BBC Bitesize - KS3 Maths - Ratio and proportion - Revision 1
A proportional relationship is one in which two quantities vary directly with each y decreases-and that the ratio between them always stays the same. The graph of the proportional relationship equation is a straight line through the origin. Practice writing equations to describe proportional relationships. Students use proportional information to determine the relative scales of planets and large Students learn about how simple fractions are used to describe gears and gear trains that reduce or increase speed. [Grade: | Topics: scale , proportion, ratio, area, density] [Grade: 7 - 10 | Topics:Simple linear equations] .
The proportionality constant is the product of the mass and gravitational acceleration. For a body moving in a circle with constant angular speed, the linear speed tangential speed is proportional to the angular speed. The constant of proportionality is the radius of the circle. The weight of the displaced fluid is directly proportional to the volume of the displaced fluid.
In simple terms, the principle states that the buoyancy force on an object is equal to the weight of the fluid displaced by the object.
At constant pressure, the volume V of a given mass of an ideal gas increases or decreases by the same factor as its temperature T on the absolute temperature scale i.
The properties of direct proportion can be usefully applied in each of the examples above. Here are two other important examples. Currency exchanges an example of property 2: The reciprocal of the proportionality constant used for the first conversion is applied for the second.
So let's say that, let's say that I have, let's say that x-- Let me do this, I already used yellow, let me use blue. So let's x, let's say that's a measure of time and y is a measure of distance.
TIMES MODULE M35 - Proportion
Or, let me put it this way, x is time in terms of seconds. Let me write it this way. So, x, x is going to be in seconds and then, y is going to be in meters. So, this is meters, the units, and this right over here is seconds.
Ratios, Proportion, and Rates
So, after one second, we have traveled, oh, I don't know, seven meters. After two seconds, we've traveled 14 meters. After three seconds, we've traveled 21 meters, and you can verify that this is a proportional relationship. The ratio between y and x is always seven. Seven over one, 14 over two, 21 over three.
But, I wanna write that in terms of it's units. So, y over x is going to be, if we look at this point right over here, it's seven meters over one second. Seven meters over one second, or it's equal to seven meters per second. If you look at it right over here, if you say y over x, it's 14 meters, 14 meters, in two seconds, in two seconds. A randomized clinical trial was conducted to test the effectiveness of low-dose aspirin in preventing heart attacks.
Subjects were randomly assigned to receive either low-dose aspirin or an inactive placebo. There were 11, subjects in the aspirin group, and, after 5 years of observation, there had been a total of 10 fatal heart attacks in this group.
Ratios and proportions and how to solve them
What was the proportion having a fatal heart attack in the aspirin group? After computing the decimal fraction, convert your answer into the number of subjects having a fatal heart attack per 10, subjects. Round off your answer to the number of whole subjects per 10, Do not include decimals.
Rates Rates are a special type of ratio that incorporate the dimension of time into the denominator. Familiar examples include measurements of speed miles per hour or water flow gallons per minute.
Equations for proportional relationships
Suppose a car traveled 24 miles in 2 hours, then continued and traveled miles in 3 hours, and then another 12 miles in 1 hour. We can compute the average rate of speed for the entire trip by adding up the total distance covered and dividing it by the total time that the trip took. A mortality rate is the proportion of deaths occurring over a span of time in a population.
An attack rate is the proportion of people developing an infectious disease after exposure to a pathogen. A case-fatality rate is the proportion of individuals who die after developing a disease. Strictly speaking, these are all proportions, but incidence rates or incidence density is a measurement of the frequency of a health outcome that is more like a true rate.
An incidence rate basically quantifies the number of health outcomes and the total exposure time i. Similar to computation of an average speed for an automobile, an incidence rate is computed by dividing the total number of health-related events that occurred by the total exposure time at risk for the group. For example, consider a hypothetical clinical trial that was conducted to determine whether taking low-dose aspirin reduced the frequency of heart attacks in middle-aged and elderly men.