Download Math Text Only

Introduction to Construction Math
Module 00102-04
Upon completion of this module, you will be able to do the following:
1.
Add, subtract, multiply, and divide whole numbers, with
and without and without a calculator.
2.
Use a standard ruler and a metric ruler to measure.
3.
Add, subtract, multiply, and divide fractions.
4.
Add, subtract, multiply, and divide decimals, with and
without a calculator.
5.
Convert decimals to percentages and percentages to
decimals.
6.
Convert fractions to decimals and decimals to fractions.
7.
Explain what the metric system is and how it is important
in the construction trade.
8.
Recognize and use metric units of length, weight, volume,
and temperature.
9.
Recognize some of the basic shapes used in the
construction industry, and apply basic geometry to measure them.
START COPYING HERE!
Section 1.0.0
Introduction
Section 2.0.0
Whole Numbers
1.0.0 Introduction
All construction jobs use some form of math, we will cover the
basics you need to know for this area of work.
2.0.0 Whole Numbers
Whole numbers are complete units without fractions or
decimals.
• Whole numbers = 2
24
89
• Non-Whole numbers = 0.45 ¾
7½
2.1.0 Parts of Whole Numbers
A digit is any one of the numeric symbols from 0 to 9.
Numbers larger than 0 = Positive Numbers
Numbers smaller than 0 = Negative Numbers
2.2.0 Adding Whole Numbers
To add means combine two values, the total is called the sum.
2.2.1 Carrying in Addition
If you are adding 58 + 34, you will need to carry the tens part of
the sum from the units column to the tens column and add it there.
2.2.2 Study Problems:
32 + 75 = ____ 452 + 74 = ____
73 + 45 = ____ 323 + 758 = ____
2.3.0 Subtracting Whole Numbers
Subtracting one number from another is finding the difference
between them.
2.3.1 Study Problems:
87 – 38 = ____
26 – 17 = ____
92 – 34 = ____
826 – 717 = ____
2.4.0 Multiplying Whole Numbers
The most efficient way to add the same number together many
times, is multiplication.
2.4.1 Study Problems:
1. Adding 4+ 4+ 4+ 4+ 4 can be wrote as? _______
2. 9 x 8 = ____
3. 9 x 6 = ____
2.4.3 Study Problems:
12 x 21 = ____
11 x 15 = ____
452 x 4 = ____
2.5.0 Dividing Whole Numbers
When dividing, the number you are dividing by is called the
divisor.
If you have 364 boxes of drywall screws that must be divided
equally between 7 job sites, how many boxes does each site get?
Answer= 52
You have a piece of pipe that is 150 feet long. If you cut the
pipe into 10 pieces of equal length, how long will each piece of pipe
be? Answer= 15 feet
2.5.1 Study Problems:
15 / 3 = ____
36 / 4 = ____
2.5.2 Dividing More Complex Whole Numbers
To solve these problems, use long divisions.
2.5.3 Study Problems:
1. 12 263
2. 16 4218
3. 15 4532
4. A plumbing job requires 100 feet of plastic pipe available in 20feet sections. You will need ____ sections.
2.6.0 Using Calculators
The calculator is a marvelous tool for saving time.
To clear a calculator, you must press the ON/C key.
Section 3.0.0
Measurement
Section 4.0.0
Fractions
3.0.0 Working with Measurement
A yard stick is a standard ruler that is 3 feet long.
In this section you learn about standard rulers and architect scales.
3.1.0 Using the Standard Ruler
It is very important you learn how to read a ruler or tape measure.
3.2.0 Architect’s scale
The architectural scale is used on all set of plans you will read.
Scales include:
½” = 1’-0” ¾” = 1’-0” ¼” = 1’-0”
1” = 1’-0”
1-1/2” = 1’-0”
4.0.0 What are Fractions?
Fractions divide whole numbers into parts.
The bottom number of a fraction is the denominator.
The lower number (denominator) tells you the number of parts the
upper number (numerator) is being divided.
The upper number is the whole number in which you will divide.
Take for example: ½ = 1 on top is the whole number and it is being
divided by 2. Which equals .5 or ½
4.1.0 Finding Equivalent Fractions
Notice 1/2 = 2/4 = 4/8 = 8/16, this is called equivalent fractions
Lets say you want to find out how many 16th there are in 1/2 inch,
you simply multiply what to get 16?
1 x 8 = 8
2 x 8 = 16
4.1.1 Study problems
1/4 inch = ___/16 inch 2/16 inch = ___/32 inch
3/4 inch = ___/64 inch 3/16 inch = ___/32 inch
4.2.0 Reducing Fractions
If you find a fraction with an even number on top you will need to
reduce it. Like 4/16.
