
8 × 14 112
14
× 8
112
42
3
3 × ? = 42
42 ÷ 3 = ?
?
Let’s
3
To
…
We
42
If
The
So,
112
x
there
we
to
42
is
÷
solve
find
what
can
3product
for
3equal
multiply
complete
use
divided
x
=every
14
out,
are
use
14
number
this
the
a
=to
42
fact
we
42.
long
of
problem,
42
ratio
by
42?
what
8shoes,
acan
14
x
family
shoes,
3table.
division
…
14,
x…
3:8
number?
also
8we
how
is
…
triangle
we
Here,
there
…
consider
can
to
need
many
solve
find
there
will
toto
socks
the
help.
be
…
know
for
are
112
number
the
3will
shoes
what
socks.
missing
there
of
number
for
socks.
be?
number.
every
times
8 socks.
3 is equal to 42.
14
3 42
Using Equal Ratios to Find Missing Values
shoes
socks
3:8
3
8
× 26
26
× 8
208
78
3
××26
?
78
208
3 × ? = 78
78 ÷ 3 = ?
?
Let’s
3
To
…
We
78
If
The
So,
208
x
there
we
78
is
÷
solve
find
what
can
3product
for
3equal
multiply
use
divided
x
=every
26
out,
are
use
26
number
this
a=to
78
fact
we
78.
long
of
problem,
78
by
78?
what
8shoes,
can
26
x
family
shoes,
3division
…
26,
x…
number?
also
8we
how
is
triangle
we
there
…
consider
can
to
need
many
solve
find
will
toto
socks
the
help.
be
…
know
for208
number
the
will
what
socks.
missing
there
of
number
socks.
be?
number.
times 3 is equal to 78.
26
3 78
Using Equal Ratios to Find Missing Values
shoes
socks
3:8
3
8
×
× 67
?
67
× 3
201
536
8
× 67
201
536
8 × ? = 536
536 ÷ 8 = ?
?
Let’s
8
To
…
We
53
If
The
So,
201
x
there
we
536
is
÷
solve
find
what
can
8product
for
8equal
multiply
use
x=divided
every
67
out,
are
use
67
number
this
a=to
536
fact
we
536.
long
of
problem,
536
536?
what
3by
can
67
socks,
x
family
division
…
67,
socks,
8xnumber?
also
…
3we
is
triangle
how
we
…
consider
can
there
to
need
many
solve
find
will
totothe
help.
shoes
…
know
for
benumber
201
thewill
what
missing
shoes.
there
of
number
shoes.
be?
number.
times 8 is equal to 536.
67
8 536
Using Equal Ratios to Find Missing Values
cats
dogs
5:9
5 ×× 17? 85
9 × 17 153
17
× 9
153
85
5
5 × ? = 85
85 ÷ 5 = ?
?
Let’s
5
To
…
We
85
If
The
So,
153
x
there
we
to
85
is
÷
solve
find
what
can
5product
for
5equal
multiply
complete
use
divided
x
=every
17
out,
are
use
17
number
this
the
a
=to
85
fact
we
85.
long
of
problem,
85
ratio
by
85?
what
9cats,
acan
17
x
family
cats,
5table.
division
…
17,
and
…
5:9
number?
also
how
we
there
…
triangle
9we
Here,
consider
is
can
many
to
need
…
will
solve
find
there
dogs
to
be
tothe
help.
…
know
for
153
are
will
number
the
5dogs.
cats
there
what
missing
for
of
number
be?
dogs.
every
number.
times
9 dogs.
5 is equal to 85.
17
5 85
Using Equal Ratios to Find Missing Values
cats
dogs
5:9
5
9
× 38
38
× 9
342
190
5
×× 38
?
190
342
5 × ? = 190
190 ÷ 5 = ?
?
Let’s
5
To
…
We
190
If
The
So,
342
x
there
we
190
is
solve
find
what
can
5÷product
for
equal
multiply
use
x5divided
every
38
out,
=
are
use
number
this
38
a=to
190
fact
we
190.
long
of
problem,
190
190?
what
9by
can
38
cats,
x
family
division
…
38,
cats,
5and
number?
also
…how
we
triangle
9we
there
consider
is
can
many
to
need
…solve
find
will
toto
dogs
be
the
help.
…
know
for
342
number
will
the
dogs.
what
there
missing
of
number
be?
dogs.
number.
times 5 is equal to 190.
38
5 190
Using Equal Ratios to Find Missing Values
Closing Question
Using Equal Ratios to Find Missing Values
cats
dogs
5:9
5
9
××84
?
84
× 5
420
756
9
× 84
420
756
9 × ? = 756
756 ÷ 9 = ?
?
Let’s
9
To
…
We
756
If
The
So,
420
x
there
we
756
is
solve
find
what
can
9÷product
for
equal
multiply
use
x9divided
every
84
out,
=
are
use
number
this
84
a=to
756
fact
we
756.
long
of
problem,
756
756?
what
5by
can
84
dogs,
x
family
division
…
84,
dogs,
9and
number?
also
…we
how
triangle
5we
there
consider
is
can
to
need
many
…solve
find
will
toto
cats
the
help.
be
…
know
for420
number
will
thewhat
cats.
there
missing
of
number
be?
cats.
number.
times 9 is equal to 756.
84
9 756