Real life applications of ratio and proportion are numerous! The concept occurs in many places in mathematics

When you prepare recipes, paint your house, or repair gears in a large machine or in a car transmission, you use ratios and proportions.

Say a recipe to make brownie requires 4 cups of flour for 6 persons

You may want to know how much flour to put for 24 persons

You just cannot go wrong when you take this first step:

The setup you see above can be translated into the following proportion:

4 cups/X |
= 6/24 |

Probably one of the best applications we can find is that of gears in a car transmission.

A gear look like a circle and it has teeth all around it.

Transmissions contain several combinations of large and small gears.

Say for instance a small gear (20 teeth) drives a large gear(40 teeth).

The large gear will turn at half the speed of the small gear.

20/ 4 = |
1/2 |

However, this situation increases the turning force (or torque) of the large gear.

In general, the larger the gear the bigger the torque.

Therefore, you can see that knowing the ratio of gears; can help us determine the speed and how much torque each gear will deploy.

This concept is important when putting a transmission together. The situation we just describe may for instance set the proper gear ratio for moving a load.

However, at cruising speed, gears may have the same ratio so that the amounts of torque that enter the transmission equal the amount of torque that goes out.