In our daily life, there are many occasions when we compare two quantities.
This topic gives an overview of;
Ratios are used to compare quantities. Ratios help us to compare quantities and determine the relation between them. A ratio is a comparison of two similar quantities obtained by dividing one quantity by the other. Since a ratio is only a comparison or relation between quantities, it is an abstract number. For instance, the ratio of 6 miles to 3 miles is only 2, not 2 miles. Ratios are written with the” : “symbol.
If two quantities cannot be expressed in terms of the same unit, there cannot be a ratio between them. Hence to compare two quantities, the units must be the same.
Consider an example to find the ratio of 3 km to 300 m.First convert both the distances to the same unit.
So, 3 km = 3 × 1000 m = 3000 m.
Thus, the required ratio, 3 km : 300 m is 3000 : 300 = 10 : 1
Different ratios can also be compared with each other to know whether they are equivalent or not. To do this, we need to write the ratios in the form of fractions and then compare them by converting them to like fractions. If these like fractions are equal, we say the given ratios are equivalent. We can find equivalent ratios by multiplying or dividing the numerator and denominator by the same number. Consider an example to check whether the ratios 1 : 2 and 2 : 3 equivalent.
To check this, we need to know whether
We find that which means that
Therefore, the ratio 1 :2 is not equivalent to the ratio 2 : 3.
The ratio of two quantities in the same unit is a fraction that shows how many times one quantity is greater or smaller than the other. Four quantities are said to be in proportion, if the ratio of first and second quantities is equal to the ratio of third and fourth quantities. If two ratios are equal, then we say that they are in proportion and use the symbol ‘:: ’ or ‘=’ to equate the two ratios.
Ratio and proportion problems can be solved by using two methods, the unitary method and equating the ratios to make proportions, and then solving the equation.
To check whether 8, 22, 12, and 33 are in proportion or not, we have to find the ratio of 8 to 22 and the ratio of 12 to 33.
Therefore, 8, 22, 12, and 33 are in proportion as 8 : 22 and 12 : 33 are equal. When four terms are in proportion, the first and fourth terms are known as extreme terms and the second and third terms are known as middle terms. In the above example, 8, 22, 12, and 33 were in proportion. Therefore, 8 and 33 are known as extreme terms while 22 and 12 are known as middle terms.
The method in which we first find the value of one unit and then the value of the required number of units is known as unitary method.
Consider an example to find the cost of 9 bananas if the cost of a dozen bananas is Rs 20.
1 dozen = 12 units
Cost of 12 bananas = Rs 20
∴ Cost of 1 bananas = Rs
∴ Cost of 9 bananas = Rs
This method is known as unitary method.
Cite this Simulator: