1. Fractions, Decimals, Percent

2. Fractions Fractions are ratios of two numbers. They are written as a top number separated from a bottom number by a fraction bar. The top number is called the numerator and the bottom number is the denominator. A common fraction is a number where the numerator and denominator are whole numbers and the denominator is not equal to 0. A fraction whose denominator is 0 is meaningless since 0 can go into any number infinite number of times. Consider that the numerator value is the number of parts of the denominator value. If the fraction is 1/2, this indicates 1 part out of 2. For example, 1/2 of a pair of gloves is one of the two gloves.

3. Fractions Another way of viewing fractions is to say that the numerator is divided by the denominator. This means that 1/4 is the result of dividing 1 into 4 parts. For example, if one apple is divided into four equal parts, each part would be 1/4 of the original. Fractions in which the numerator is smaller than the denominator are called proper fractions. Thus 3/4 is a proper fraction. Fractions in which the numerator is larger than the denominator are called improper fractions. The number, 5/4, is an example of an improper fraction.

4. Fractions To illustrate the meaning of 5/4, consider that there are two pies, each of which has been divided into 1/4.s. The number 5/4 represents a total of 5 of the 1/4 pieces. We can also say that this equals one pie (four 1/4.s) plus 1/4 or 1 1/4 pies. The fraction 1 1/4 is called a mixed number. It consists of the sum of a whole number and a proper fraction. In working with fractions it is often necessary to convert from mixed numbers to improper fractions and back.

5. Fractions A mixed number is converted to an improper fraction by multiplying the whole number by the denominator and then adding the product to the numerator. The sum is then put over the denominator.

6. ADDITION AND SUBTRACTION OF FRACTIONS Sometimes it is necessary to add or subtract fractions. This can be accomplished by observing the following rules: –The fractions must have the same (common) denominator –The numerators are added together (or subtracted) and placed over the common denominator.

7. ADDITION AND SUBTRACTION OF FRACTIONS To add fractions that do not have the same denominator, first write the fractions as equivalent fractions with a common denominator. For example, if we want to add 1/4 and 2/5, we first need to find the lowest common denominator (LCD). In this case the LCM is 20. Add the fractions and reduce to simplest form if required. The same procedure is followed when subtracting fractions.

8. ADDITION AND SUBTRACTION OF FRACTIONS When adding whole numbers, mixed numbers and fractions, the following rules apply: –To add a whole number and a fraction, write down the whole number and then the fraction. –3 + ¾ = 3 ¾ –To add a whole number and a mixed number, add the whole numbers and write down the fraction. –4 1/5 + 2/5 = 4 3/5

9. MULTIPLYING FRACTIONS The product of the multiplication of two fractions is the product of the numerators over the product of the denominators. To multiply a whole number by a fraction write the whole number as a fraction with a denominator of 1 and then multiply as above.

10. DIVIDING FRACTIONS To divide fractions, invert the divisor and change the division sign to multiplication and solve for the product. Reduce to simplest form as required. Division of fractions with whole numbers and mixed numbers is managed in a similar way to multiplication. The whole numbers are changed to fractions with a denominator of 1 and the mixed numbers are changed to improper fractions.

11. DECIMAL NUMBERS The number system that we use today is called the decimal system. It derives its name from dec, meaning ten. All numbers in the system is based on some combination of the ten digits:0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 In the number system these digits not only have face value, but they have place value as well. For example, in the number 25, the face value of the 2 is two, but the place value is ten, and the face value of 5 is five but its place value is one face value of 5 is five but its place value is one. The decimal system is also used to represent numbers less than one (fractions). Calculators use the decimal system to indicate decimal fractions. Numbers less than 1 are separated from 1, or greater by a decimal point (.).

12. DECIMAL NUMBERS The digits in decimal numbers also have face value as well as place value. For example, in the decimal number 0.14, the 1 has a face value of one and a place value of one tenth. The 4 has a face value of four and a place value of one hundredth. The following illustration, 1 is shown having different place values.

13. PERCENT Percentages are used often in everyday life. We talk about mortgage and interest rates, opinion poll results, pay increases, and many other statistics involving percentages. The power engineer may also use percentage in discussing flow rates, firing rates, or tank levels, etc. The phrase per cent comes from a Latin expression meaning.out of each hundred.. The symbol for per cent is.%.. The expression 75% means 75 out of 100. This is the same as the fraction 75/100. It is also the same as 0.75. To change a percent to a fraction or a decimal, drop the % sign and divide by 100. To change a fraction or decimal to percent, multiply by 100 and add the percent sign.

14. PERCENT