 6th Grade - Proportionality

# 4 - Proportionality

## Proportionality

If 3 items cost 21 dollars, how much do 5 items cost?

In order to know the answer you can calculate the price of one item and multiply the result by 5. But take a look at this other method : You can also make a small drawing like the one below and draw a cross-shaped arrow moving towards the empty square. By multiplying the two first numbers crosswise and by dividing the result by the third number, you get the fourth number. This method enables us to solve more complicated problems.  therefore 5 items cost 35 dollars.

A farm with 27 cows produce 300 L of milk, how much milk does a 15 cow farm produce?  therefore 15 cows produce about 166,7 L of milk.

3 sweets cost 14 cents. We have 1,96 dollar left. How many sweets can we buy ? In the table we must always have the same units, therefore in this case we must convert the 1,96 dollar into cents. therefore we can buy 42 sweets.

## Proportionality table

The table below is a proportionality table because we must always multiply by the same number to move from the x line to the y line. We say that the magnitude of x and y are proportional.

 x 2 7 9 15 100 150 151 y 6 21 27 45 300 450 453

## Speed

The following formula allows us to calculate speed : We write more simply : If you have to use this formula, be careful of the units : to obtain a speed in mph, you must convert the distance in miles and the time into hours. If we travel 270 miles in 3 hours, the mean speed is mph.

Problem :
A runner runs 1700 meters in 5 minutes, calculate the speed in km/h.

In order to use the formula, you must first of all convert the metres into kilometres and the minutes into hours with the help of a cross product.   , therefore the mean speed is 20,4 km/h.

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