Mathematics
Grade9
Easy
Question
If the product of extremes is equal to the product of means, then it is in
- Proportion
- Geometric mean
- Harmonic mean
- Arithmetic mean
Hint:
In a proportion; the first and the last terms are called the extremes; whereas the second and the third terms are called the means.
The correct answer is: Proportion
In general, four numbers are said to be in proportion, if the ratio of the first two quantities is equal to the ratio of the last two. In general, the symbol for representing a proportion is “: :”
(i) The numbers a, b, c and d are in proportional if the ratio of the first two quantities is equal to the ratio of the last two quantities, i.e., a : b : : c : d and is read as ‘a is to b is as c is to d’. The symbol ‘ : : ‘ stands for ‘is as’.
(ii) Each quantity in a proportion is called its term or its proportional.
(iii) In a proportion; the first and the last terms are called the extremes; whereas the second and the third terms are called the means.
If four numbers a, b, c and d are in proportional (i.e., a : b : : c : d), then a and d are known as extreme terms and b and c are called middle terms.
(v) The fourth term of a proportion is called fourth proportional.
(vi) For every proportion, the product of the extremes is always equal to the product of the means, i.e., a : b : : c : d if and only if ad = bc.
For example; in proportion 3 : 4 : : 9 : 12;
Product of extremes = 3 × 12 = 36 and product of means = 4 × 9 = 36
Thus, if the product of extremes is equal to the product of means, then it is in proportion.
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