To reduce, first ask what is the largest number I can divide into the
fraction. In the case of 4/16, it is 4.
Second, divide both the top number and bottom number by the
largest number you can divide.
4 / 4 =1
16 / 4 = 4
What is the lowest term of the fraction 4/32? 1/8
4.2.1 Study Problems
Reduce the following:
2/16
4/64
12/32
4.3.0 Comparing Fractions
What is the first step to finding the lowest common denominator of
two fractions? Reduce each fraction to its lowest terms.
So which is biggest 3/4 or 5/8?
To find out you need to multiply the two bottom numbers
together…you get 32.
3 x 8 = 24
5 x 4 = 20
4 x 8 = 32
8 x 4 = 32
Now it is easy to compare the fractions, but this method maybe more
difficult.
Finding the least common denominator…
Step 1
Reduce each fraction to its lowest terms.
Step 2
Find lowest common multiple, this could be one of the
bottom numbers you already have.
Step 3
If no common multiple, then multiply bottoms together.
Example of finding least common denominator…
Is 3/4 bigger than 5/8?
Using the previous steps, 8 and 4 are common multiples.
So if this is the case, then you can do the following and save time…
3 x 2 = 6
5
4 x 2 = 8
8
This method is faster for the common multiples.
4.3.1 Study Problems (find least common denominator)
1) 2/6 & 3/4 ____
2) 1/4 & 3/8 ____
3) 1/4 & 3/16 ____
4) 4/32 & 5/8 ____
Answers:
1)
12
2)
8
3)
16
4)
32
4.4.0 Adding Fractions
Several times you have to add fractions.
Adding ¼ + ¾ is simple. 4/4 or 1.
But adding 3/4 + 5/8 is more difficult. So look for the least common
denominator. 8
Change ¾ 3 x 2 = 6 4 x 2 = 8
So you have
6 + 5 = 11
8 = 8 = 8
Your answer is 11/8
1/4 + 3/8 = ______ Answer is 5/8.
4.5.0 Subtracting Fractions
This is very similar to adding fractions.
What is the difference between 3/4 - 5/8 =
6 - 5 = 1
8 = 8 = 8 Your answer is 1/8
Subtracting Cont’d
Sometimes you have to subtract a fraction from a whole number.
5
8
1-5/8
-¼
-½
-¾
Borrow a 1 from 5 and 8.
5 = 4 + 4/4
8 = 7 + 2/2
-1/4
-1/2
4 + 3/4
7+½
4¾
7½
For 1-5/8 do the following
1 5/8
(change fractions like you already learned)
- 3/4
7/8
Test Problem:
8
4
12
8
Answer = 1/6
4.6.0 Multiplying Fractions
In a word problem the word of usually means you are multiplying.
Like what is 2/8 of 9? Think of the problem this way 2/8 x 9/1.
Remember any whole number is placed above a 1 (except 0).
Multiply this:
4 x 5 = 20
8 x 6 = 48
Now reduce 20 / 48 to get 5 / 12
4.7.0 Dividing Fractions
Step 1
When dividing fractions, the first step is to invert the
fraction you are dividing by.
Step 2
Change the division sign to multiplication sign
Step 3
Multiply the fractions
Step 4
Reduce if possible
Section 5.0.0
Decimals
Section 6.0.0
Conversions
5.0.0 Decimals
Decimals represent a value smaller than a whole number.
5.1.0 Reading a Machinist’s Rule
On the job, you may need to use decimals to read instruments or flow
rates.
A machinist’s rule has whole number markings, but the little lines in
between are broken down by tenth of an inch.
Example: A screw is three and seven tenth long. 3 – 7/10
Using decimals, this is written as 3.70 inches.
5.2.0 Comparing Whole Numbers with Decimals
Whole #
Decimals
1
ones
1.0
10
tens
.1 tenths
100 hundreds
.01 hundredths
1,000thousands
.001thousandths
Read the number as it is written, example: 0.56 is said “fifty-six
hundredths”
Mixed numbers would be said as “fifteen and seven-tenths” for 15.7
5.2.1 Study Problems
0.4 = ____ eighteen hundredths = _____
0.05 = ____
Five and eight-tenths = _____
5.3.0 Comparing Decimals
Remember as the number grows it is larger.
Is 42 bigger than 40, yes.
Is 0.42 bigger than 0.4?
Only exception is if you are dealing with negative numbers.
Then -0.40 is bigger than -0.42, cause you -.4 is closer to zero.
Put the following decimals in order from smallest to largest: 0.012,
0.210, 0.112, 0.201
Answer = 0.012,
0.112,
0.201,
0.210
5.4.0 Adding and Subtracting Decimals
There is only one major rule to remember when adding and
subtracting decimals:
Keep you decimal points lined up!
