Name _______________________________________ Date __________________ Class __________________
Measurement and Geometry
Review for Mastery: Converting Customary Units
You can use the table below to convert customary units.
Weight
Length
1 foot = 12 inches
1 yard = 36 inches
1 yard = 3 feet
1 mile = 5,280 feet
1 mile = 1,760 yards
Capacity
1 pound = 16 ounces
1 ton = 2,000 pounds
1 cup = 8 fluid ounces
1 pint = 2 cups
1 quart = 2 pints
1 quart = 4 cups
1 gallon = 4 quarts
1 gallon = 128 fluid
ounces
To figure out how many pounds are in 32 ounces, set up a
proportion where the first ratio uses the fact that 16 ounces are
in 1 pound. The second ratio should have the value you know, 32 ounces,
and a variable for the value you are trying to find, x pounds.
16 ounces = 32 ounces
1 pound
x pounds
Then solve the proportion.
16 ounces = 32 ounces
1 pound
x pounds
First, find the cross products.
16x = 32
Think: 32 ÷ 16 = x
Then, use a related math sentence
to solve the equation.
x=2
So, there are 2 pounds in 32 ounces.
Use the table above to set up a proportion. Then find each of
the values.
1. the number of pounds in 80 ounces
2. the number of quarts in 6 gallons
1 = _________________
16
4 = _________________
1
________________________
_______________________
3. the number of yards in 5 miles
_____________________
4. the number of cups in 20 pints
____________________
Holt McDougal Mathematics
Name _______________________________________ Date __________________ Class __________________
Measurement and Geometry
Review for Mastery: Converting Metric Units
There are patterns in powers of ten.
10 • 1 = 10
10 • 10 = 100
10 • 10 • 10 = 1,000
The number of times 10 is a factor equals the number of zeros in
the power of ten.
You can use these patterns to multiply and divide by powers of ten.
The number of zeros or the number of tens tells you how many
places to move the decimal point.
If you are dividing by a power of ten,
move the decimal point left.
If you are multiplying by a power of ten,
move the decimal point right.
7,345 ÷ 100 = 73.45
23.4 • 10 •10 •10 = 23,400
two zeros, two places
three tens, three places
73.45
23,400
21
123
Multiply or divide.
2. 1,347.8 ÷ (10 • 10)
1. 4.25 • 10 • 10 • 10 • 10
_______________________________________
3. 9.4 ÷ 1,000
________________________________________
4. 18.05 • 100
_______________________________________
________________________________________
The metric system uses powers of ten.
Each place value is 10 times as large as the place value to the right.
1,000
1
0.1
0.01
thousands hundreds tens
ones
tenths
hundredths thousandths
kilo
meters deci
2 m = ___ cm
100
hecto
10
deka
centi
0.001
milli
The centimeter unit is 2 places to the right of the meter.
2 m = 200 cm Move the decimal point 2 places to the right.
Use the chart to convert each measure.
5. 3.4 km = ___________________ mm
6. 7 dm = ___________________ hm
7. 4.32 dam = ___________________ m
8. 34.8 cm = ___________________ dm
Holt McDougal Mathematics
Name _______________________________________ Date __________________ Class __________________
Measurement and Geometry
Review for Mastery: Area of Rectangles and Parallelograms
You can use grid paper to estimate and find area of figures. The
area of a figure is the amount of surface it covers. Area is measured
in square units.
To estimate the area of the figure below, first find the number of fully
shaded squares. Next, find the number of nearly full squares. Then,
find the number of half or nearly half-shaded squares.
There are 6 fully shaded squares.
There are 2 nearly full squares.
There are 8 half-shaded squares.
1
(8 •
= 4)
2
Find the estimated total number of squares shaded.
6 + 2 + 4 = 12. The area of the figure is about 12 square units.
Estimate the area of each figure.
2.
1.
_______________________________________
________________________________________
To find the area of a rectangle, find the total number of square units.
There are 3 rows of 5 squares.
3 • 5 = 15
So, the area of the rectangle is 15 square units.
Find the area of each rectangle.
3.
4.
_______________________________________
________________________________________
Holt McDougal Mathematics
Name _______________________________________ Date __________________ Class __________________
Measurement and Geometry
Review for Mastery: Area of Rectangles and Parallelograms
(continued)
To find the area of a parallelogram, first turn your parallelogram into
a rectangle.
Then find the area of the rectangle.
Because the area of a rectangle is A = ℓω, the
area of a parallelogram is A = bh.
4•2=8
So, the area of the parallelogram is 8 square
units.
