Examples of proportions
Example 1
Let us solve the motivational example we had, using the algorithm for solving proportion equations. For 2,5 cups of flour, add 2 tablespoons of oil. If we added 10 cups of flour, how much oil would we need?
First, let us denote the amount of oil by . We have the following table:
We start by creating a proportion equation:
Let us simplify the equation, as the units on the left-hand side are cancelled, and we can also simplify the numbers on the left-hand side by dividing both the numerator and the denominator by 2,5:
Now we perform the cross multiplication by multiplying the red terms, and the blue terms:
that is,
This is already the solution of the equation. Hence, we need 8 tablespoons of oil.
| flour | oil |
| 2,5 cups | 2 tbsp |
| 10 cups | |
Example 2
In February 2023, Euros and Japanese Yens had the following exchange rate: 1 EUR = 143 JPY. How many Euros is 2860 Japanese Yens?
We can solve this problem by using proportion equations. Let us create the following table first:
We have a proportion equation:
We can cancel the JPY units on the right-hand side:
Now, let us perform the cross multiplication by multiplying the red terms, and the blue terms:
that is,
We can swap the left-hand side and the right-hand side to obtain:
To solve this equation, we divide both sides by the coefficient of , that is, we divide both sides by 143:
Therefore, 5330 Japanese Yens corresponds to 20 Euros.
| Euros | Yens |
| 1 EUR | 143 JPY |
| 2860 JPY |
Example 3
We know that the average velocity () can be calculated as the ratio of the distance travelled () and the time spent (), that is, . If a car travels with a velocity of 80 km/h, how long does it take to travel 500 km?
Method 1: traditional equation solving.
Method 2: proportion equation.
Let us write to obtain a proportion equation:
Now, we can proceed by performing the cross multiplication:
It takes 6,25 hours to travel 500 kilometers.