Business math ch 2

Adding like fractions

1. Add the numerators and place total over the denominator 2. If the total of your numerators is the same as your denominator, convert to whole number, if the total numerator is larger than denominator, convert to mixed number

Reducing Fractions to lowest terms by inspection

1. By inspection, find the largest whole number (greatest common divisor) that will divide evenly into the numerator and denominator (does not change the fraction value) 2. Divide the numerator and denominator by the greatest common divisor. Now you have reduced the fraction to its lowest terms, since no number (except 1) can divide evenly into the numerator and denominator

Dividing mixed numbers

1. Convert all mixed number to improper fractions 2. Invert the divisor (take it's reciprocal) and multiply. If your final answer is an improper fraction, reduce it to lowest terms. You can do this by finding the greatest common divisor or by using the cancellation technique

Multiplying mixed numbers

1. Convert the mixed numbers to improper fractions 2. Multiply the numerators and denominators 3. Reduce the answer to lowest terms or use the cancellation method 2 1/3 x 1 1/2 = 7/3 x 3/2 Cancel the 3's out 7/3 x 3/2 = 7/1 x 1/2 = 7/2 = 3 1/2

Subtracting unlike fractions

1. Find the LCD 2. Raise the fraction to it's equivalent value 3. Subtract the numerators and place the answer over the LCD 4. If necessary, reduce the answer to lowest terms

Dividing proper fractions

1. Invert (turn upside down) the divisor (second fraction). The inverted number is the reciprocal 2. Multiply the fractions 3. Reduce the answer to the lowest terms or use the cancellation method

Converting mixed numbers to improper fractions

1. Multiply the denominator of the fraction by the whole number 2. Add the product from step 1 to the numerator 3. Place the total from step 2 over the denominator

Multiplying proper fractions

1. Multiply the numerators and denominators 2. reduce the answer to the lowest terms or use the cancellation method

Subtracting like fractions

1. Subtract the numerators and place over common denominator 2. reduce if necessary

adding mixed numbers

1. add the fractions (need common denominator) 2. add whole numbers 3. combine the totals of steps 1 and 2. Be sure you do not have an improper fraction in your final answer. Convert the improper fraction to a whole or mixed number. Add the whole numbers resulting from the improper fraction conversion to the total whole numbers of step 2. If necessary, reduce the answer to lowest terms

Finding LCD for two or more fractions

1. copy denominator and arrange in a row 2. divide the denominators by the smallest prime number that will go into two numbers 3. continue until no prime number divides into 2 numbers 4. multiply all the numbers in the divisors and last row to find the lcd 5. raise all fractions to have a common denominator and complete

Raising fractions to higher terms when the denominator is known

1. divide the new denominator by the old denominator to get the common number that raises the fraction to higher terms 2. multiply the common number from step 1 by the old numerator and place it as the new numerator over the new denominator

Adding unlike fractions

1. find the lcd 2. change each fraction to a like fraction with the LCD 3. add the numerators and place the total over the lcd 4. if necessary, reduce the answer to lowest terms

Using prime numbers to find the LCD

Ex. 1/3 + 1/8 + 1/9 + 1/12 1. copy the denominators and arrange them in a row 3 8 9 12 2. divide the denominators in step 1 by prime numbers. start with the smallest number that will divide into at least 2 of the denominators. Bring down any number that is not divisible. Keep in mind that the lowest prime number is 2. 2/ 3 8 9 12 _______________ 2/ 3 4 9 6 3. Continue step 2 until no more prime number will divide evenly into at least 2 numbers 3 is now used since 2 can no longer divide evenly into at least 2 numbers 3/ 3 2 9 3 ____________ 1 2 3 1 Now we have 2/3 8 9 12 _______________ 2/3 4 9 6 _______________ 3/3 2 9 3 ________________ 1 2 3 1 4. To find the LCD multiply all the numbers in the divisors (2,2,3) we used 2 as prime number, then 2, then 3 and then in the last row (1, 2, 3 ,1) [2x2x3] x [1x2x3x1] = 72 (LCD) 5. Raise each fraction so that each denominator will be 72 and then add fractions 24/72 + 9/72 + 8/72 + 6/72 = 47/72

Fraction

Expresses a part of a whole number

Lowest terms

Expressing a fraction when no number divides evenly into the numerator and denominator except the number 1 5/10 -> 1/2

Higher terms

Expressing a fraction with a new numerator and denominator that is equivalent to the original 2/9 -> 6/27

Converting improper fractions to whole or mixed number

Step 1. Divide the numerator of the improper fraction by the denominator Step 2. a. if you have no remainder, the quotient is a whole number b. if you have a remainder, the whole number part of the mixed number is the quotient. The remainder is placed over the old denominator as the proper fraction of the mixed number

The horizontal line

Indicates division

Reducing fractions to lowest terms might result in

More than one division

Unlike fractions

Proper fractions with different denominators,

Like fractions

Proper fractions with the same denominators,

ILeast common denominator (LCD)

Smallest nonzero whole number into which all denominators will divide evenly,

Step Approach for finding the greatest common divisor

Step 1. Divide the smaller number (numerator) of the fraction into the larger number (denominator) 2. Divide the remainder of step 1 into the divisor of Step 2 3. Divide the remainder of step 2 into the divisor of step 2 Continue this division process until the remainder is a 0, which means the last divisor is the greatest common divisor

Reciprocal of a fraction

The interchanging of the numerator and the denominator. Inverted number is the reciprocal 6/7 -> 7/6 The divisor becomes the reciprocal 1/8 divided by 2/3 (2/3 is the divisor)

Greatest common divisor

The largest possible number that will divide evenly into both the numerator and denominator

Mixed number

The sum of a whole number greater than zero and a proper fraction

Common denominator

To add two or more fractions, denominators must be the same,

Numerator

Top of the fraction - equal parts of the whole

Subtracting mixed numbers

When borrowing is not necessary 1. Subtract fractions, making sure to find the LCD 2. Subtract whole numbers 3. Reduce When borrowing is necessary 1. Make sure the fractions have the LCD 2. Borrow from the whole number of the minuend (top number) 3. Subtract the whole numbers and fractions 4. Reduce

Prime number

Whole number greater than 1 that is only divisible by itself and 1, 1 is not a prime number

Multiplying fractions is easier than adding and subtracting because

You do not have to find a common denominator

Denominator

bottom of the fraction - total number of equal parts

Cancellation

educing process that is used to simplify the multiplication and division of fractions 1/6 x 4/7 = 1/3 x 2/7

FInding lcd by inspection

ex. 3/7+5/21 7 goes into 21 thus 21 is the LCD 7 becomes 21 because and 3 becomes 9 because 7x3 = 21 and you do the same to the numerator so 3x3 = 9

improper fraction

has a value equal to or greater than 1; it's numerator is equal to or greater than it's denominator

A proper fraction

has a value less than 1; it's numerator is smaller than it's denominator