Ratio and Proportions Math trick Problem and solution
A ratio is a fraction that compares two quantities that are measured in the same units.
Ratio of two quantities a and b of the same kind is a/b is denoted by the a:b, and read as a is to b.
Properties of the ratios:
- The value of ratio never changed or we can say it is remains unchanged, if each of its terms are multiplied or divided by a same non-zero number.
- For a>b, if the same positive number is added to each term, the ratio decreases.
- For a<b, if the same positive number is added to each term, the ratio increases.
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The ratio that compares one part to another part is called part-to-part ratio, denoted by part:part.
Example: If a bag contains marbles of colors red and blue with quantities 3 & 5 respectively, then ratio of the red marbles is known as part:part ratio
This would be denoted as;
Red marbles: Blue marbles
If a set of objects is divided into two groups, in the ratio a:b, then the first group contains a/(a+b) objects and the second group contains b/(a+b) objects. This ratio is called part-to-whole ratio denoted as part:whole. Hence, the objects a and b would be a:(a+b) and b:(a+b) ratios with respect to the total objects.
Example: From recent example, the part-to-whole ratios can be shown as;
For red marbles= 3:8
For blue marbles= 5:8
- Ratio is the relation existing between any two quantities of the same kind.
- Order of the terms in the ratio is important. in the general for a is not equal b, the ratio a:b and b:a are different.
- Ratio of two quantities is an absolute number if it has no unit.
In a partnership if the investment are in the ratio a:b and the periods are in the ratio m:n, then they share the profits in the ratio am:bn.
How to Determine a Ratio:
Ratio represent how one number is related to another number.
A ratio may be written as A:B or A/B or by the phrase “A to B” .
A ratio of 1:5 says that the second number is five times as large as the first.
The following steps will allow a ratio to be determination if two numbers are known.
Determine the ratio of 24 to 40.
Divided both terms of the ratio by the greatest common factor ( 24/8=3, 40/8=5)
The ratio of 24 to 40 is 3:5
- Ratio is another name of the fraction. An equation in which two ratio are equal is called a proportions.
- Ratio is a quotient of one number a to another number b. It can be expressed in three ways.
The ratio a:b is read as a to b.
Example: Find the ratio of x to y from the equation 3x²+y²=4xy