TO EMAIL MRS.PULCHER                     pulcherp@christina.k12.de.us

How to Get Fractions to Lowest Terms

To get a fraction to lowest terms, find the largest number that will divide evenly into both the numerator and the denominator. (This will not change the fraction's value; the reduced (simplified) fraction will be an equivalent.)

Example:
Write 6/18 in lowest terms.

The largest number that will divide evenly into both the numerator and the denominator is 6.

6 18

÷

6 6

=

1 3

Thus, the fraction 6/18 is the same as the fraction 1/3 when simplified to lowest terms.

 

EQUIVALENT FRACTIONS

To find equivalent fractions, multiply (or divide) the numerator and the denominator by the same number.  Remember that the same number over itself is 1.

2  _{= 1}      3  _{= 1}     4  _{= 1}                                              

2             3           4 

Example:    Equivalent fractions for   

3     and   10

4             30  

3   x  6   ₌  18                 10  ¸   5   ₌    2

4   x  6      24                30  ¸   5       3

 

                                                                                Mixed Numbers & Improper Fractions

                                                                                                            

 Mixed  Numbers A mixed number contains a whole number and a fraction                                 

Changing a Mixed Number to an Improper Fraction                Multiply the denominator of the fraction by the whole

number.  Add that product to the numerator.  The new sum will be placed over the denominator. 

 Note:  The denominator does not change.

                                                                               

       IMPROPER FRACTIONS  Improper fractions are   

        greater than 1.  The numerator is larger than the

        denominator.

Changing an Improper Fraction to a Mixed Number     

Divide the numerator by the denominator.  The quotient will be

the whole number, and the fraction will by the remainder over the divisor.                                                                                                                                                               

 

Summary   

Notice that you can check your answer by doing the opposite operation.  In other words once you change a mixed number to an improper fraction, you can change the improper fraction back to the mixed number and vice versa (meaning once you change an improper fraction to a mixed number, you can change it back to an improper fraction).  If you don't come up with the same answer then you have made an error somewhere and need to try again.

 

CONVERTING FRACTIONS, DECIMALS, AND PERCENTAGES

 

Converting fractions to decimals:  Divide numerator by the denominator.  Example - 3/8 is fraction

 

       .375                    0.375 is decimal

8 / 3.000

      24

        60

          56

            40

            40

 

Converting fractions to percents:  1) Change to a decimal first by dividing the numberator by denominator (as above).   2) Multiply answer by 100 and add a percent sign. 

Example - 3/8 as fraction is 0.375 as decimal

              0.375 x 100 = 37.5%  

       Note:  multiplying by 100 is the same as moving the decimal    

                 point two places to the right.

 CHANGE DECIMAL TO PERCENT AND PERCENT TO DECIMAL

                        To change a decimal to a percent multiply by 100

OR move the decimal point two places to the right

And add a percent sign BUT

To change a percent to a decimal divide by 100

OR move the decimal point two places to the left

And drop the percent sign.

RATIOS

Ratios are comparisons of two numbers.  They are like fractions in that they can be equivalent and simplified, but fractions are a part of a whole while ratios are comparing two things, such as items, people, money, etc.  Example - if there are 15 girls and 10 boys in a classroom, the ratio is 15/10 girls to boys.  This can also be written as 15:10 and 15 to 10.  It can be simplied to 3/2 which says that for every 3 girls in a classroom there are 2 boys.

PROPORTIONS

A proportion is an equation with a ratio on each side.  It is a statement that two ratios are equal.  Example - 21/14 = 3/2

When one of the numbers in a proportion is unknown, you can cross multiply to get the unknown.  Example -    

   x/9 =  18/54

      54 x  =   9 x 18     (cross multiplication)

         54 x =   162 

     54/54 x =  162/54  (divide both sides by 54)

                 x   =   3                     3/9 = 18/54