Question

Question #92027

Answer 1

A = n B
A and B are proportional
A = n/B
A and B are inversely proportional.

Explanation:

It should be clear now.

Answer 2

Direct: as one quantity increases, the other also increases.

Inverse: as one quantity increases, the other decreases.

Explanation:

In a proportion, we are comparing the amounts of two quantities.

In a direct proportion, as one of the quantities INCREASES the other also INCREASES.

In an inverse proportion, as one quantity INCREASES the other DECREASES.

Direct:
MORE boxes of cereal will cost MORE money.
MORE people will eat MORE food.
LESS money will buy FEWER sweets.
MORE clothes will need MORE suitcases.

Inverse:
A task shared by MORE people will take LESS time.
Travelling at a FAST speed will take LESS time for a journey.
If MORE people share a pizza. each person will get LESS.
MORE expensive price means FEWER items can be bought for the same amount of money.

Each type of proportion has a constant. (`k`)

In DIRECT proportion, find the constant by DIVIDING the matching quantities. (they are equivalent fractions:)

`18/27 = 10/15 = 24/36 = 50/75 = 38/57 = 2/3 = k`

In INVERSE proportion, find the constant by MULTIPLYING the matching quantities:

`2xx30 = 5xx12 = 15xx4 = 3xx20 =10xx6= 60 =k`

If you call the two quantities `x and y`, then we have:

Direct proportion: `k = x/y`

Inverse proportion: `x xx y = k`

Hope this helps.