Module V Ratios and Proportions

Module V Ratios and Proportions

1. Ratio

   • Is a quotient of two quantities.
     • The ratio of the number A to the number B is:
       • A to B A/B or A:B
         • The ratio of 6hr to 3 days is thus: 6 hrs/3 days = 6 hrs/ 72 hrs = 6/72 = 1/12
     • When ratios are used in comparing units of measure, the units should be the same

2. Proportions

   • A proportion is a statement that says that two ratios are equal
     • 3/4 = 15/20
       • a/b = c/d
         • a, b, c, d are te therms of the proportion. a and b are called the Extremes and the b and c therms are called the Means
           • bd*a/b = bd*c/d
           • Cross Products: If a/b = c/d then the cross products ad and bc are equal
             • 63/x=9/5 63*5=9x 315=9x 35=x
             • Application: Biologist use this method to estimate the number of fish in a lake. Suppose they tag 300 fish on April 1. They return one month later and take a sample of 400 fish, 5 of the 400 fish were previously tagged.
               • Solution: 300/x=5/400 5x=120,000 x=24,000
                 • 24,000 fish in the lake

3. Direct Variation

   • Y varies directly as X, or Y is directly proportional to X, if there exists a nonzero constant K such that Y=KX or equivalentñy Y/X=K K=constant of variation
     • y=50 when x=20, y? when x=14 y=kx 50=k*20 5/2=k y=5/2x y=5/2*14=35 y=35 when x=14
     • constant of variation is the constant factor in the definition of the function

4. Inverse Variation

   • Y varies inversily as X if there exist a nonzero real number K such that : y=k/x´ or equivalently, xy=k
     • Also Y varies inversily as the nyh power of X if there exists a nonzero real number K such that: y=k/x^n
       • The weight of an object above Earth varies inversily as the square of its distance from the center of Earth. A vehicle is at 6700 miles and an astronaut here weights 57 pounds. Another vehicle is at 4090 miles from Earth. what is the weigh of the astronaut here?
         • w=weight and d= distance from the center of Earth w=k/d^2
           • 57=k/(6700)^2 k=57(6700)^2 w=57(6700)^2 = 153 punds

5. Juan Armando Pérez Vital A01400839