# Question #92027

May 11, 2017

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

#### Explanation:

It should be clear now.

May 11, 2017

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:)

$\frac{18}{27} = \frac{10}{15} = \frac{24}{36} = \frac{50}{75} = \frac{38}{57} = \frac{2}{3} = k$

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

$2 \times 30 = 5 \times 12 = 15 \times 4 = 3 \times 20 = 10 \times 6 = 60 = k$

If you call the two quantities $x \mathmr{and} y$, then we have:

Direct proportion: $k = \frac{x}{y}$

Inverse proportion: $x \times y = k$

Hope this helps.