Basic Math Review
This unit reviews whole numbers, fractions, decimals, and the conversion process.
Each digit in the whole number represents a place value. This means that each digit has a value that depends on its place or location in the whole number.
For example: In the whole number 5,679, the place value of 5 is five thousand, and the place value of the 6 is six hundred.
• Numbers larger than zero (such as 1, 2, 3) are positive (+) numbers.
• Numbers less than zero (such as -1,-2,-3) are negative (-) numbers.
• Zero is neither positive nor negative.
(Except for zero, numbers without a minus sign is front of them are positive.)
To add means to combine the value of two or more numbers. The total when you add two or more numbers is called the sum. The sign for addition is the plus sign (+).
For example: 56 + 32 = 88
Subtraction means finding the difference between two numbers, or taking one number away from another. The subtraction sign (-) is also called the minus sign. The result (answer) of a subtraction problem is called the difference.
For example: 56 – 32 = 24
Multiplication is a quick way to add the same numbers together many times. The symbol for multiplication is the × sign.
For example: A box of screwdrivers contains 5 pieces. How many screwdrivers would eight boxes contain in all?
5 × 8 = 40 screwdrivers
5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 = 40 screwdrivers
Division is the opposite of multiplication. The symbol for division is the ÷ sign.
Instead of adding a number several times like in multiplication, in division the number is being subtracted several times.
You can solve a problem faster by using division instead of subtracting the same number over and over.
For example: You have 40 boxes to deliver to 8 different job sites. How many boxes would you deliver to each site?
40 ÷ 8 = 5
40 – 8 – 8 – 8 – 8 – 8 = 0 (Here, you had to subtract 8 five times; so the answer is 5.)
A fraction divides whole units into parts. Fractions are written as two numbers separated by a slash or by horizontal line. For example 1/2 or 1/4.
Think of fraction as a division problem. The lower number (denominator) of the fraction tells you the number of parts by which the upper number (numerator) is being divided. The slash or the horizontal line means the same thing as the ÷ sign.
The fraction 1/2 means 1 divided by 2 or one divided into two equal parts. Read this fraction as 'one-half'.
Equivalent fractions have the same value, or are equal. For example, 1/2, 2/4, 4/8, and 8/16 are equivalent fractions.
Example: If you cut off a piece of wood 8/16 inches long and a trainee cuts off another piece 1/2 inches long, the two pieces would be the same length.
In some situations, you need to convert the numbers you want to work with so that all your numbers are in the same form.
For example: You may have some numbers that appear as percentage, and some that appears as fractions.
Decimals 0.25, the percentage 25%, and the fraction 1/4 all mean the same thing.
To work successfully with the different forms of numbers like these, you will need to know how to convert them from one form into another.
What is percentage?
Think of a whole number divided into 100 parts. You can express any part of the whole as a percentage. Percentage is an easy way to express part of a whole. (Decimals and fractions also express parts of a whole.)
Fraction to decimals:
To convert a fraction to a decimal, do what the fraction tells you to do; that is, divide the numerator by the denominator.
The metric system is a system of measurement that uses a base-ten method of determining weight, length, volume, and temperature. In other words, all measurements are counted in tens.
There are only seven basic units of measurements in the modern metric system, including the meter, liter, and gram. Multiples or fractions of the basic units are expressed as a power of 10.
A standard set of prefixes is used to denote these larger or smaller numbers. That way you will always know that a kilometer is 1000 meters just by looking at the prefix.
Square and Square Roots:
Plumbing calculation may require you to square numbers as well as take square roots of numbers.
To square a number, multiply the number by itself. To show that a number is being squared, write a superscript 2 to the right of the number.
For example: 3 squared is written as 32, which is
3 × 3 = 9
Square and Square Roots (continued):
To take the square root means to find the numbers that, when multiplied by itself result in the original number.
The radical sign indicates the root of a number. The square root of 9 is shown below.