Middle School Math Proportions : 2

Introduction :

            Proportions are nothing more than two ratios or fractions set equal to one another. Proportions have several very handy properties that make working with them much easier to manage. In proportions correctly and how to solve the problems created with the proportions.

          
 A proportion is an equation involving two fractions. The ratio of the numerators and denominators of the fractions must be equal. A proportion is a statement saying that two fractions are equivalent or equal in value. The fractions can be reduced in the normal way – and they can be reduced in some rather unique ways, too. This property and several others to solve for unknown parts of a proportion.

                        Given the proportion a / b = c / d, the following also

                                                             a x d = b x c

Definition and examples problems on middle school math proportions:

Definition proportion(Middle School Level):

                    If two ratios are not like, then we declare that they are not in proportion. In a declaration of proportion, the four quantities concerned when taken in order are known as respective terms. First and fourth terms are known as extreme terms. Second and third terms are known as middle expressions.If two ratios are equal, we say that they are in proportion and exercise the symbol ‘::’ or ‘=’ to equate the two ratios.

Example problems for middle school math proportion:

Problem 1:

              Are the ratios 20g: 24g and 40 kg: 48 kg in proportion?

Solution:

                  20 g: 24 g = 20 / 24

                                    = 5: 6

                 40 kg: 48 kg = 40 / 48

                                   = 5: 6

                  So, 20: 24 = 40: 48.

Therefore, the ratios 20 g: 24 g and 40 kg: 48 kg are in proportion,

                i.e. 20 : 24 :: 40 : 48

The middle terms in this are 24, 40 and the extreme terms are 20, 48.

Problem 2:

               Are 15, 20, 45 and 60 in proportion?

Solution:

              Ratio of 15 to 20 = 15 /20

                                            = 3: 4.

             Ratio of 45 to 60 = 45 / 60

                                           = 3: 4.

             Since, 15: 20 = 45: 60.

Therefore, 15, 20, 45, 60 are in proportion.

Applications on middle school math proportions:

      If we want to draw a plan of a house, it is not possible to draw the plan in actual dimensions (or size).

      Let the ratio between drawn length and actual length be a: b

                      1) If a is less than b, we get a reduced figure.

                     2) If a = b, we get equal scale figure (same size figure)

                     3) If a is greater than b, we get an enlarged figure.

      
For example,

                  1) A house plan map – a reduced figure

                  2) Geometrical figure drawn in note book – equal scale figure

                  3) Bacteria seen through microscope – enlarged figure

Note: The ratio a / b is called the representative fraction (a and b must be in the same unit).