BCT 104 Construction Math Week 8
Discovery Project 8 Ratios, Factors
Name: ________________________
Ratios or factors can be used in many construction math problems to simplify the process.
Ratio: A ratio is the relationship of two numbers. For example: ( 6: 12) or (6 to 12),
which is a common rise to run roof pitch.
Most ratios will reflect a direct proportion of the units involved.
6
X
=
.
12
36
To solve for the unknown X multiply 6 x 36 = 216 and divide by 12. (X) = 18 inches.
You can reduce some ratios so (6 :12) may also be expressed as (1 : 2). As applied to a
rafter/run relationship, this states that there is 1 rise per each 2. run.
To find the rise of a 36 inch run for a 6/12 roof pitch, using the ratio
When solving for the unknown X using ratios, first cross multiply then divide.
RULES:
Two Rules when setting up a proportion:
1. Always set up your fractions so same units are on same sides
2. Always place smaller units over larger units in the fraction
Factors: Factors are a useful short cut method when dealing with standard units. The
factor is determined by completing the division process of the ratios leaving only the
multiplication by the factor to solve for the unknown.
Example: Using the same roof pitch, to determine the factor, divide the rise (6) by the run
(12) = .5. The factor or multiplier is (.5 rise to each 1 run).
Any 6/12 roof pitch run can be multiplied by .5 to find an unknown rise.
Example, 36 x .5 = 18 inches, or 3 x .5 = 1.5 = 18 inches
Charts listing the factors for standard units can be a useful time saver.
Make a lineal foot to board foot factor conversion chart.
1 x 2 ________
1 x 3 ________
1 x 4 ________
1 x 6 ________
1 x 8 ________
1 x 10 ________
1 x 12 ________
2 x 2 ________
2 x 3 ________
2 x 4 _________
2 x 6 _________
2 x 8 _________
2 x 10 _________
2 x 12 _________
4 x 4 _________
4 x 6 _________
4 x 8 _________
4 x 10 _________
4 x 12 _________
4 x 14 _________
4 x 16 _________
6 x 6 _________
6 x 8 _________
6 x 10 _________
6 x 12 _________
6 x 14 _________
6 x 16 _________
An indirect proportion or inverse ratio may need to be used to solve some problems.
Inverse ratio: This is when the unknown portion of the ratio moves in an opposite
direction of its accompanying term.
A good sample problem to help understand inverse ratio would be with roofing materials
and roof exposure.
The amount of roofing squares required for a particular area increases when the shake
exposure to the weather is decreased.
Example, if the shake per code exposure is 10, the roofing supplier will supply the # of
bundles to cover a square at that exposure. If the job specs call to decrease the exposure
from 10 ( example 35 sqs.) to 7, an inverse ratio should be used to solve for (X).
10 7
:
Solve for X by multiplying the original exposure by the number of roofing
35 X
squares, and then divide by the new exposure. Example: 10 x 35 sqs. = 350 divided
by 7 = 50 sqs.
See if you can find an inverse ratio problem in the next section.
Concrete ratios:
One cubic yard of concrete = _________ cubic ft. of concrete.
Ratios are commonly used to estimate concrete flat work, such as patios, drives, walks,
garage floors etc. Calculate the amount of surface area one cubic yd. of concrete will
cover at 4 in depth._____________________
Find the volume of one sq. ft. of area (12 x 12 x 4). Convert to ft.(.333 x 1 x 1) =
.333 cubic ft. Divide one yd. or 27 cu. Ft. by .333 = 81 sq. ft. area at 4 thick.
What ratio could you use to solve the next problem?
_____ as _____
A patio 26 ft. X 34 ft. will require ___________ cu. yds. of concrete at 4 thick.
What ratio could you use to solve the next problem?
_____ as _____
One cubic yd. of concrete poured 9 thick will cover __________ sq. ft.
Concrete foundations are also an area where using ratios can save time in calculations.
For any given wall/footing combination you can establish a ratio of lineal feet poured to
one cubic yard of concrete.
Example: One cu. yd. concrete will fill ____ lineal feet of a 6 x 12 footing.
Solution: Convert footing inches to feet then multiply. .5 x 1 x 1 = .5 cu. ft. per each
lineal foot of foundation footing. Divide 27 cu. Ft. by .5 = 54 lineal feet.
The ratio is 1 cu. yd. to 54 lin ft. for a 6 in. x 12 in. footing.
What ratio could you use to solve the next problem?
_____ as _____
Find the cu. yds. of concrete required for 310 lin. ft. of 6 x 12 footing. ________
When doing concrete yardage calculations always round up to the nearest half yard.
Lineal ft. of a wall & footing per cu. yd. of concrete is commonly used in estimating.
A multiplying factor for the same size footing as above could be used. 1/54 = .0185.
The same problem can also be solved by multiplying 310 lin. ft. x .0185 = 5.74 or 6 cu.
yds.
Find the ratio of lineal feet to one yard for the following standard foundation walls and
footings as a unit. Calculate the concrete yards for the practice lin. ft. of each example.
One story
footing
wall
ratio
practice lin. ft.
cu.yds.
6 x 12
24 x 6
________
345 lin. ft.
__________
6 x 12
36 x 6
________
632 lin. ft.
__________
6 x 12
48 x 6
________
583 lin. ft.
__________
7 x 15
24 x 8
________
237 lin. ft.
__________
7 x 15
36 x 8
________
430 lin. ft.
__________
7 x 15
48 x 8
________
641 lin. ft.
__________
Two story
One cu. yd. of concrete will pour #___________ 8 deep x 18 diameter round pier pads.
What ratio could you use to solve the next problem?
_____ as _____
Practice: Use the ratio to solve, how many cu. yards of concrete it will take to pour 72 of
the above pier pads.___________