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Welcome to our Math lesson on **Definition of Proportion**, this is the first lesson of our suite of math lessons covering the topic of **Proportion**, you can find links to the other lessons within this tutorial and access additional Math learning resources below this lesson.

If two quantities involved in a situation (we call them variables) are related in such a way that if one quantity changes, the other quantity changes at the same (or opposite) degree, we say that these quantities are in proportion with (or proportional to) each other. In simpler words, a proportion indicates to us how one thing changes in relation to another.

For example, if a car travels 240 km with 8L of gasoline, it can travel other for other 720 km with 24 L of gasoline if moving at the same rate (speed). The unit rate u.r. of gasoline consumption therefore is

u.r. = *240 km**/**8 L* = 30 *km**/**L*

Also

u.r. = *720 km**/**24 L* = 30 *km**/**L*

Since there two unit rates are equal, we say they are in proportion. Hence, it is clear that a proportion includes two equal fractions, i.e. if

then a and c are proportional (as well as b and d).

In other words, if ** a/b** and

We can also write the above proportion in the form

a:b = c:d

where a is the first term, b is the second term, c is the third term and d is the fourth term of the proportion. The terms a and d are called outer terms or extremes, while b and c are called inner terms or means of the proportion.

Which of the following pairs of fractions are in proportion?

and*4**/**18**3**/**15*and*21**/**7**12**/**4*and*24**/**36**9**/**15*

First, we express each fraction in the simplest terms. In a certain sense, a fraction expressed in the simplest terms is similar to the unit rate (in fact, one of the two associated unit rates) we discussed earlier. Thus,

=*4**/**18*=*4 ÷ 2**/**18 ÷ 2**2**/**9*and

=*3**/**15*=*3 ÷ 3**/**15 ÷ 3**1**/**5*

Since these two fractions are not equal, the quantities they represent are not in proportion.- 2
=*1**/**7*= 3*3**/**1*and

=*12**/**4*= 3*3**/**1*

These fractions are equal, so the quantities they represent are in proportion. =*24**/**36*=*24 ÷ 12**/**36 ÷ 12**2**/**3*and

=*9**/**15*=*9 ÷ 3**/**15 ÷ 3**3**/**5*

Since these two fractions are not equal, the quantities they represent are not in proportion.

Enjoy the "Definition of Proportion" math lesson? People who liked the "Proportion lesson found the following resources useful:

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- Check your calculations for Ratio and Proportion questions with our excellent Ratio and Proportion calculators which contain full equations and calculations clearly displayed line by line. See the Ratio and Proportion Calculators by iCalculator™ below.
- Continuing learning ratio and proportion - read our next math tutorial: Properties of Proportion. Geometric Mean

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