Ratios and Proportions
Ratio Ratios are used to compare quantities. To compare two quantities, the units of the quantities must be the same. 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 to like fractions. If these like fractions are equal, then the ratios are said to be equivalent. e.g. Cost of 6 pens is Rs 90. What would be the cost of 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 = Rs 150. Proportion 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. Unitary method Unitary method is the method of finding the value of one unit (unit rate) at first and then the value of required number of units. Percentages Percentage is another method used to compare quantities. Percent is derived from the Latin word ‘per centum’, which means per hundred. Percentage is the numerator, of a fraction, whose denominator is hundred. Percent is represented by the symbol - %. e.g. $\frac{\text{21}}{\text{100}}$ or 21%

#### Summary

Ratio Ratios are used to compare quantities. To compare two quantities, the units of the quantities must be the same. 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 to like fractions. If these like fractions are equal, then the ratios are said to be equivalent. e.g. Cost of 6 pens is Rs 90. What would be the cost of 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 = Rs 150. Proportion 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. Unitary method Unitary method is the method of finding the value of one unit (unit rate) at first and then the value of required number of units. Percentages Percentage is another method used to compare quantities. Percent is derived from the Latin word ‘per centum’, which means per hundred. Percentage is the numerator, of a fraction, whose denominator is hundred. Percent is represented by the symbol - %. e.g. $\frac{\text{21}}{\text{100}}$ or 21%

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