## 18 January 2014 Ratios are used to compare quantities.  Ratios help us to compare quantities and determine the relation between them.  We write ratios in the form of fractions, and then compare them by converting them into like fractions.  If these like fractions are equal, then we say that the given ratios are equivalent.

Eg:6 pens cost Rs 90.  What would be the cost 10 such pens?

Solution:
Cost of 6 pens :Rs 90
Cost of 1 pen = 90/6=Rs 15
Hence, cost of 10 pens =10×15=150
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. When two ratios are equivalent, the four quantities are said to be in proportion.
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.

#### Percentages:

Percentage is another method used to compare quantities. Percentages are numerators of fractions with the denominator 100.

#### Meaning of percentage:

Per cent is derived from the Latin word ‘per centum’, which means per hundred.
Per cent is represented by the symbol - %.
Ratios and Proportions
• The ratio of two quantities in the same units is a fraction that shows how many times one quantity is greater/smaller than the other.
• To calculate the ratio of two quantities, the units must be the same.
• Compare different ratios to determine whether they are equivalent ratios or not.
• If two fractions are equal then the given ratios are equivalent.
• When two ratios are equivalent then the four quantities are said to be in proportion.
• Ratio and proportion problems can be solved by using two methods, unitary method and equating ratios to make proportions and solve
• the equation.
• Percentage means per hundred. It is another method used to compare quantities.
• Fractions can be compared by converting them into percentages.
Conversions
To convert a percentage into fraction:
Step 1: Drop the percentage sign, and then divide the number by hundred.
To convert a percentage into a decimal:
Step 1: Remove the percent sign.
Step 2: Divide the number by hundred of move the decimal point two places to the left in the numerator.
To convert a decimal into percentage:
Step 1: Convert the decimal into a fraction
Step 2: Multiply the fraction by hundred or shift the decimal point two places to the right
Step 3: Put a percent sign next to the number
Application of Percentages
If you are given any three of these quantities the fourth one can be calculate using the interest formula.

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