Name:________________________________________________________________________________Date:_____/_____/__________
Fill-in-the-blanks:
Word Bank:
different,
one,
comparison
1. A ratio is a _______________ of two numbers.
2. A rate is special kind of ratio where each number represents a
_________________unit.
3. A unit rate is a special kind of rate, where the comparison is
always out of _______________!
Do the following ratios form a proportion? (Yes or No)
Cross-multiply!
Solve:
6.
3
11
4.
15
5
=
6
2
5.
20
35
=
2
3
Remember: Cross-multiply first, then DIVIDE by coefficient!
=
x
66
7.
10
𝑥
=
4
5
8. The ratio of jelly beans to
chocolate eggs in the Easter basket is
8 : 3. If there are 20 jelly beans in the
basket, then approximately how
many chocolate eggs are there?
Set up PROPORTION and solve:
9. For every 2 dogs at the shelter,
there are 3 cats. If there are 10 dogs
at the shelter, how many TOTAL
dogs AND cats are there?
Set up PROPORTION and solve:
=
=
NAME:____________________________________________________________________________ DATE: ______/_______/_______
Math-7 NOTES
What:
scale proportions
Why:
. . . so I can use proportions to solve problems involving scale drawings.
Vocabulary:
scale drawing/model — represents something that is too ________________
or too _________________ to be drawn at actual size.
scale factor-- gives the ratio of the paper measurement to the
________________ measurement. (If the scale is 3 cm = 9 mi., then the scale factor is 𝟏𝟑 )
How to solve a scale drawing problem using a proportion:
Note: The following is not the only way to set up a scale proportion, but it is the way we will
use in order to be consistent!
Step One: Set up given map/ blueprint scale as a ratio with paper
measurement on top and ____________________ measurement on the bottom.
Step Two: Set up other side of proportion by placing what you know (as given
in problem) in the correct position (paper on top and real-life on the bottom).
“x” goes in the remaining spot (represents the __________________________).
Example:
A certain map has a scale of ½ inch = 20 miles. If two towns are 50 miles
apart, how far apart are they on the map?
Start with the
SCALE– given in
the problem!
0.5 𝑖𝑛
20 𝑚
25
20
=
=
𝑥
50 𝑚
20𝑥
20
x = 1.25 inches
What else does
the problem
already tell us??
Blueprint Examples:
Together:
On your own:
Scale: 2 cm = 5ft
1)
If a room is 20 cm in length on the
blueprint, what is its actual length?
Map scenarios:
Together:
Scale:
2)
If two towns are 56 km apart in
real-life, how far apart are they on
the map?
What is the scale?
Together:
5)
The distance from Pleasantville to
Jefferson is 25 miles, but measures
2.5 cm on the map. What is the
map’s scale?
𝟒
in = 2 ft
If a room is 20 ft long in real-life,
what is its length on the blueprint?
On your own:
Scale: 2cm = 9 km
3)
𝟏
Scale: 0.75 in = 20 mi
4)
If the distance between two towns
on the map is 2 in, how far apart
are they in real-life?
On your own:
6)
The kitchen is 3 cm in length on
the blueprint, but measures 15 ft in
actual length. What is the
blueprint’s scale?
Wrap-it-Up/Summary:
1) What is the method we practiced for setting up proportions involving scale drawings?
IXL: 7th Grade, J.7 (scratch work required)
NAME:___________________________________________________________________________
DATE: ______/_______/_______
For each word problem, you must set up a proportion (label the correct units), and show steps required to
solve. You may stop once you achieve a MINIMUM smart score of 70% (can keep going if desired), or once
you have spent 15 minutes or more. No scratch work will result in a loss of points!
Example:
Answer (showing my work):
𝟑 𝒄𝒎
𝟐𝟏 𝒎
Type answer
in box.
𝟑𝒙
𝟑
=
=
𝟏 𝒄𝒎
𝒙
𝟐𝟏
𝟑
x=7m
Proportion:
Proportion:
=
Proportion:
Proportion:
Proportion:
=
Proportion:
Proportion:
=
=
Proportion:
=
=
=
Proportion:
=
=
Proportion:
Proportion:
=
Proportion:
Proportion:
Proportion:
=
Proportion:
Proportion:
=
Proportion:
=
Proportion:
=
=
Proportion:
=
=
=
Proportion:
Proportion:
=
=
Proportion:
Proportion:
=
=
Proportion:
=
=
NAME:_____________________________________________________________________________
DATE: ______/_______/_______
“Scale drawings”
Use below space to set up the proportions required to complete above table:
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
Use below space to set up the proportions required to complete above table:
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.