Example: You want to add 14.76 and 0.834?
Do you write it as:
14.76
+ 0.834
Or do you write it as:
NO
14.76
+ 0.834
YES
Yesterday the job site received a gravel delivery of 5.7 cubic yards.
The contractor has already used 2.3 cubic yards. The contractor has
_____ cubic yards left.
Answer = 3.4
5.4.1 Study Problems
2.5 + 4.20 + 5 = ____ 6.43 + 86.4 = ______
5.5.0 Multiplying Decimals
Remember when multiplying to count how many decimals you have
then put that decimal in its place in the answer.
Setup your equation:
4.5
x7
Multiply
315
Count the number of decimals = 1
Count from the right on 315 and place the decimal = 31.5
One sheet of drywall weighs 48.7 pounds. You have ordered 50
sheets, so you total order will weigh ____ pounds.
Answer = 2,435.0
5.6.0 Dividing Decimals
When would you use it?
Say you have a piece of pipe that is 44.5” long, you need to cut 22”
pieces from it. How many pieces can you get?
5.7.0 Rounding Decimals
Sometimes you answer is more precise than you need.
Say you need pipe and it costs $3.76 per foot, you spend $800, how
much tubing will you buy? The precise is 212.7659574
But you are only interested in to the nearest tenth.
If the digit to the right of the tenths spot is higher than 5 round up, but
if it is less than 4, keep it the same.
Rounding cont’d
You need to mix 42 pounds of mortar. Each pound of mortar mix
requires 0.03 liters of water. How many liters of water do you need?
(Round your answer to the nearest tenth.)
Answer = 1.3
5.8.0 Using a Calculator
Using a calculator for decimals is the same as using it for whole
numbers.
Just remember when typing 45.7 you hit 4, then 5, then ., then 7.
6.0.0 Conversion Processes
You will have to convert numbers so they are in the same form, some
of which you might need to convert is:
Decimals
Percentages
Fractions
6.1.0 Converting Decimals to Percent & Percent to Decimal
When converting a percent to decimal, you must first drop the percent
sign. You then move the decimal point two places to the left.
Example: 89% = 0.89 100% = 1.00
5% = 0.05
Basically you can also do it by dividing the percent by 100.
6.2.0 Converting Fractions to Decimals
You will need to change fraction to decimal at times.
Divide the numerator by the denominator.
6.3.0 Converting Decimal to Fraction
Lets say you want to find the fraction of .25
Put 25 on top of 100, drop the decimal and place a one below, then
add 0 for each number given.
Reduce the fraction, in this case take 25 off the top and bottom
numbers
Section 7.0.0
Metric System
Section 8.0.0
Construction Geometry
7.0.0 Intro to Metric Systems
The metric system is base-ten system.
Used for weight, length, volume, and temperature
7.1.0 Units of Weight, Length, Volume, and Temperature
The name of measurement tells you want you are measuring.
7.2.0 Using a Metric Ruler
Blueprint measurements most often are given in centimeters or
millimeters.
7.3.0 Converting Measurements
Sometimes you need to change from inches to centimeters.
Refer to a chart for simplicity.
8.0.0 Construction Geometry
Geometry might sound scary, but you already know most of it.
8.1.0 Angles
To measure angles, you use an instrument called a protractor.
8.2.0 Shapes
Common shapes you will deal with in construction is squares,
rectangles, triangles, and circles.
8.2.1 Rectangles
Four sided figure with four 90 degree angles. Two sets of parallel
lines, in which all four are not equal to each other.
8.2.2 Squares
A square has four sides with four 90 degree angles. All four sides
ARE equal.
8.2.3 Triangles
While the measurement of the individual angles in a triangle can vary,
their sum is always 180 degrees.
8.2.4 Circles
A closed curved line around a center point. A circle measures 360
degrees.
8.3.0 Area of shapes
Area is the measurement of the surface of an object.
The formula to calculate the area of a rectangle is length x width.
The formula to calculate the area of a square is length x width.
The formula to calculate the area of a circle is pi x radius2.
The formula to calculate the area of a triangle is 0.5 x base x height.
You have to lay a floor for a 14 foot square shed. The area is ____
square feet.
Answer = 196.0
8.4.0 Volume of Shapes
The amount of space occupied in three dimensions is its volume. It is
measured in cubic inches, feet, and yards.
Rectangle Volume = length x width x depth
Square Volume = length x width x depth
Cube (square) is a special type of 3-D object where length, width, and
depth are all equal.
Cylinder Volume = pi x radius2 x height
Triangle Volume = 0.5 x base x height x depth
SPIRALS ARE DUE FRIDAY Sept 17!
WRITTEN TEST FRIDAY Sept 17!