Find the area of each parallelogram.
5.
6.
_______________________________________
________________________________________
Sometimes you need to subtract a smaller area from a larger area.
A rectangular yard is made up of a
rectangular flower garden surrounding a
rectangular vegetable garden. The yard is
9 ft by 7 ft. The vegetable garden is 3 ft by
2 ft. What is the area of the flower garden?
First find the area of the yard and the area of the vegetable garden.
Area of yard: A = lw = (9 • 7) = 63
Area of vegetable garden: A = lw = (3 • 2) = 6
Then subtract the area of the vegetable garden
from the area of the yard to find the area
of the flower garden.
63 − 6 = 57
So the area of the flower garden is 57 square feet.
Solve.
7. A rectangular yard is made up of a rectangular grass lawn
surrounding a rectangular patio. The yard is 12 ft by 10 ft.
The patio is 4 ft by 5 ft. What is the area of the grass lawn?
Measurement and Geometry
Holt McDougal Mathematics
Name _______________________________________ Date __________________ Class __________________
Review for Mastery: Area of Triangles and Trapezoids
To find the area of a triangle, first turn your triangle into a rectangle.
Next, find the area of the rectangle. 6 • 3 = 18
The triangle is half the area of the formed rectangle or A = 1 bh, so
2
divide the product by 2.
18 ÷ 2 = 9
So, the area of the triangle is 9 square units.
Find the area of each triangle.
1.
2.
_______________________________________
________________________________________
To find the area of a trapezoid,
first turn the trapezoid into two
triangles and a rectangle.
Find the area of each triangle.
A = 1 bh
2
A = 1 (2 • 5) = 1 • 10 = 5
2
2
Find the area of the rectangle.
A = lw
A = 4 • 5 = 20
Now find the sum of the areas.
5 + 5 + 20 = 30 So, the area of the trapezoid is 30 square units.
Find the area of each trapezoid.
3.
4.
_______________________________________
________________________________________
Holt McDougal Mathematics
Name _______________________________________ Date __________________ Class __________________
Measurement and Geometry
Review for Mastery: Area of Composite Figures
Sometimes you can use area formulas you know to help you find
the area of other figures.
To find the area of the figure below, first divide the figure into figures
you know.
The figure is made up of a triangle,
a parallelogram, and a rectangle.
Next, find the area of each figure.
Triangle
Parallelogram
Rectangle
A = 1 bh
2
A = bh
A = ℓω
= 1 (3 • 4)
2
=3•4
=4•5
=6
= 12
= 20
Then, find the sum of all of the areas.
6 + 12 + 20 = 38
The area of the figure is 38 square units.
Find the area of each figure.
1.
2.
_______________________________________
3.
________________________________________
4.
_______________________________________
________________________________________
Holt McDougal Mathematics
Name _______________________________________ Date __________________ Class __________________
Measurement and Geometry
Review for Mastery: Volume of Prisms
Volume is the number of cubic units needed to fill a space. To find
the volume of a rectangular prism, first find the area of the base.
length = 3 units
width = 2 units
A=ℓ
= 3 • 2 = 6 square units.
The area of the base tells you how many cubic units are in the first
layer of the prism.
Next, multiply the result by the number of layers in the prism.
The prism has 4 layers, so multiply 6 by 4.
6 • 4 = 24
So, the volume of the rectangular prism is 24 cubic units.
Find the volume of each rectangular prism.
1.
2.
_______________________________________
________________________________________
To find the area of a triangular prism, first find the area of the base.
A = 1 bh
2
= 1 (5 • 4)
2
= 10 square units
Then multiply the result by the height of the prism.
10 • 3 = 30
The volume of the triangular prism is 30 cubic units.
Find the volume of each triangular prism.
3.
4.
_______________________________________
________________________________________
Holt McDougal Mathematics
Name _______________________________________ Date __________________ Class __________________
Measurement and Geometry
Review for Mastery: Surface Area
You can use what you know about finding the area of polygon to find
the surface area of a three-dimensional figure.
To find the surface area of the regular triangular prism above, first
find the area of each face.
2 congruent triangular bases
1
bh
2
1
= (4 • 3)
2
= 6 square units
A=
3 rectangular faces
A = ℓw
=4•6
= 24 square units
Then, find the sum of all of the faces of the prism.
SA = 6 + 6 + 24 + 24 + 24
= 84 square units
Find the surface area of each figure.
1.
2.
_______________________________________
________________________________________
Holt McDougal Mathematics
Holt McDougal Mathematics