Rato & proportion
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This document defines and explains ratio, proportion, and the different types of variation. It contains the following key points: 1. A ratio compares two quantities using division, where the quantities must be in the same unit. 2. A proportion states that the ratios of two sets of quantities are equal. The product of the extremes equals the product of the means. 3. Direct variation occurs when quantities change in the same direction. Inverse variation occurs when they change in opposite directions. 4. A constant of proportionality describes the mathematical relationship between variables in direct or inverse variation.
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Subject: Quantitative Aptitude
TechMathI - 2.6
This document provides examples and explanations of logical equivalences and properties that can be used to prove conditional statements in algebra and geometry. It includes the converse, inverse, and contrapositive of a conditional statement, properties of equality, substitution, and justifying steps to prove conditional statements through algebraic manipulation.
12. ratio & prapotion
1. Ratio and proportion are important concepts involving relationships between quantities. A ratio represents the fraction between two quantities, while a proportion exists when ratios are equal.
2. Key formulas and concepts include: the product of means equals the product of extremes; finding fourth, third, and mean proportionals; comparing and compounding ratios; and direct and inverse variation.
3. Examples demonstrate calculating ratios, proportions, and proportionals from word problems involving money, mixtures, and other real-world scenarios.
Similar to Rato & proportion (7)
Rato & proportion
- 1. RATIO & PROPORTION Prepared by S K TRIPATHI TGT ( Maths) K V, VIKASPURI NEW DELHI
- 2. RATIO & PROPORTION Comparing of two quantities a and b can be done by two methods (i) Difference= a-b (ii)Division= a/b
- 3. RATIO Ratio of two quantities is simple division of one quantity by the other a ratio b = a / b a:b The quantities must be in same unit , however if not in same unit convert in same unit the find the ratio
- 4. PROBLEMS Ratio of 85 and 102 = 85 / 102 = (85 / 17 ) / (102 / 17 ) =5/6 =5:6 Ratio of 55 cm and 1 m = 55 cm / 1 m = (55 cm ) / (100 cm) = ( 55 / 5 ) / ( 100 / 5 ) = 11 : 20
- 5. PROPORTION If ratio of quantities a and b is equal to that of c and d Quantities a , b , c and d are called in proportion a:b=c:d a:b::c:d Quantities 5 , 6 , 25 and 30 are in proportion 5 / 6 = 25 / 30
- 6. Extremes and Means If ratio of quantities a and b is equal to that of c and d a:b=c:d Terms a and d are called Extremes Terms b and c are called Means
- 7. GENERAL PRINCIPAL OF PROPORTION If ratio of quantities a and b is equal to that of c and d a:b=c:d a/b=c/d a d =bc Product of Extremes = Product of Means
- 8. DIRECT Variation If a quantity varies with respect to other such that LIKE change occurs in both, the variation is DIRECT VARIATION If quantity a varies with respect to b such that a increases b increases a decreases b decreases a varies directly as b a b
- 9. INVERSE Variation If a quantity varies with respect to other such that UNLIKE change occurs in both, the variation is INVERSE VARIATION If quantity a varies with respect to b such that a increases b decreases a decreases b increases a varies inversely as b a 1/b
- 10. CONSTANT of PROPORTIONALITY If quantity a varies If quantity a varies with respect to b such with respect to b such that a that a varies directly as b varies inversely as b a b a 1/b a=kb a=k/b K is called constant of ab=k proportionality K is called constant of proportionality