How can I understand direct, inverse and joint variation in math?

Answer 1

Hello.

Direct proportion is division or same direction. That is to say DIRECT(ION)

Inverse proportion is multiplication or opposite direction.

Joint variation is a combination of division and multiplication.

Example of each:

Direct Proportion example:

x varies directly with y. That means x divided by y is a constant. When one goes up, the other goes up proportionately.

When x = 6, y = 5. So what is x value when y = 50?

x/y = 6/5 which is the constant

Therefore 6/5 = ?/50 so answer is 60 because 60/50 = 6/5 = the constant.

Inverse Proportion example:

x varies inversely with y. That means x times y is a constant. When one goes up, the other goes down proportionately.

When x = 6, y = 5. So what is x value when y = 10?

x*y = 6*5 = 30 which is the constant.

Therefore 6*5 = ?*10 so answer is 3 because 3*10 = 30 = the constant.

Joint Variation example

x varies inversely with y and directly with z. That means x times y divided by z is a constant. When x goes up, y goes down and z goes up proportionately.

When x = 6 and y = 5, z = 2. So what is x value when y = 10 and z = 4?

x*y/z = 6*5/2 = 15 which is the constant.

Remember that the constant is 15 in this example.

Therefore ?*10/4 = 15 so answer is x=6 because 6*10/2 = 15 = the constant.

Please contact me for more assistance.

Thank you.

Ira