Grade 6 Module 1
Lesson 3
Equivalent Ratios
• Understanding of equivalent
ratios.
• Use tape diagrams
• Formalize a definition of
equivalent ratios
Exercise 1
•Write a one-sentence
story problem about a
ratio.
Sample
The ratio of the number
of sunny days to the
number of cloudy days in
this city is 3:1.
Exercise 1
Write the ratio in two
different forms
Answers
•3:1 3 to 1
Exercise 2
• Shanni and Mel are using ribbon to
decorate a project in their art class.
The ratio of the length of Shanni’s
ribbon to the length of Mel’s ribbon
is 7:3.
• Draw a tape diagram to represent
this ratio.
Represent ratio in a table
Shanni’s Ribbon Mel’s Ribbon
7
3
Represent ratio in a table
Shanni’s Ribbon Mel’s Ribbon
7
14
3
6
Represent ratio in a table
Shanni’s Ribbon Mel’s Ribbon
7
14
21
3
6
9
Tape Diagram
Shanni
Mel
Tape Diagram
What does each unit on
the tape diagram
represent?
Tape Diagram
What if each unit on the tape
diagrams represent 1 inch?
What are the lengths of the
ribbons?
What is the ratio of the lengths
of the ribbons?
Tape Diagram
What if each unit on the tape
diagrams represents 2 meters?
What are the lengths of the
ribbons?
How did you find that?
Tape Diagram
What is the ratio of the lengths
of Shanni’s ribbon to the length
of Mel’s ribbon now?
What if each unit represents 3
inches? What are the lengths of
the ribbons? Record
Tape Diagram
If each of the units
represents 3 inches, what
is the ratio of the length of
Shanni’s ribbon to the
length of Mel’s ribbon?
Tape Diagrams
We just explored three different
possibilities for the length of the
ribbon; did the number of units in
our tape diagrams ever change?
What did these 3 ratios, 7:3, 14:6,
21:9, all have in common?
Tape Diagram
Mathematicians call these
ratios equivalent. What ratios
can we say are equivalent to
7:3?
Tape Diagram
Draw a tape diagram to represent
this ratio:
7:3
14:6
21:9
7 inches to 3 inches
14 meters to 6 meters
21 inches to 9 inches
Tape Diagram
Shanni
Mel
1 in 1 in 1 in 1 in 1 in 1 in 1 in
1 in 1 in 1 in
7 inches to 3 inches
7:3
Tape Diagram
Shanni
Mel
2m 2m 2m 2m 2m 2m 2m
2m 2m 2m
14 meters to 6 meters
14:6
Tape Diagram
Shanni
Mel
3 in 3 in 3 in 3 in 3 in 3 in 3 in
3 in 3 in 3 in
21 inches to 9 inches
21:9
Exercise 3 (a)
Mason
Laney
Exercise 3 (a)
Mason
= 4 miles
Laney
= ? miles
Exercise 3 (a)
Mason
2 mi 2 mi
= 4 miles
Laney
2 mi 2 mi 2 mi = 6 miles
Exercise 3 (b)
Mason
=?m
Laney
= 930 m
Exercise 3 (b)
Mason
310m 310m
= 620 m
Laney
310m 310m 310m = 930 m
Exercise 3(c)
What ratios can we say
are equivalent to 2:3?
Exercise 3(c)
4:6 and 620:930
Exercise 4(a)
Wrong
=8
Right
=?
Exercise 4(a)
Wrong
r
r
Right
r
r
=8
r
r
r
r
r
r
= 36
Exercise 4(b)
Wrong
= 20
Right
=?
Exercise 4(b)
Wrong
= 20
Right
= 90
Exercise 4(d)
Wrong
=
Right
=?
4(f)
• 2:3 and 4:6 are equivalent
because they represent the
same value. The diagram
never changed, only the
value of each unit in the
diagram.
Closing
Two ratios A:B and C:D are equivalent ratios
if there is a positive number, c, such that C =
cA and D = cB.
Ratios are equivalent if there is a positive
number that can be multiplied by both
quantities in one ratio to equal the
corresponding quantities in the second
ratio.