Ratio Definition and 20 Discussions

In mathematics, a ratio indicates how many times one number contains another. For example, if there are eight oranges and six lemons in a bowl of fruit, then the ratio of oranges to lemons is eight to six (that is, 8∶6, which is equivalent to the ratio 4∶3). Similarly, the ratio of lemons to oranges is 6∶8 (or 3∶4) and the ratio of oranges to the total amount of fruit is 8∶14 (or 4∶7).
The numbers in a ratio may be quantities of any kind, such as counts of people or objects, or such as measurements of lengths, weights, time, etc. In most contexts, both numbers are restricted to be positive.
A ratio may be specified either by giving both constituting numbers, written as "a to b" or "a∶b", or by giving just the value of their quotient a/b. Equal quotients correspond to equal ratios.
Consequently, a ratio may be considered as an ordered pair of numbers, a fraction with the first number in the numerator and the second in the denominator, or as the value denoted by this fraction. Ratios of counts, given by (non-zero) natural numbers, are rational numbers, and may sometimes be natural numbers. When two quantities are measured with the same unit, as is often the case, their ratio is a dimensionless number. A quotient of two quantities that are measured with different units is called a rate.

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  1. lucaszito

    Pulley system for cardboard pulp shredder/mixer

    Hi everybody, first message on this forum ! I am building a machine for a friend who works with cardboard pulp, he is also a performance artist and would like a machine where 2 or 3 performers can activate the machine by hand with pulleys and wheels, and shred the pieces of cardboard that are...
  2. caters

    What is the ratio after 1 month given certain conditions?

    So this question is a math question having to do with me calculating the rate of population growth starting from a population of 100,000. I have already gotten the first 3 steps done (sex ratio, ratio of cycle time, and pregnancy ratio) after a week among those in the fertile timeframe...
  3. L

    Gears create more torque? Prove it

    Hi guys, I was sizing up a servo motor the other day and started thinking. While we all know gear ratios will effectively "convert" speed into torque. I couldn't help wondering about the initial starting conditions.. The problem below... Lets say I have a motor with a max load of 1Kg...
  4. G

    Ratio of the Electric field to the Magnetic field

    Dear all. I would like to know the general expression of the ratio of the electric field strength E to the magnetic flux density B. I know E/B = c, where c is the speed of light, for a vacuum, but I want to know if this is stil valid for any material where the electric and magnetic fields are...
  5. M

    Chemistry Why moles of (S2O3 2-) is equal to mol of ( MnO4-) times 5

    Homework Statement The ratio of KMnO4 to I2 is given by 2 MnO4 - + 16 H+ + 10 I - ⇌ 2 Mn2+ + 5 I2 + 8 H2O the ratio is 2:5 - The ratio of I2 to S2O3 2- is given by 1 I2 + 2 S2O32- ⇌ 2 I-+ S4O5 2- the ratio is 1:2 therefore n(S2O3 2- ) = n(MnO4 - ) x 5 Homework Equations Why the mole of...
  6. R

    H/D ratio and neutron leakage

    Homework Statement A sphere has a height to diameter ratio of 1.00. The greater the surface area to volume ratio of a shape, the greater the neutron leakage. To increase neutron leakage should H/D be positive or negative? Homework Equations H/D The Attempt at a Solution Positive? Good...
  7. Vital

    Understanding the ratio formula

    Homework Statement Hello! Please, help me to understand the mathematical logic behind one of the financial instruments called the "money market yield". Here is the equation: money market yield = [ 360 x r BD ] / [360 - (t x rBD)] where rBD is the band discount rate, and for simplicity we...
  8. S

    I 10 different classes of ratio

    In the book 'ZERO THE BIOGRAPHY OF A DANGEROUS IDEA' Charles Seife says, "Because ratios were the key to understanding nature, the Pythagoreans and later Greek Mathematicians spent much of their energy investigating their properties. Eventually, they categorized proportions into 10 different...
  9. YNesterov

    How to find m1 in T = ( m1c1T1 + m2c2T2 ) / ( m1c1 + m2c2 )

    Homework Statement How to find mass of one of the two liquids being mixed if we know all other variables in this formula T = ( m1c1T1 + m2c2T2 ) / ( m1c1 + m2c2 ) ? Homework Equations T = ( m1c1T1 + m2c2T2 ) / ( m1c1 + m2c2 ) The Attempt at a Solution
  10. A

    Find the ratio of two line segments in a triangle

    1. The problem statement, all variables, and given/known data Triangle ABC has a point D on the line segment AB which cuts the segment in ratio AD : DB = 2 : 1. Another point E is on the line segment BC, cutting it in ratio BE : EC = 1 : 4. Point F is the intersection of the line segments AE and...
  11. W

    Calculating gear ratios for a drivetrain

    I'm trying to calculate the required gear sizes for the system shown below: The driven wheel is connected to a 600mm diameter bicycle wheel and the driver wheel connected to a 580 mm long lever arm which has a forward driving force of 40 N. I want to calculate the most efficient sizing of...
  12. R

    I Propagating Error in both numerator and denominator of ratio

    Hello, I have a set of N samples, each of which yields the measurable variables A and B. I am interested in computing the mean and standard error of the ratio A/B within the group. The catch is that I need to do background subtraction on both A and B, and the two different background values BGA...
  13. J

    Gear RPM "img attached"

    Hey Guys, So in the attached image I'm trying to determine what the rpm of the 60 tooth gear will be given the 8.4" tire will be rotating at .68 rpm, everything else is just an assumption on my part. I'm assuming the following which is probably wong: The tire being rotated at .68 rpm will...
  14. N

    Mark-Space Ratio

    Hi if I had the ratio of 4:1 and the frequency of 10Khz how would I go about finding the time?
  15. O

    Thermoelectric modules

    What is the heat/cold ratio in thermoelectric modules to generate a specific voltage pls? old Bozo
  16. F

    Finding ratio of impluse

    Two identical molecules A and B each of mass M travel with the same velocity towards a vertical wall at an angel 20 degrees with respect to the normal to the wall. A rebounds from the wall with the same speed while B sticks to the wall. Determine the ratio of the implus experience by A to that...
  17. B

    Automotive Combution, energy and pressure relation

    Hello guys, I'm currently working on a car simulation just for fun, but I'm stuck... The force to move a car is generated by burning fuel ( to be more percise, diesel or gasolin). But there are more variables: Pressure (i know this because of turbos and such) amount of fuel amount of air (or...
  18. J

    Simple question on motor rotation and pulley

    Hi all, I have a small DC motor which turns at 20 rpm. The shaft diameter is 6mm, giving a circumference of 18.85 mm. What I want to do is get an effective rate of 30 rpm. Can I do this by simply attaching a spool or spindle to the motor output shaft with a larger diameter? If so, would it...
  19. W

    Poisson's ratio for a rigid rod

    I have a conceptual misunderstanding it seems. Poisson's ratio is the ratio of elastic strain deformation of the transverse and longitudinal components. That being said, if I were to induce thermal stress (heating up) to a rod by keeping its ends (longitudinal component) rigid, would there be a...
  20. Laurine

    Solving the Severn Bridge Sag Span Mystery

    Hello everyone. I have to describe is the Severn Bridge, a suspension bridge spanning the River Severn and River Wye in England. I have found almost all the measurements, except for one: the sag span. I could only find the sag ratio (1/12) but I need to convert this ratio to meters. Can anyone...